mirror of
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Fixes
This commit is contained in:
Salvatore Filippone
Binary file not shown.
+29
-49
@@ -100,99 +100,80 @@ class="cmr-12">Example and test programs</span></a></span>
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<br /> <span class="sectionToc" ><span
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class="cmr-12">4 </span><a
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href="userhtmlse4.html#x13-120004" id="QQ2-13-13"><span
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class="cmr-12">Multigrid Background</span></a></span>
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<br /> <span
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class="cmr-12"> </span><span class="subsectionToc" ><span
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class="cmr-12">4.1 </span><a
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href="userhtmlsu6.html#x14-130004.1" id="QQ2-14-14"><span
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class="cmr-12">AMG preconditioners</span></a></span>
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<br /> <span
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class="cmr-12"> </span><span class="subsectionToc" ><span
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class="cmr-12">4.2 </span><a
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href="userhtmlsu7.html#x15-140004.2" id="QQ2-15-16"><span
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class="cmr-12">Smoothed Aggregation</span></a></span>
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<br /> <span
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class="cmr-12"> </span><span class="subsectionToc" ><span
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class="cmr-12">4.3 </span><a
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href="userhtmlsu8.html#x16-150004.3" id="QQ2-16-17"><span
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class="cmr-12">Smoothers and coarsest-level solvers</span></a></span>
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<br /> <span class="sectionToc" ><span
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class="cmr-12">5 </span><a
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href="userhtmlse5.html#x17-160005" id="QQ2-17-18"><span
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class="cmr-12">Getting Started</span></a></span>
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<br /> <span
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class="cmr-12"> </span><span class="subsectionToc" ><span
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class="cmr-12">5.1 </span><a
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href="userhtmlsu9.html#x18-170005.1" id="QQ2-18-20"><span
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class="cmr-12">4.1 </span><a
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href="userhtmlsu6.html#x14-130004.1" id="QQ2-14-15"><span
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class="cmr-12">Examples</span></a></span>
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<br /> <span class="sectionToc" ><span
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class="cmr-12">6 </span><a
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href="userhtmlse6.html#x19-180006" id="QQ2-19-25"><span
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class="cmr-12">5 </span><a
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href="userhtmlse5.html#x15-140005" id="QQ2-15-20"><span
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class="cmr-12">User Interface</span></a></span>
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<br /> <span
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class="cmr-12"> </span><span class="subsectionToc" ><span
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class="cmr-12">6.1 </span><a
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href="userhtmlsu10.html#x20-190006.1" id="QQ2-20-26"><span
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class="cmr-12">5.1 </span><a
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href="userhtmlsu7.html#x16-150005.1" id="QQ2-16-21"><span
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class="cmr-12">Method init</span></a></span>
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<br /> <span
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class="cmr-12"> </span><span class="subsectionToc" ><span
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class="cmr-12">6.2 </span><a
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href="userhtmlsu11.html#x21-200006.2" id="QQ2-21-27"><span
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class="cmr-12">5.2 </span><a
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href="userhtmlsu8.html#x17-160005.2" id="QQ2-17-22"><span
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class="cmr-12">Method set</span></a></span>
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<br /> <span
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class="cmr-12"> </span><span class="subsectionToc" ><span
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class="cmr-12">6.3 </span><a
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href="userhtmlsu12.html#x22-210006.3" id="QQ2-22-35"><span
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class="cmr-12">5.3 </span><a
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href="userhtmlsu9.html#x18-170005.3" id="QQ2-18-30"><span
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class="cmr-12">Method hierarchy</span><span
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class="cmr-12">_build</span></a></span>
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<br /> <span
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class="cmr-12"> </span><span class="subsectionToc" ><span
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class="cmr-12">6.4 </span><a
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href="userhtmlsu13.html#x23-220006.4" id="QQ2-23-36"><span
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class="cmr-12">5.4 </span><a
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href="userhtmlsu10.html#x19-180005.4" id="QQ2-19-31"><span
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class="cmr-12">Method smoothers</span><span
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class="cmr-12">_build</span></a></span>
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<br /> <span
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class="cmr-12"> </span><span class="subsectionToc" ><span
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class="cmr-12">6.5 </span><a
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href="userhtmlsu14.html#x24-230006.5" id="QQ2-24-37"><span
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class="cmr-12">5.5 </span><a
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href="userhtmlsu11.html#x20-190005.5" id="QQ2-20-32"><span
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class="cmr-12">Method build</span></a></span>
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<br /> <span
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class="cmr-12"> </span><span class="subsectionToc" ><span
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class="cmr-12">6.6 </span><a
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href="userhtmlsu15.html#x25-240006.6" id="QQ2-25-38"><span
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class="cmr-12">5.6 </span><a
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href="userhtmlsu12.html#x21-200005.6" id="QQ2-21-33"><span
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class="cmr-12">Method apply</span></a></span>
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<br /> <span
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class="cmr-12"> </span><span class="subsectionToc" ><span
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class="cmr-12">6.7 </span><a
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href="userhtmlsu16.html#x26-250006.7" id="QQ2-26-39"><span
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class="cmr-12">5.7 </span><a
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href="userhtmlsu13.html#x22-210005.7" id="QQ2-22-34"><span
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class="cmr-12">Method free</span></a></span>
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<br /> <span
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class="cmr-12"> </span><span class="subsectionToc" ><span
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class="cmr-12">6.8 </span><a
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href="userhtmlsu17.html#x27-260006.8" id="QQ2-27-40"><span
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class="cmr-12">5.8 </span><a
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href="userhtmlsu14.html#x23-220005.8" id="QQ2-23-35"><span
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class="cmr-12">Method descr</span></a></span>
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<br /> <span
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class="cmr-12"> </span><span class="subsectionToc" ><span
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class="cmr-12">6.9 </span><a
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href="userhtmlsu18.html#x28-270006.9" id="QQ2-28-41"><span
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class="cmr-12">5.9 </span><a
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href="userhtmlsu15.html#x24-230005.9" id="QQ2-24-36"><span
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class="cmr-12">Auxiliary Methods</span></a></span>
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<br /> <span class="sectionToc" ><span
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class="cmr-12">7 </span><a
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href="userhtmlse7.html#x29-330007" id="QQ2-29-47"><span
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class="cmr-12">6 </span><a
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href="userhtmlse6.html#x25-290006" id="QQ2-25-42"><span
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class="cmr-12">Adding new smoother and solver objects to AMG4PSBLAS</span></a></span>
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<br /> <span class="sectionToc" ><span
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class="cmr-12">8 </span><a
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href="userhtmlse8.html#x30-340008" id="QQ2-30-48"><span
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class="cmr-12">7 </span><a
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href="userhtmlse7.html#x26-300007" id="QQ2-26-43"><span
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class="cmr-12">Error Handling</span></a></span>
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<br /> <span class="sectionToc" ><span
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class="cmr-12">A </span><a
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href="userhtmlse9.html#x31-35000A" id="QQ2-31-49"><span
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href="userhtmlse8.html#x27-31000A" id="QQ2-27-44"><span
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class="cmr-12">License</span></a></span>
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||||
<br /> <span class="likesectionToc" ><a
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||||
href="userhtmlli4.html#x32-36000A" id="QQ2-32-50"><span
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||||
href="userhtmlli4.html#x28-32000A" id="QQ2-28-45"><span
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class="cmr-12">References</span></a></span>
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<br /> <span class="sectionToc" ><a
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href="userhtmlli4.html#Q1-32-51"><span
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href="userhtmlli4.html#Q1-28-46"><span
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class="cmr-12">References</span></a></span>
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</div>
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@@ -204,7 +185,6 @@ class="cmr-12">References</span></a></span>
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</body></html>
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@@ -21,17 +21,11 @@
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.cmtt-12{font-family: monospace,monospace;}
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.cmcsc-10x-x-120{font-size:109%;}
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.cmr-8{font-size:72%;}
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.cmr-6{font-size:54%;}
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.cmmi-12{font-size:109%;font-style: italic;}
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.cmmi-8{font-size:72%;font-style: italic;}
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.cmmi-6{font-size:54%;font-style: italic;}
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.cmsy-10x-x-120{font-size:109%;}
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.cmsy-8{font-size:72%;}
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.cmex-10x-x-120{font-size:109%;}
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.msbm-10x-x-120{font-size:109%;}
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.cmmi-10x-x-109{font-style: italic;}
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.cmsy-10x-x-109{}
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.cmex-10x-x-109{}
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.cmtt-10x-x-109{font-family: monospace,monospace;}
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.cmtt-10x-x-109{font-family: monospace,monospace;}
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.cmtt-10x-x-109{font-family: monospace,monospace;}
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+29
-49
@@ -100,99 +100,80 @@ class="cmr-12">Example and test programs</span></a></span>
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<br /> <span class="sectionToc" ><span
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class="cmr-12">4 </span><a
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href="userhtmlse4.html#x13-120004" id="QQ2-13-13"><span
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class="cmr-12">Multigrid Background</span></a></span>
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<br /> <span
|
||||
class="cmr-12"> </span><span class="subsectionToc" ><span
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class="cmr-12">4.1 </span><a
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href="userhtmlsu6.html#x14-130004.1" id="QQ2-14-14"><span
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class="cmr-12">AMG preconditioners</span></a></span>
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<br /> <span
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class="cmr-12"> </span><span class="subsectionToc" ><span
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class="cmr-12">4.2 </span><a
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href="userhtmlsu7.html#x15-140004.2" id="QQ2-15-16"><span
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class="cmr-12">Smoothed Aggregation</span></a></span>
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<br /> <span
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class="cmr-12"> </span><span class="subsectionToc" ><span
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class="cmr-12">4.3 </span><a
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href="userhtmlsu8.html#x16-150004.3" id="QQ2-16-17"><span
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class="cmr-12">Smoothers and coarsest-level solvers</span></a></span>
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<br /> <span class="sectionToc" ><span
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class="cmr-12">5 </span><a
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href="userhtmlse5.html#x17-160005" id="QQ2-17-18"><span
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class="cmr-12">Getting Started</span></a></span>
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<br /> <span
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class="cmr-12"> </span><span class="subsectionToc" ><span
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class="cmr-12">5.1 </span><a
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href="userhtmlsu9.html#x18-170005.1" id="QQ2-18-20"><span
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class="cmr-12">4.1 </span><a
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href="userhtmlsu6.html#x14-130004.1" id="QQ2-14-15"><span
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class="cmr-12">Examples</span></a></span>
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<br /> <span class="sectionToc" ><span
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class="cmr-12">6 </span><a
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href="userhtmlse6.html#x19-180006" id="QQ2-19-25"><span
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class="cmr-12">5 </span><a
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||||
href="userhtmlse5.html#x15-140005" id="QQ2-15-20"><span
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||||
class="cmr-12">User Interface</span></a></span>
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<br /> <span
|
||||
class="cmr-12"> </span><span class="subsectionToc" ><span
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||||
class="cmr-12">6.1 </span><a
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href="userhtmlsu10.html#x20-190006.1" id="QQ2-20-26"><span
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class="cmr-12">5.1 </span><a
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||||
href="userhtmlsu7.html#x16-150005.1" id="QQ2-16-21"><span
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class="cmr-12">Method init</span></a></span>
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<br /> <span
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class="cmr-12"> </span><span class="subsectionToc" ><span
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class="cmr-12">6.2 </span><a
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href="userhtmlsu11.html#x21-200006.2" id="QQ2-21-27"><span
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class="cmr-12">5.2 </span><a
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href="userhtmlsu8.html#x17-160005.2" id="QQ2-17-22"><span
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class="cmr-12">Method set</span></a></span>
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<br /> <span
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class="cmr-12"> </span><span class="subsectionToc" ><span
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class="cmr-12">6.3 </span><a
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href="userhtmlsu12.html#x22-210006.3" id="QQ2-22-35"><span
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class="cmr-12">5.3 </span><a
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href="userhtmlsu9.html#x18-170005.3" id="QQ2-18-30"><span
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class="cmr-12">Method hierarchy</span><span
|
||||
class="cmr-12">_build</span></a></span>
|
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<br /> <span
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class="cmr-12"> </span><span class="subsectionToc" ><span
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class="cmr-12">6.4 </span><a
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href="userhtmlsu13.html#x23-220006.4" id="QQ2-23-36"><span
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class="cmr-12">5.4 </span><a
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href="userhtmlsu10.html#x19-180005.4" id="QQ2-19-31"><span
|
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class="cmr-12">Method smoothers</span><span
|
||||
class="cmr-12">_build</span></a></span>
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||||
<br /> <span
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class="cmr-12"> </span><span class="subsectionToc" ><span
|
||||
class="cmr-12">6.5 </span><a
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href="userhtmlsu14.html#x24-230006.5" id="QQ2-24-37"><span
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class="cmr-12">5.5 </span><a
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||||
href="userhtmlsu11.html#x20-190005.5" id="QQ2-20-32"><span
|
||||
class="cmr-12">Method build</span></a></span>
|
||||
<br /> <span
|
||||
class="cmr-12"> </span><span class="subsectionToc" ><span
|
||||
class="cmr-12">6.6 </span><a
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href="userhtmlsu15.html#x25-240006.6" id="QQ2-25-38"><span
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class="cmr-12">5.6 </span><a
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href="userhtmlsu12.html#x21-200005.6" id="QQ2-21-33"><span
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class="cmr-12">Method apply</span></a></span>
|
||||
<br /> <span
|
||||
class="cmr-12"> </span><span class="subsectionToc" ><span
|
||||
class="cmr-12">6.7 </span><a
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href="userhtmlsu16.html#x26-250006.7" id="QQ2-26-39"><span
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class="cmr-12">5.7 </span><a
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href="userhtmlsu13.html#x22-210005.7" id="QQ2-22-34"><span
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class="cmr-12">Method free</span></a></span>
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||||
<br /> <span
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class="cmr-12"> </span><span class="subsectionToc" ><span
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class="cmr-12">6.8 </span><a
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||||
href="userhtmlsu17.html#x27-260006.8" id="QQ2-27-40"><span
|
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class="cmr-12">5.8 </span><a
|
||||
href="userhtmlsu14.html#x23-220005.8" id="QQ2-23-35"><span
|
||||
class="cmr-12">Method descr</span></a></span>
|
||||
<br /> <span
|
||||
class="cmr-12"> </span><span class="subsectionToc" ><span
|
||||
class="cmr-12">6.9 </span><a
|
||||
href="userhtmlsu18.html#x28-270006.9" id="QQ2-28-41"><span
|
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class="cmr-12">5.9 </span><a
|
||||
href="userhtmlsu15.html#x24-230005.9" id="QQ2-24-36"><span
|
||||
class="cmr-12">Auxiliary Methods</span></a></span>
|
||||
<br /> <span class="sectionToc" ><span
|
||||
class="cmr-12">7 </span><a
|
||||
href="userhtmlse7.html#x29-330007" id="QQ2-29-47"><span
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||||
class="cmr-12">6 </span><a
|
||||
href="userhtmlse6.html#x25-290006" id="QQ2-25-42"><span
|
||||
class="cmr-12">Adding new smoother and solver objects to AMG4PSBLAS</span></a></span>
|
||||
<br /> <span class="sectionToc" ><span
|
||||
class="cmr-12">8 </span><a
|
||||
href="userhtmlse8.html#x30-340008" id="QQ2-30-48"><span
|
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class="cmr-12">7 </span><a
|
||||
href="userhtmlse7.html#x26-300007" id="QQ2-26-43"><span
|
||||
class="cmr-12">Error Handling</span></a></span>
|
||||
<br /> <span class="sectionToc" ><span
|
||||
class="cmr-12">A </span><a
|
||||
href="userhtmlse9.html#x31-35000A" id="QQ2-31-49"><span
|
||||
href="userhtmlse8.html#x27-31000A" id="QQ2-27-44"><span
|
||||
class="cmr-12">License</span></a></span>
|
||||
<br /> <span class="likesectionToc" ><a
|
||||
href="userhtmlli4.html#x32-36000A" id="QQ2-32-50"><span
|
||||
href="userhtmlli4.html#x28-32000A" id="QQ2-28-45"><span
|
||||
class="cmr-12">References</span></a></span>
|
||||
<br /> <span class="sectionToc" ><a
|
||||
href="userhtmlli4.html#Q1-32-51"><span
|
||||
href="userhtmlli4.html#Q1-28-46"><span
|
||||
class="cmr-12">References</span></a></span>
|
||||
</div>
|
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|
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@@ -204,7 +185,6 @@ class="cmr-12">References</span></a></span>
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||||
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||||
</body></html>
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+16
-16
@@ -26,9 +26,6 @@ class="cmr-12">] </span></p></div>
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class="cmr-12">Abstract</span></h3>
|
||||
<a
|
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id="Q1-2-2"></a>
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|
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<!--l. 5--><p class="noindent" ><span
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class="cmcsc-10x-x-120">AMG4PSBLAS (A<span
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class="small-caps">l</span><span
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@@ -79,9 +76,12 @@ class="cmr-12">) is a package of parallel algebraic multilevel preconditioners i
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<span
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class="cmr-12">PSCToolkit (Parallel Sparse Computation Toolkit) software framework. It is a progress</span>
|
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<span
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class="cmr-12">of a software development project started in 2007, named MLD2P4, which</span>
|
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class="cmr-12">of a software development project started in 2007, named MLD2P4, which originally</span>
|
||||
<span
|
||||
class="cmr-12">implemented a multilevel version of some domain decomposition preconditioners of</span>
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||||
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||||
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<span
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class="cmr-12">additive-Schwarz type and was based on a parallel decoupled version of the well known</span>
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<span
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@@ -89,9 +89,9 @@ class="cmr-12">smoothed aggregation method to generate the multilevel hierarchy
|
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<span
|
||||
class="cmr-12">matrices. In the last years, within the context of the EU-H2020 EoCoE project</span>
|
||||
<span
|
||||
class="cmr-12">(Energy Oriented Center of Excellence), the package was extended including</span>
|
||||
class="cmr-12">(Energy Oriented Center of Excellence), the package is being extended for</span>
|
||||
<span
|
||||
class="cmr-12">new algorithms and functionalities for setup and application of new AMG</span>
|
||||
class="cmr-12">including new algorithms and functionalities to setup and apply new AMG</span>
|
||||
<span
|
||||
class="cmr-12">preconditioners with the final aims of improving efficiency and scalability when tens of</span>
|
||||
<span
|
||||
@@ -102,25 +102,25 @@ class="cmr-12">symmetric positive definite linear systems. Due to the significan
|
||||
class="cmr-12">of changes and the increase in scope, we decided to rename the package as</span>
|
||||
<span
|
||||
class="cmr-12">AMG4PSBLAS.</span>
|
||||
<!--l. 10--><p class="indent" > <span
|
||||
class="cmr-12">AMG4PSBLAS has been designed to provide scalable and easy-to-use</span>
|
||||
<!--l. 14--><p class="indent" > <span
|
||||
class="cmr-12">AMG4PSBLAS is designed to provide scalable and easy-to-use preconditioners in</span>
|
||||
<span
|
||||
class="cmr-12">preconditioners in the context of the PSBLAS (Parallel Sparse Basic Linear Algebra</span>
|
||||
class="cmr-12">the context of the PSBLAS (Parallel Sparse Basic Linear Algebra Subprograms)</span>
|
||||
<span
|
||||
class="cmr-12">Subprograms) computational framework and can be used in conjuction with the Krylov</span>
|
||||
class="cmr-12">computational framework and can be used in conjuction with the Krylov solvers</span>
|
||||
<span
|
||||
class="cmr-12">solvers available in this framework. Our package is based on a completely algebraic</span>
|
||||
class="cmr-12">available in this framework. Our package is based on a completely algebraic approach</span>
|
||||
<span
|
||||
class="cmr-12">approach and users level interfaces assume that the system matrix and preconditioners</span>
|
||||
class="cmr-12">and users level interfaces assume that the system matrix and preconditioners are</span>
|
||||
<span
|
||||
class="cmr-12">are represented as PSBLAS distributed sparse matrices. AMG4PSBLAS enables the</span>
|
||||
class="cmr-12">represented as PSBLAS distributed sparse matrices. AMG4PSBLAS enables the user</span>
|
||||
<span
|
||||
class="cmr-12">user to easily specify different features of an algebraic multilevel preconditioner, thus</span>
|
||||
class="cmr-12">to easily specify different features of an algebraic multilevel preconditioner, thus</span>
|
||||
<span
|
||||
class="cmr-12">allowing to experiment with different preconditioners for the problem and parallel</span>
|
||||
<span
|
||||
class="cmr-12">computers at hand.</span>
|
||||
<!--l. 21--><p class="indent" > <span
|
||||
<!--l. 25--><p class="indent" > <span
|
||||
class="cmr-12">The package employs object-oriented design techniques in Fortran</span><span
|
||||
class="cmr-12"> 2003, with</span>
|
||||
<span
|
||||
@@ -134,7 +134,7 @@ class="cmr-12">parallel implementation is based on a Single Program Multiple Dat
|
||||
class="cmr-12">paradigm; the inter-process communication is based on MPI and is managed mainly</span>
|
||||
<span
|
||||
class="cmr-12">through PSBLAS.</span>
|
||||
<!--l. 29--><p class="indent" > <span
|
||||
<!--l. 33--><p class="indent" > <span
|
||||
class="cmr-12">This guide provides a brief description of the functionalities and the user interface</span>
|
||||
<span
|
||||
class="cmr-12">of AMG4PSBLAS.</span>
|
||||
|
||||
+37
-62
@@ -74,132 +74,110 @@ class="cmr-12">Example and test programs</span></a></span>
|
||||
<br /> <span class="sectionToc" ><span
|
||||
class="cmr-12">4 </span><a
|
||||
href="userhtmlse4.html#x13-120004"><span
|
||||
class="cmr-12">Multigrid Background</span></a></span>
|
||||
class="cmr-12">Getting Started</span></a></span>
|
||||
<br /> <span
|
||||
class="cmr-12"> </span><span class="subsectionToc" ><span
|
||||
class="cmr-12">4.1 </span><a
|
||||
href="userhtmlsu6.html#x14-130004.1"><span
|
||||
class="cmr-12">AMG preconditioners</span></a></span>
|
||||
<br /> <span
|
||||
class="cmr-12"> </span><span class="subsectionToc" ><span
|
||||
class="cmr-12">4.2 </span><a
|
||||
href="userhtmlsu7.html#x15-140004.2"><span
|
||||
class="cmr-12">Smoothed Aggregation</span></a></span>
|
||||
<br /> <span
|
||||
class="cmr-12"> </span><span class="subsectionToc" ><span
|
||||
class="cmr-12">4.3 </span><a
|
||||
href="userhtmlsu8.html#x16-150004.3"><span
|
||||
class="cmr-12">Smoothers and coarsest-level solvers</span></a></span>
|
||||
<br /> <span class="sectionToc" ><span
|
||||
class="cmr-12">5 </span><a
|
||||
href="userhtmlse5.html#x17-160005"><span
|
||||
class="cmr-12">Getting Started</span></a></span>
|
||||
<br /> <span
|
||||
class="cmr-12"> </span><span class="subsectionToc" ><span
|
||||
class="cmr-12">5.1 </span><a
|
||||
href="userhtmlsu9.html#x18-170005.1"><span
|
||||
class="cmr-12">Examples</span></a></span>
|
||||
<br /> <span class="sectionToc" ><span
|
||||
class="cmr-12">6 </span><a
|
||||
href="userhtmlse6.html#x19-180006"><span
|
||||
class="cmr-12">5 </span><a
|
||||
href="userhtmlse5.html#x15-140005"><span
|
||||
class="cmr-12">User Interface</span></a></span>
|
||||
<br /> <span
|
||||
class="cmr-12"> </span><span class="subsectionToc" ><span
|
||||
class="cmr-12">6.1 </span><a
|
||||
href="userhtmlsu10.html#x20-190006.1"><span
|
||||
class="cmr-12">5.1 </span><a
|
||||
href="userhtmlsu7.html#x16-150005.1"><span
|
||||
class="cmr-12">Method init</span></a></span>
|
||||
<br /> <span
|
||||
class="cmr-12"> </span><span class="subsectionToc" ><span
|
||||
class="cmr-12">6.2 </span><a
|
||||
href="userhtmlsu11.html#x21-200006.2"><span
|
||||
class="cmr-12">5.2 </span><a
|
||||
href="userhtmlsu8.html#x17-160005.2"><span
|
||||
class="cmr-12">Method set</span></a></span>
|
||||
<br /> <span
|
||||
class="cmr-12"> </span><span class="subsectionToc" ><span
|
||||
class="cmr-12">6.3 </span><a
|
||||
href="userhtmlsu12.html#x22-210006.3"><span
|
||||
class="cmr-12">5.3 </span><a
|
||||
href="userhtmlsu9.html#x18-170005.3"><span
|
||||
class="cmr-12">Method hierarchy</span><span
|
||||
class="cmr-12">_build</span></a></span>
|
||||
<br /> <span
|
||||
class="cmr-12"> </span><span class="subsectionToc" ><span
|
||||
class="cmr-12">6.4 </span><a
|
||||
href="userhtmlsu13.html#x23-220006.4"><span
|
||||
class="cmr-12">5.4 </span><a
|
||||
href="userhtmlsu10.html#x19-180005.4"><span
|
||||
class="cmr-12">Method smoothers</span><span
|
||||
class="cmr-12">_build</span></a></span>
|
||||
<br /> <span
|
||||
class="cmr-12"> </span><span class="subsectionToc" ><span
|
||||
class="cmr-12">6.5 </span><a
|
||||
href="userhtmlsu14.html#x24-230006.5"><span
|
||||
class="cmr-12">5.5 </span><a
|
||||
href="userhtmlsu11.html#x20-190005.5"><span
|
||||
class="cmr-12">Method build</span></a></span>
|
||||
<br /> <span
|
||||
class="cmr-12"> </span><span class="subsectionToc" ><span
|
||||
class="cmr-12">6.6 </span><a
|
||||
href="userhtmlsu15.html#x25-240006.6"><span
|
||||
class="cmr-12">5.6 </span><a
|
||||
href="userhtmlsu12.html#x21-200005.6"><span
|
||||
class="cmr-12">Method apply</span></a></span>
|
||||
<br /> <span
|
||||
class="cmr-12"> </span><span class="subsectionToc" ><span
|
||||
class="cmr-12">6.7 </span><a
|
||||
href="userhtmlsu16.html#x26-250006.7"><span
|
||||
class="cmr-12">5.7 </span><a
|
||||
href="userhtmlsu13.html#x22-210005.7"><span
|
||||
class="cmr-12">Method free</span></a></span>
|
||||
<br /> <span
|
||||
class="cmr-12"> </span><span class="subsectionToc" ><span
|
||||
class="cmr-12">6.8 </span><a
|
||||
href="userhtmlsu17.html#x27-260006.8"><span
|
||||
class="cmr-12">5.8 </span><a
|
||||
href="userhtmlsu14.html#x23-220005.8"><span
|
||||
class="cmr-12">Method descr</span></a></span>
|
||||
<br /> <span
|
||||
class="cmr-12"> </span><span class="subsectionToc" ><span
|
||||
class="cmr-12">6.9 </span><a
|
||||
href="userhtmlsu18.html#x28-270006.9"><span
|
||||
class="cmr-12">5.9 </span><a
|
||||
href="userhtmlsu15.html#x24-230005.9"><span
|
||||
class="cmr-12">Auxiliary Methods</span></a></span>
|
||||
<br /> <span
|
||||
class="cmr-12"> </span><span
|
||||
class="cmr-12"> </span><span class="subsubsectionToc" ><span
|
||||
class="cmr-12">6.9.1 </span><a
|
||||
href="userhtmlsu18.html#x28-280006.9.1" id="QQ2-28-42"><span
|
||||
class="cmr-12">5.9.1 </span><a
|
||||
href="userhtmlsu15.html#x24-240005.9.1" id="QQ2-24-37"><span
|
||||
class="cmr-12">Method: dump</span></a></span>
|
||||
<br /> <span
|
||||
class="cmr-12"> </span><span
|
||||
class="cmr-12"> </span><span class="subsubsectionToc" ><span
|
||||
class="cmr-12">6.9.2 </span><a
|
||||
href="userhtmlsu18.html#x28-290006.9.2" id="QQ2-28-43"><span
|
||||
class="cmr-12">5.9.2 </span><a
|
||||
href="userhtmlsu15.html#x24-250005.9.2" id="QQ2-24-38"><span
|
||||
class="cmr-12">Method: clone</span></a></span>
|
||||
<br /> <span
|
||||
class="cmr-12"> </span><span
|
||||
class="cmr-12"> </span><span class="subsubsectionToc" ><span
|
||||
class="cmr-12">6.9.3 </span><a
|
||||
href="userhtmlsu18.html#x28-300006.9.3" id="QQ2-28-44"><span
|
||||
class="cmr-12">5.9.3 </span><a
|
||||
href="userhtmlsu15.html#x24-260005.9.3" id="QQ2-24-39"><span
|
||||
class="cmr-12">Method: sizeof</span></a></span>
|
||||
<br /> <span
|
||||
class="cmr-12"> </span><span
|
||||
class="cmr-12"> </span><span class="subsubsectionToc" ><span
|
||||
class="cmr-12">6.9.4 </span><a
|
||||
href="userhtmlsu18.html#x28-310006.9.4" id="QQ2-28-45"><span
|
||||
class="cmr-12">5.9.4 </span><a
|
||||
href="userhtmlsu15.html#x24-270005.9.4" id="QQ2-24-40"><span
|
||||
class="cmr-12">Method: allocate</span><span
|
||||
class="cmr-12">_wrk</span></a></span>
|
||||
<br /> <span
|
||||
class="cmr-12"> </span><span
|
||||
class="cmr-12"> </span><span class="subsubsectionToc" ><span
|
||||
class="cmr-12">6.9.5 </span><a
|
||||
href="userhtmlsu18.html#x28-320006.9.5" id="QQ2-28-46"><span
|
||||
class="cmr-12">5.9.5 </span><a
|
||||
href="userhtmlsu15.html#x24-280005.9.5" id="QQ2-24-41"><span
|
||||
class="cmr-12">Method: free</span><span
|
||||
class="cmr-12">_wrk</span></a></span>
|
||||
<br /> <span class="sectionToc" ><span
|
||||
class="cmr-12">7 </span><a
|
||||
href="userhtmlse7.html#x29-330007"><span
|
||||
class="cmr-12">6 </span><a
|
||||
href="userhtmlse6.html#x25-290006"><span
|
||||
class="cmr-12">Adding new smoother and solver objects to AMG4PSBLAS</span></a></span>
|
||||
<br /> <span class="sectionToc" ><span
|
||||
class="cmr-12">8 </span><a
|
||||
href="userhtmlse8.html#x30-340008"><span
|
||||
class="cmr-12">7 </span><a
|
||||
href="userhtmlse7.html#x26-300007"><span
|
||||
class="cmr-12">Error Handling</span></a></span>
|
||||
<br /> <span class="sectionToc" ><span
|
||||
class="cmr-12">A </span><a
|
||||
href="userhtmlse9.html#x31-35000A"><span
|
||||
href="userhtmlse8.html#x27-31000A"><span
|
||||
class="cmr-12">License</span></a></span>
|
||||
<br /> <span class="sectionToc" ><a
|
||||
href="userhtmlli4.html#Q1-32-51"><span
|
||||
href="userhtmlli4.html#Q1-28-46"><span
|
||||
class="cmr-12">References</span></a></span>
|
||||
|
||||
|
||||
|
||||
</div>
|
||||
|
||||
|
||||
@@ -210,9 +188,6 @@ class="cmr-12">References</span></a></span>
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
<!--l. 1--><div class="crosslinks"><p class="noindent"><span
|
||||
class="cmr-12">[</span><a
|
||||
href="userhtmlse1.html" ><span
|
||||
|
||||
@@ -12,10 +12,10 @@
|
||||
>
|
||||
<!--l. 2--><div class="crosslinks"><p class="noindent"><span
|
||||
class="cmr-12">[</span><a
|
||||
href="userhtmlse9.html" ><span
|
||||
href="userhtmlse8.html" ><span
|
||||
class="cmr-12">prev</span></a><span
|
||||
class="cmr-12">] [</span><a
|
||||
href="userhtmlse9.html#tailuserhtmlse9.html" ><span
|
||||
href="userhtmlse8.html#tailuserhtmlse8.html" ><span
|
||||
class="cmr-12">prev-tail</span></a><span
|
||||
class="cmr-12">] [</span><a
|
||||
href="#tailuserhtmlli4.html"><span
|
||||
@@ -25,11 +25,11 @@ href="userhtml.html#userhtmlli4.html" ><span
|
||||
class="cmr-12">up</span></a><span
|
||||
class="cmr-12">] </span></p></div>
|
||||
<h3 class="likesectionHead"><a
|
||||
id="x32-36000A"></a><span
|
||||
id="x28-32000A"></a><span
|
||||
class="cmr-12">References</span></h3>
|
||||
<!--l. 2--><p class="noindent" >
|
||||
<a
|
||||
id="Q1-32-51"></a>
|
||||
id="Q1-28-46"></a>
|
||||
<div class="thebibliography">
|
||||
<p class="bibitem" ><span class="biblabel">
|
||||
<span
|
||||
@@ -661,10 +661,10 @@ class="cmr-12">Transactions on Mathematical Software, 44, (2018) 39:1–39:2
|
||||
|
||||
<!--l. 145--><div class="crosslinks"><p class="noindent"><span
|
||||
class="cmr-12">[</span><a
|
||||
href="userhtmlse9.html" ><span
|
||||
href="userhtmlse8.html" ><span
|
||||
class="cmr-12">prev</span></a><span
|
||||
class="cmr-12">] [</span><a
|
||||
href="userhtmlse9.html#tailuserhtmlse9.html" ><span
|
||||
href="userhtmlse8.html#tailuserhtmlse8.html" ><span
|
||||
class="cmr-12">prev-tail</span></a><span
|
||||
class="cmr-12">] [</span><a
|
||||
href="userhtmlli4.html" ><span
|
||||
|
||||
+17
-17
@@ -122,18 +122,18 @@ class="cmr-12">23</span></a><span
|
||||
class="cmr-12">]</span></span> <span
|
||||
class="cmr-12">are available, which can be</span>
|
||||
<span
|
||||
class="cmr-12">combined with weighted versions of Jacobi, hybrid forward/backward Gauss-Seidel,</span>
|
||||
class="cmr-12">combined with Jacobi hybrid forward/backward Gauss-Seidel, block-Jacobi, and</span>
|
||||
<span
|
||||
class="cmr-12">block-Jacobi, and additive Schwarz smoothers. Also </span><span
|
||||
class="cmr-12">additive Schwarz smoothers. Also </span><span
|
||||
class="cmmi-12">ℓ</span><sub><span
|
||||
class="cmr-8">1</span></sub> <span
|
||||
class="cmr-12">versions of Jacobi, block-Jacobi</span>
|
||||
class="cmr-12">versions of Jacobi, block-Jacobi and Gauss-Seidel</span>
|
||||
<span
|
||||
class="cmr-12">and Gauss-Seidel smoothers are available. An algebraic approach is used to generate a</span>
|
||||
class="cmr-12">smoothers are available. An algebraic approach is used to generate a hierarchy of</span>
|
||||
<span
|
||||
class="cmr-12">hierarchy of coarse-level matrices and operators, without explicitly using any</span>
|
||||
class="cmr-12">coarse-level matrices and operators, without explicitly using any information</span>
|
||||
<span
|
||||
class="cmr-12">information on the geometry of the original problem, e.g., the discretization of a PDE.</span>
|
||||
class="cmr-12">on the geometry of the original problem, e.g., the discretization of a PDE.</span>
|
||||
<span
|
||||
class="cmr-12">To this end, two different coarsening strategies, based on aggregation, are</span>
|
||||
<span
|
||||
@@ -294,8 +294,8 @@ class="cmr-12">smoothers and solvers for building new versions of the preconditi
|
||||
<span
|
||||
class="cmr-12">Section</span><span
|
||||
class="cmr-12"> </span><a
|
||||
href="userhtmlse7.html#x29-330007"><span
|
||||
class="cmr-12">7</span><!--tex4ht:ref: sec:adding --></a><span
|
||||
href="userhtmlse6.html#x25-290006"><span
|
||||
class="cmr-12">6</span><!--tex4ht:ref: sec:adding --></a><span
|
||||
class="cmr-12">).</span>
|
||||
<!--l. 75--><p class="indent" > <span
|
||||
class="cmr-12">This guide is organized as follows. General information on the distribution of the</span>
|
||||
@@ -317,35 +317,35 @@ class="cmr-12">preconditioners with the Krylov solvers implemented in PSBLAS are
|
||||
class="cmr-12">in</span><span
|
||||
class="cmr-12"> Section</span><span
|
||||
class="cmr-12"> </span><a
|
||||
href="userhtmlse5.html#x17-160005"><span
|
||||
class="cmr-12">5</span><!--tex4ht:ref: sec:started --></a><span
|
||||
href="userhtmlse4.html#x13-120004"><span
|
||||
class="cmr-12">4</span><!--tex4ht:ref: sec:started --></a><span
|
||||
class="cmr-12">, where the Fortran codes of a few sample programs are also shown.</span>
|
||||
<span
|
||||
class="cmr-12">A reference guide for the user interface routines is provided in Section</span><span
|
||||
class="cmr-12"> </span><a
|
||||
href="userhtmlse6.html#x19-180006"><span
|
||||
class="cmr-12">6</span><!--tex4ht:ref: sec:userinterface --></a><span
|
||||
href="userhtmlse5.html#x15-140005"><span
|
||||
class="cmr-12">5</span><!--tex4ht:ref: sec:userinterface --></a><span
|
||||
class="cmr-12">.</span>
|
||||
<span
|
||||
class="cmr-12">Information on the extension of the package through the addition of new</span>
|
||||
<span
|
||||
class="cmr-12">smoothers and solvers is reported in Section</span><span
|
||||
class="cmr-12"> </span><a
|
||||
href="userhtmlse7.html#x29-330007"><span
|
||||
class="cmr-12">7</span><!--tex4ht:ref: sec:adding --></a><span
|
||||
href="userhtmlse6.html#x25-290006"><span
|
||||
class="cmr-12">6</span><!--tex4ht:ref: sec:adding --></a><span
|
||||
class="cmr-12">. The error handling mechanism</span>
|
||||
<span
|
||||
class="cmr-12">used by the package is briefly described in Section</span><span
|
||||
class="cmr-12"> </span><a
|
||||
href="userhtmlse8.html#x30-340008"><span
|
||||
class="cmr-12">8</span><!--tex4ht:ref: sec:errors --></a><span
|
||||
href="userhtmlse7.html#x26-300007"><span
|
||||
class="cmr-12">7</span><!--tex4ht:ref: sec:errors --></a><span
|
||||
class="cmr-12">. The copyright terms</span>
|
||||
<span
|
||||
class="cmr-12">concerning the distribution and modification of AMG4PSBLAS are reported in</span>
|
||||
<span
|
||||
class="cmr-12">Appendix</span><span
|
||||
class="cmr-12"> </span><a
|
||||
href="userhtmlse9.html#x31-35000A"><span
|
||||
href="userhtmlse8.html#x27-31000A"><span
|
||||
class="cmr-12">A</span><!--tex4ht:ref: sec:license --></a><span
|
||||
class="cmr-12">.</span>
|
||||
|
||||
|
||||
@@ -42,7 +42,7 @@ class="cmr-12">where contact points for further information can be also found.</
|
||||
<!--l. 12--><p class="indent" > <span
|
||||
class="cmr-12">The software is available under a modified BSD license, as specified in Appendix</span><span
|
||||
class="cmr-12"> </span><a
|
||||
href="userhtmlse9.html#x31-35000A"><span
|
||||
href="userhtmlse8.html#x27-31000A"><span
|
||||
class="cmr-12">A</span><!--tex4ht:ref: sec:license --></a><span
|
||||
class="cmr-12">;</span>
|
||||
<span
|
||||
|
||||
+348
-142
@@ -1,7 +1,7 @@
|
||||
<!DOCTYPE html PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN"
|
||||
"http://www.w3.org/TR/html4/loose.dtd">
|
||||
<html >
|
||||
<head><title>Multigrid Background</title>
|
||||
<head><title>Getting Started</title>
|
||||
<meta http-equiv="Content-Type" content="text/html; charset=iso-8859-1">
|
||||
<meta name="generator" content="TeX4ht (https://tug.org/tex4ht/)">
|
||||
<meta name="originator" content="TeX4ht (https://tug.org/tex4ht/)">
|
||||
@@ -30,172 +30,378 @@ class="cmr-12">] </span></p></div>
|
||||
<h3 class="sectionHead"><span class="titlemark"><span
|
||||
class="cmr-12">4 </span></span> <a
|
||||
id="x13-120004"></a><span
|
||||
class="cmr-12">Multigrid Background</span></h3>
|
||||
class="cmr-12">Getting Started</span></h3>
|
||||
<!--l. 5--><p class="noindent" ><span
|
||||
class="cmr-12">Multigrid preconditioners, coupled with Krylov iterative solvers, are widely used in the</span>
|
||||
class="cmr-12">We describe the basics for building and applying AMG4PSBLAS one-level and</span>
|
||||
<span
|
||||
class="cmr-12">parallel solution of large and sparse linear systems, because of their optimality in the</span>
|
||||
<span
|
||||
class="cmr-12">solution of linear systems arising from the discretization of scalar elliptic Partial</span>
|
||||
<span
|
||||
class="cmr-12">Differential Equations (PDEs) on regular grids. Optimality, also known as algorithmic</span>
|
||||
<span
|
||||
class="cmr-12">scalability, is the property of having a computational cost per iteration that depends</span>
|
||||
<span
|
||||
class="cmr-12">linearly on the problem size, and a convergence rate that is independent of the problem</span>
|
||||
<span
|
||||
class="cmr-12">size.</span>
|
||||
<!--l. 13--><p class="indent" > <span
|
||||
class="cmr-12">Multigrid preconditioners are based on a recursive application of a two-grid process</span>
|
||||
<span
|
||||
class="cmr-12">consisting of smoother iterations and a coarse-space (or coarse-level) correction. The</span>
|
||||
<span
|
||||
class="cmr-12">smoothers may be either basic iterative methods, such as the Jacobi and Gauss-Seidel</span>
|
||||
<span
|
||||
class="cmr-12">ones, or more complex subspace-correction methods, such as the Schwarz ones. The</span>
|
||||
<span
|
||||
class="cmr-12">coarse-space correction consists of solving, in an appropriately chosen coarse space, the</span>
|
||||
<span
|
||||
class="cmr-12">residual equation associated with the approximate solution computed by the</span>
|
||||
<span
|
||||
class="cmr-12">smoother, and of using the solution of this equation to correct the previous</span>
|
||||
<span
|
||||
class="cmr-12">approximation. The transfer of information between the original (fine) space and</span>
|
||||
<span
|
||||
class="cmr-12">the coarse one is performed by using suitable restriction and prolongation</span>
|
||||
<span
|
||||
class="cmr-12">operators. The construction of the coarse space and the corresponding transfer</span>
|
||||
<span
|
||||
class="cmr-12">operators is carried out by applying a so-called coarsening algorithm to the</span>
|
||||
<span
|
||||
class="cmr-12">system matrix. Two main approaches can be used to perform coarsening:</span>
|
||||
<span
|
||||
class="cmr-12">the geometric approach, which exploits the knowledge of some physical grid</span>
|
||||
<span
|
||||
class="cmr-12">associated with the matrix and requires the user to define transfer operators</span>
|
||||
<span
|
||||
class="cmr-12">from the fine to the coarse level and vice versa, and the algebraic approach,</span>
|
||||
<span
|
||||
class="cmr-12">which builds the coarse-space correction and the associate transfer operators</span>
|
||||
<span
|
||||
class="cmr-12">using only matrix information. The first approach may be difficult when the</span>
|
||||
<span
|
||||
class="cmr-12">system comes from discretizations on complex geometries; furthermore, ad hoc</span>
|
||||
<span
|
||||
class="cmr-12">one-level smoothers may be required to get an efficient interplay between</span>
|
||||
<span
|
||||
class="cmr-12">fine and coarse levels, e.g., when matrices with highly varying coefficients are</span>
|
||||
<span
|
||||
class="cmr-12">considered. The second approach performs a fully automatic coarsening and</span>
|
||||
<span
|
||||
class="cmr-12">enforces the interplay between fine and coarse level by suitably choosing the</span>
|
||||
<span
|
||||
class="cmr-12">coarse space and the coarse-to-fine interpolation (see, e.g., </span><span class="cite"><span
|
||||
class="cmr-12">multilevel (i.e., AMG) preconditioners with the Krylov solvers included in PSBLAS</span>
|
||||
<span class="cite"><span
|
||||
class="cmr-12">[</span><a
|
||||
href="userhtmlli4.html#XBriggs2000"><span
|
||||
class="cmr-12">3</span></a><span
|
||||
class="cmr-12">,</span><span
|
||||
class="cmr-12"> </span><a
|
||||
href="userhtmlli4.html#XStuben_01"><span
|
||||
class="cmr-12">27</span></a><span
|
||||
class="cmr-12">,</span><span
|
||||
class="cmr-12"> </span><a
|
||||
href="userhtmlli4.html#Xdd2_96"><span
|
||||
class="cmr-12">25</span></a><span
|
||||
class="cmr-12">]</span></span> <span
|
||||
class="cmr-12">for</span>
|
||||
<span
|
||||
class="cmr-12">details.)</span>
|
||||
<!--l. 37--><p class="indent" > <span
|
||||
class="cmr-12">MLD2P4 uses a pure algebraic approach, based on the smoothed aggregation</span>
|
||||
<span
|
||||
class="cmr-12">algorithm </span><span class="cite"><span
|
||||
class="cmr-12">[</span><a
|
||||
href="userhtmlli4.html#XBREZINA_VANEK"><span
|
||||
class="cmr-12">2</span></a><span
|
||||
class="cmr-12">,</span><span
|
||||
class="cmr-12"> </span><a
|
||||
href="userhtmlli4.html#XVANEK_MANDEL_BREZINA"><span
|
||||
class="cmr-12">29</span></a><span
|
||||
href="userhtmlli4.html#XPSBLASGUIDE"><span
|
||||
class="cmr-12">16</span></a><span
|
||||
class="cmr-12">]</span></span><span
|
||||
class="cmr-12">, for building the sequence of coarse matrices and transfer</span>
|
||||
<span
|
||||
class="cmr-12">operators, starting from the original one. A decoupled version of this algorithm</span>
|
||||
class="cmr-12">. The following steps are required:</span>
|
||||
<ol class="enumerate1" >
|
||||
<li
|
||||
class="enumerate" id="x13-12002x1"><span
|
||||
class="cmti-12">Declare the preconditioner data structure</span><span
|
||||
class="cmr-12">. It is a derived data type,</span>
|
||||
<span class="obeylines-h"><span class="verb"><span
|
||||
class="cmtt-12">amg_</span></span></span><span
|
||||
class="cmti-12">x</span><span class="obeylines-h"><span class="verb"><span
|
||||
class="cmtt-12">prec_</span></span></span> <span class="obeylines-h"><span class="verb"><span
|
||||
class="cmtt-12">type</span></span></span><span
|
||||
class="cmr-12">, where </span><span
|
||||
class="cmti-12">x </span><span
|
||||
class="cmr-12">may be </span><span class="obeylines-h"><span class="verb"><span
|
||||
class="cmtt-12">s</span></span></span><span
|
||||
class="cmr-12">, </span><span class="obeylines-h"><span class="verb"><span
|
||||
class="cmtt-12">d</span></span></span><span
|
||||
class="cmr-12">, </span><span class="obeylines-h"><span class="verb"><span
|
||||
class="cmtt-12">c</span></span></span> <span
|
||||
class="cmr-12">or </span><span class="obeylines-h"><span class="verb"><span
|
||||
class="cmtt-12">z</span></span></span><span
|
||||
class="cmr-12">, according to the basic data</span>
|
||||
<span
|
||||
class="cmr-12">type of the sparse matrix (</span><span class="obeylines-h"><span class="verb"><span
|
||||
class="cmtt-12">s</span></span></span> <span
|
||||
class="cmr-12">= real single precision; </span><span class="obeylines-h"><span class="verb"><span
|
||||
class="cmtt-12">d</span></span></span> <span
|
||||
class="cmr-12">= real double precision;</span>
|
||||
<span class="obeylines-h"><span class="verb"><span
|
||||
class="cmtt-12">c</span></span></span> <span
|
||||
class="cmr-12">= complex single precision; </span><span class="obeylines-h"><span class="verb"><span
|
||||
class="cmtt-12">z</span></span></span> <span
|
||||
class="cmr-12">= complex double precision). This data</span>
|
||||
<span
|
||||
class="cmr-12">structure is accessed by the user only through the AMG4PSBLAS routines,</span>
|
||||
<span
|
||||
class="cmr-12">following an object-oriented approach.</span>
|
||||
</li>
|
||||
<li
|
||||
class="enumerate" id="x13-12004x2"><span
|
||||
class="cmti-12">Allocate and initialize the preconditioner data structure, according to a</span>
|
||||
<span
|
||||
class="cmti-12">preconditioner type chosen by the user</span><span
|
||||
class="cmr-12">. This is performed by the routine</span>
|
||||
<span class="obeylines-h"><span class="verb"><span
|
||||
class="cmtt-12">init</span></span></span><span
|
||||
class="cmr-12">, which also sets defaults for each preconditioner type selected by</span>
|
||||
<span
|
||||
class="cmr-12">the user. The preconditioner types and the defaults associated with them</span>
|
||||
<span
|
||||
class="cmr-12">are given in Table</span><span
|
||||
class="cmr-12"> </span><a
|
||||
href="#x13-120151"><span
|
||||
class="cmr-12">1</span><!--tex4ht:ref: tab:precinit --></a><span
|
||||
class="cmr-12">, where the strings used by </span><span class="obeylines-h"><span class="verb"><span
|
||||
class="cmtt-12">init</span></span></span> <span
|
||||
class="cmr-12">to identify the</span>
|
||||
<span
|
||||
class="cmr-12">preconditioner types are also given. Note that these strings are valid also if</span>
|
||||
<span
|
||||
class="cmr-12">uppercase letters are substituted by corresponding lowercase ones.</span>
|
||||
</li>
|
||||
<li
|
||||
class="enumerate" id="x13-12006x3"><span
|
||||
class="cmti-12">Modify the selected preconditioner type, by properly setting preconditioner</span>
|
||||
<span
|
||||
class="cmti-12">parameters. </span><span
|
||||
class="cmr-12">This is performed by the routine </span><span class="obeylines-h"><span class="verb"><span
|
||||
class="cmtt-12">set</span></span></span><span
|
||||
class="cmr-12">. This routine must be</span>
|
||||
<span
|
||||
class="cmr-12">called only if the user wants to modify the default values of the parameters</span>
|
||||
<span
|
||||
class="cmr-12">associated with the selected preconditioner type, to obtain a variant of that</span>
|
||||
<span
|
||||
class="cmr-12">preconditioner. Examples of use of </span><span class="obeylines-h"><span class="verb"><span
|
||||
class="cmtt-12">set</span></span></span> <span
|
||||
class="cmr-12">are given in Section</span><span
|
||||
class="cmr-12"> </span><a
|
||||
href="userhtmlsu6.html#x14-130004.1"><span
|
||||
class="cmr-12">4.1</span><!--tex4ht:ref: sec:examples --></a><span
|
||||
class="cmr-12">; a complete</span>
|
||||
<span
|
||||
class="cmr-12">list of all the preconditioner parameters and their allowed and default values</span>
|
||||
<span
|
||||
class="cmr-12">is provided in Section</span><span
|
||||
class="cmr-12"> </span><a
|
||||
href="userhtmlse5.html#x15-140005"><span
|
||||
class="cmr-12">5</span><!--tex4ht:ref: sec:userinterface --></a><span
|
||||
class="cmr-12">, Tables</span><span
|
||||
class="cmr-12"> </span><a
|
||||
href="userhtmlsu8.html#x17-160092"><span
|
||||
class="cmr-12">2</span><!--tex4ht:ref: tab:p_cycle --></a><span
|
||||
class="cmr-12">-</span><a
|
||||
href="userhtmlsu8.html#x17-160158"><span
|
||||
class="cmr-12">8</span><!--tex4ht:ref: tab:p_smoother_1 --></a><span
|
||||
class="cmr-12">.</span>
|
||||
</li>
|
||||
<li
|
||||
class="enumerate" id="x13-12008x4"><span
|
||||
class="cmti-12">Build the preconditioner for a given matrix</span><span
|
||||
class="cmr-12">. If the selected preconditioner is</span>
|
||||
<span
|
||||
class="cmr-12">multilevel, then two steps must be performed, as specified next.</span>
|
||||
<ol class="enumerate2" >
|
||||
<li
|
||||
class="enumerate" id="x13-12009x0"><span
|
||||
class="cmti-12">Build the AMG hierarchy for a given matrix. </span><span
|
||||
class="cmr-12">This is performed by the</span>
|
||||
|
||||
|
||||
|
||||
<span
|
||||
class="cmr-12">routine </span><span class="obeylines-h"><span class="verb"><span
|
||||
class="cmtt-12">hierarchy_build</span></span></span><span
|
||||
class="cmr-12">.</span>
|
||||
</li>
|
||||
<li
|
||||
class="enumerate" id="x13-12010x0"><span
|
||||
class="cmti-12">Build the preconditioner for a given matrix. </span><span
|
||||
class="cmr-12">This is performed by the</span>
|
||||
<span
|
||||
class="cmr-12">routine </span><span class="obeylines-h"><span class="verb"><span
|
||||
class="cmtt-12">smoothers_build</span></span></span><span
|
||||
class="cmr-12">.</span></li></ol>
|
||||
<!--l. 41--><p class="noindent" ><span
|
||||
class="cmr-12">If the selected preconditioner is one-level, it is built in a single step, performed by</span>
|
||||
<span
|
||||
class="cmr-12">the routine </span><span class="obeylines-h"><span class="verb"><span
|
||||
class="cmtt-12">bld</span></span></span><span
|
||||
class="cmr-12">.</span>
|
||||
</li>
|
||||
<li
|
||||
class="enumerate" id="x13-12012x5"><span
|
||||
class="cmti-12">Apply the preconditioner at each iteration of a Krylov solver. </span><span
|
||||
class="cmr-12">This is performed by</span>
|
||||
<span
|
||||
class="cmr-12">the method </span><span class="obeylines-h"><span class="verb"><span
|
||||
class="cmtt-12">apply</span></span></span><span
|
||||
class="cmr-12">. When using the PSBLAS Krylov solvers, this step is</span>
|
||||
<span
|
||||
class="cmr-12">completely transparent to the user, since </span><span class="obeylines-h"><span class="verb"><span
|
||||
class="cmtt-12">apply</span></span></span> <span
|
||||
class="cmr-12">is called by the PSBLAS routine</span>
|
||||
<span
|
||||
class="cmr-12">implementing the Krylov solver (</span><span class="obeylines-h"><span class="verb"><span
|
||||
class="cmtt-12">psb_krylov</span></span></span><span
|
||||
class="cmr-12">).</span>
|
||||
</li>
|
||||
<li
|
||||
class="enumerate" id="x13-12014x6"><span
|
||||
class="cmti-12">Free the preconditioner data structure</span><span
|
||||
class="cmr-12">. This is performed by the routine </span><span class="obeylines-h"><span class="verb"><span
|
||||
class="cmtt-12">free</span></span></span><span
|
||||
class="cmr-12">.</span>
|
||||
<span
|
||||
class="cmr-12">This step is complementary to step 1 and should be performed when the</span>
|
||||
<span
|
||||
class="cmr-12">preconditioner is no more used.</span></li></ol>
|
||||
<!--l. 52--><p class="indent" > <span
|
||||
class="cmr-12">All the previous routines are available as methods of the preconditioner object. A</span>
|
||||
<span
|
||||
class="cmr-12">is implemented, where the smoothed aggregation is applied locally to each</span>
|
||||
class="cmr-12">detailed description of them is given in Section</span><span
|
||||
class="cmr-12"> </span><a
|
||||
href="userhtmlse5.html#x15-140005"><span
|
||||
class="cmr-12">5</span><!--tex4ht:ref: sec:userinterface --></a><span
|
||||
class="cmr-12">. Examples showing the basic use of</span>
|
||||
<span
|
||||
class="cmr-12">submatrix </span><span class="cite"><span
|
||||
class="cmr-12">[</span><a
|
||||
href="userhtmlli4.html#XTUMINARO_TONG"><span
|
||||
class="cmr-12">28</span></a><span
|
||||
class="cmr-12">]</span></span><span
|
||||
class="cmr-12">. A brief description of the AMG preconditioners implemented in</span>
|
||||
<span
|
||||
class="cmr-12">MLD2P4 is given in Sections</span><span
|
||||
class="cmr-12">AMG4PSBLAS are reported in Section</span><span
|
||||
class="cmr-12"> </span><a
|
||||
href="userhtmlsu6.html#x14-130004.1"><span
|
||||
class="cmr-12">4.1</span><!--tex4ht:ref: sec:multilevel --></a><span
|
||||
class="cmr-12">-</span><a
|
||||
href="userhtmlsu8.html#x16-150004.3"><span
|
||||
class="cmr-12">4.3</span><!--tex4ht:ref: sec:smoothers --></a><span
|
||||
class="cmr-12">. For further details the reader is referred to</span>
|
||||
<span class="cite"><span
|
||||
class="cmr-12">[</span><a
|
||||
href="userhtmlli4.html#Xpara_04"><span
|
||||
class="cmr-12">4</span></a><span
|
||||
class="cmr-12">,</span><span
|
||||
class="cmr-12"> </span><a
|
||||
href="userhtmlli4.html#Xaaecc_07"><span
|
||||
class="cmr-12">5</span></a><span
|
||||
class="cmr-12">,</span><span
|
||||
class="cmr-12"> </span><a
|
||||
href="userhtmlli4.html#Xapnum_07"><span
|
||||
class="cmr-12">8</span></a><span
|
||||
class="cmr-12">,</span><span
|
||||
class="cmr-12"> </span><a
|
||||
href="userhtmlli4.html#XMLD2P4_TOMS"><span
|
||||
class="cmr-12">9</span></a><span
|
||||
class="cmr-12">]</span></span><span
|
||||
class="cmr-12">4.1</span><!--tex4ht:ref: sec:examples --></a><span
|
||||
class="cmr-12">.</span>
|
||||
<!--l. 47--><p class="indent" > <span
|
||||
class="cmr-12">We note that optimal multigrid preconditioners do not necessarily correspond to</span>
|
||||
<div class="table">
|
||||
|
||||
|
||||
|
||||
<!--l. 56--><p class="indent" > <a
|
||||
id="x13-120151"></a><hr class="float"><div class="float"
|
||||
>
|
||||
|
||||
|
||||
|
||||
<div class="center"
|
||||
>
|
||||
<!--l. 57--><p class="noindent" >
|
||||
<div class="tabular"> <table id="TBL-1" class="tabular"
|
||||
cellspacing="0" cellpadding="0"
|
||||
><colgroup id="TBL-1-1g"><col
|
||||
id="TBL-1-1"></colgroup><colgroup id="TBL-1-2g"><col
|
||||
id="TBL-1-2"></colgroup><colgroup id="TBL-1-3g"><col
|
||||
id="TBL-1-3"></colgroup><tr
|
||||
class="hline"><td><hr></td><td><hr></td><td><hr></td></tr><tr
|
||||
style="vertical-align:baseline;" id="TBL-1-1-"><td style="white-space:nowrap; text-align:left;" id="TBL-1-1-1"
|
||||
class="td11"><span
|
||||
class="cmcsc-10x-x-109"><span
|
||||
class="small-caps">t</span><span
|
||||
class="small-caps">y</span><span
|
||||
class="small-caps">p</span><span
|
||||
class="small-caps">e</span> </span></td><td style="white-space:normal; text-align:left;" id="TBL-1-1-2"
|
||||
class="td11"><!--l. 61--><p class="noindent" ><span
|
||||
class="cmcsc-10x-x-109"><span
|
||||
class="small-caps">s</span><span
|
||||
class="small-caps">t</span><span
|
||||
class="small-caps">r</span><span
|
||||
class="small-caps">i</span><span
|
||||
class="small-caps">n</span><span
|
||||
class="small-caps">g</span></span> </td><td style="white-space:normal; text-align:left;" id="TBL-1-1-3"
|
||||
class="td11"><!--l. 61--><p class="noindent" ><span
|
||||
class="cmcsc-10x-x-109"><span
|
||||
class="small-caps">d</span><span
|
||||
class="small-caps">e</span><span
|
||||
class="small-caps">f</span><span
|
||||
class="small-caps">a</span><span
|
||||
class="small-caps">u</span><span
|
||||
class="small-caps">l</span><span
|
||||
class="small-caps">t</span> <span
|
||||
class="small-caps">p</span><span
|
||||
class="small-caps">r</span><span
|
||||
class="small-caps">e</span><span
|
||||
class="small-caps">c</span><span
|
||||
class="small-caps">o</span><span
|
||||
class="small-caps">n</span><span
|
||||
class="small-caps">d</span><span
|
||||
class="small-caps">i</span><span
|
||||
class="small-caps">t</span><span
|
||||
class="small-caps">i</span><span
|
||||
class="small-caps">o</span><span
|
||||
class="small-caps">n</span><span
|
||||
class="small-caps">e</span><span
|
||||
class="small-caps">r</span></span> </td></tr><tr
|
||||
class="hline"><td><hr></td><td><hr></td><td><hr></td></tr><tr
|
||||
style="vertical-align:baseline;" id="TBL-1-2-"><td style="white-space:nowrap; text-align:left;" id="TBL-1-2-1"
|
||||
class="td11">No preconditioner </td><td style="white-space:normal; text-align:left;" id="TBL-1-2-2"
|
||||
class="td11"><!--l. 62--><p class="noindent" ><span class="obeylines-h"><span class="verb"><span
|
||||
class="cmtt-10x-x-109">’NONE’</span></span></span> </td><td style="white-space:normal; text-align:left;" id="TBL-1-2-3"
|
||||
class="td11"><!--l. 62--><p class="noindent" >Considered to use the PSBLAS Krylov solvers
|
||||
with no preconditioner. </td>
|
||||
</tr><tr
|
||||
class="hline"><td><hr></td><td><hr></td><td><hr></td></tr><tr
|
||||
style="vertical-align:baseline;" id="TBL-1-3-"><td style="white-space:nowrap; text-align:left;" id="TBL-1-3-1"
|
||||
class="td11">Diagonal </td><td style="white-space:normal; text-align:left;" id="TBL-1-3-2"
|
||||
class="td11"><!--l. 64--><p class="noindent" ><span class="obeylines-h"><span class="verb"><span
|
||||
class="cmtt-10x-x-109">’DIAG’</span></span></span>,
|
||||
<span class="obeylines-h"><span class="verb"><span
|
||||
class="cmtt-10x-x-109">’JACOBI’</span></span></span>,
|
||||
<span class="obeylines-h"><span class="verb"><span
|
||||
class="cmtt-10x-x-109">’L1-JACOBI’</span></span></span> </td><td style="white-space:normal; text-align:left;" id="TBL-1-3-3"
|
||||
class="td11"><!--l. 64--><p class="noindent" >Diagonal preconditioner. For any zero diagonal
|
||||
entry of the matrix to be preconditioned, the
|
||||
corresponding entry of the preconditioner is set
|
||||
to 1. </td>
|
||||
</tr><tr
|
||||
class="hline"><td><hr></td><td><hr></td><td><hr></td></tr><tr
|
||||
style="vertical-align:baseline;" id="TBL-1-4-"><td style="white-space:nowrap; text-align:left;" id="TBL-1-4-1"
|
||||
class="td11">Gauss-Seidel </td><td style="white-space:normal; text-align:left;" id="TBL-1-4-2"
|
||||
class="td11"><!--l. 67--><p class="noindent" ><span class="obeylines-h"><span class="verb"><span
|
||||
class="cmtt-10x-x-109">’GS’</span></span></span>,
|
||||
<span class="obeylines-h"><span class="verb"><span
|
||||
class="cmtt-10x-x-109">’L1-GS’</span></span></span> </td><td style="white-space:normal; text-align:left;" id="TBL-1-4-3"
|
||||
class="td11"><!--l. 67--><p class="noindent" >Hybrid Gauss-Seidel (forward), that is, global
|
||||
block Jacobi with Gauss-Seidel as local solver. </td>
|
||||
</tr><tr
|
||||
class="hline"><td><hr></td><td><hr></td><td><hr></td></tr><tr
|
||||
style="vertical-align:baseline;" id="TBL-1-5-"><td style="white-space:nowrap; text-align:left;" id="TBL-1-5-1"
|
||||
class="td11">Symmetrized Gauss-Seidel</td><td style="white-space:normal; text-align:left;" id="TBL-1-5-2"
|
||||
class="td11"><!--l. 70--><p class="noindent" ><span class="obeylines-h"><span class="verb"><span
|
||||
class="cmtt-10x-x-109">’FBGS’</span></span></span>,
|
||||
<span class="obeylines-h"><span class="verb"><span
|
||||
class="cmtt-10x-x-109">’L1-FBGS’</span></span></span> </td><td style="white-space:normal; text-align:left;" id="TBL-1-5-3"
|
||||
class="td11"><!--l. 70--><p class="noindent" >Symmetrized hybrid Gauss-Seidel, that is,
|
||||
forward Gauss-Seidel followed by backward
|
||||
Gauss-Seidel. </td>
|
||||
</tr><tr
|
||||
class="hline"><td><hr></td><td><hr></td><td><hr></td></tr><tr
|
||||
style="vertical-align:baseline;" id="TBL-1-6-"><td style="white-space:nowrap; text-align:left;" id="TBL-1-6-1"
|
||||
class="td11">Block Jacobi </td><td style="white-space:normal; text-align:left;" id="TBL-1-6-2"
|
||||
class="td11"><!--l. 73--><p class="noindent" ><span class="obeylines-h"><span class="verb"><span
|
||||
class="cmtt-10x-x-109">’BJAC’</span></span></span>,
|
||||
<span class="obeylines-h"><span class="verb"><span
|
||||
class="cmtt-10x-x-109">’L1-BJAC’</span></span></span> </td><td style="white-space:normal; text-align:left;" id="TBL-1-6-3"
|
||||
class="td11"><!--l. 73--><p class="noindent" >Block-Jacobi with ILU(0) on the local blocks. </td>
|
||||
</tr><tr
|
||||
class="hline"><td><hr></td><td><hr></td><td><hr></td></tr><tr
|
||||
style="vertical-align:baseline;" id="TBL-1-7-"><td style="white-space:nowrap; text-align:left;" id="TBL-1-7-1"
|
||||
class="td11">Additive Schwarz </td><td style="white-space:normal; text-align:left;" id="TBL-1-7-2"
|
||||
class="td11"><!--l. 74--><p class="noindent" ><span class="obeylines-h"><span class="verb"><span
|
||||
class="cmtt-10x-x-109">’AS’</span></span></span> </td><td style="white-space:normal; text-align:left;" id="TBL-1-7-3"
|
||||
class="td11"><!--l. 74--><p class="noindent" >Additive Schwarz (AS), with overlap 1 and
|
||||
ILU(0) on the local blocks. </td>
|
||||
</tr><tr
|
||||
class="hline"><td><hr></td><td><hr></td><td><hr></td></tr><tr
|
||||
style="vertical-align:baseline;" id="TBL-1-8-"><td style="white-space:nowrap; text-align:left;" id="TBL-1-8-1"
|
||||
class="td11">Multilevel </td><td style="white-space:normal; text-align:left;" id="TBL-1-8-2"
|
||||
class="td11"><!--l. 76--><p class="noindent" ><span class="obeylines-h"><span class="verb"><span
|
||||
class="cmtt-10x-x-109">’ML’</span></span></span> </td><td style="white-space:normal; text-align:left;" id="TBL-1-8-3"
|
||||
class="td11"><!--l. 76--><p class="noindent" >V-cycle with one hybrid forward Gauss-Seidel
|
||||
(GS) sweep
|
||||
as pre-smoother and one hybrid backward GS
|
||||
sweep as post-smoother, decoupled smoothed
|
||||
aggregation as coarsening algorithm, and LU
|
||||
(plus triangular solve) as coarsest-level solver.
|
||||
See the default values in Tables <a
|
||||
href="userhtmlsu8.html#x17-160092">2<!--tex4ht:ref: tab:p_cycle --></a>-<a
|
||||
href="userhtmlsu8.html#x17-160158">8<!--tex4ht:ref: tab:p_smoother_1 --></a> for further
|
||||
details of the preconditioner. </td>
|
||||
</tr><tr
|
||||
class="hline"><td><hr></td><td><hr></td><td><hr></td></tr><tr
|
||||
style="vertical-align:baseline;" id="TBL-1-9-"><td style="white-space:nowrap; text-align:left;" id="TBL-1-9-1"
|
||||
class="td11"> </td></tr></table></div>
|
||||
<br /> <div class="caption"
|
||||
><span class="id">Table 1: </span><span
|
||||
class="content">Preconditioner types, corresponding strings and default choices. </span></div><!--tex4ht:label?: x13-120151 -->
|
||||
</div>
|
||||
|
||||
|
||||
|
||||
</div><hr class="endfloat" />
|
||||
</div>
|
||||
<!--l. 91--><p class="indent" > <span
|
||||
class="cmr-12">Note that the module </span><span class="obeylines-h"><span class="verb"><span
|
||||
class="cmtt-12">amg_prec_mod</span></span></span><span
|
||||
class="cmr-12">, containing the definition of the preconditioner</span>
|
||||
<span
|
||||
class="cmr-12">minimum execution times in a parallel setting. Indeed, to obtain effective parallel</span>
|
||||
class="cmr-12">data type and the interfaces to the routines of AMG4PSBLAS, must be used</span>
|
||||
<span
|
||||
class="cmr-12">multigrid preconditioners, a tradeoff between the optimality and the cost of</span>
|
||||
class="cmr-12">in any program calling such routines. The modules </span><span class="obeylines-h"><span class="verb"><span
|
||||
class="cmtt-12">psb_base_mod</span></span></span><span
|
||||
class="cmr-12">, for the</span>
|
||||
<span
|
||||
class="cmr-12">building and applying the smoothers and the coarse-space corrections must be</span>
|
||||
class="cmr-12">sparse matrix and communication descriptor data types, and </span><span class="obeylines-h"><span class="verb"><span
|
||||
class="cmtt-12">psb_krylov_mod</span></span></span><span
|
||||
class="cmr-12">,</span>
|
||||
<span
|
||||
class="cmr-12">achieved. Effective parallel preconditioners require algorithmic scalability to</span>
|
||||
class="cmr-12">for interfacing with the Krylov solvers, must be also used (see Section</span><span
|
||||
class="cmr-12"> </span><a
|
||||
href="userhtmlsu6.html#x14-130004.1"><span
|
||||
class="cmr-12">4.1</span><!--tex4ht:ref: sec:examples --></a><span
|
||||
class="cmr-12">).</span>
|
||||
<br
|
||||
class="newline" />
|
||||
<!--l. 98--><p class="indent" > <span
|
||||
class="cmbx-12">Remark 1. </span><span
|
||||
class="cmr-12">Coarsest-level solvers based on the LU factorization, such as those</span>
|
||||
<span
|
||||
class="cmr-12">be coupled with implementation scalability, i.e., a computational cost per</span>
|
||||
class="cmr-12">implemented in UMFPACK, MUMPS, SuperLU, and SuperLU</span><span
|
||||
class="cmr-12">_Dist, usually lead to</span>
|
||||
<span
|
||||
class="cmr-12">iteration which remains (almost) constant as the number of parallel processors</span>
|
||||
class="cmr-12">smaller numbers of preconditioned Krylov iterations than inexact solvers, when the</span>
|
||||
<span
|
||||
class="cmr-12">increases.</span>
|
||||
<!--l. 56--><p class="noindent" >
|
||||
class="cmr-12">linear system comes from a standard discretization of basic scalar elliptic PDE</span>
|
||||
<span
|
||||
class="cmr-12">problems. However, this does not necessarily correspond to the shortest execution time</span>
|
||||
<span
|
||||
class="cmr-12">on parallel computers.</span>
|
||||
<div class="subsectionTOCS">
|
||||
<span
|
||||
class="cmr-12"> </span><span class="subsectionToc" ><span
|
||||
class="cmr-12">4.1 </span><a
|
||||
href="userhtmlsu6.html#x14-130004.1"><span
|
||||
class="cmr-12">AMG preconditioners</span></a></span>
|
||||
<br /> <span
|
||||
class="cmr-12"> </span><span class="subsectionToc" ><span
|
||||
class="cmr-12">4.2 </span><a
|
||||
href="userhtmlsu7.html#x15-140004.2"><span
|
||||
class="cmr-12">Smoothed Aggregation</span></a></span>
|
||||
<br /> <span
|
||||
class="cmr-12"> </span><span class="subsectionToc" ><span
|
||||
class="cmr-12">4.3 </span><a
|
||||
href="userhtmlsu8.html#x16-150004.3"><span
|
||||
class="cmr-12">Smoothers and coarsest-level solvers</span></a></span>
|
||||
class="cmr-12">Examples</span></a></span>
|
||||
</div>
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
+204
-360
@@ -1,7 +1,7 @@
|
||||
<!DOCTYPE html PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN"
|
||||
"http://www.w3.org/TR/html4/loose.dtd">
|
||||
<html >
|
||||
<head><title>Getting Started</title>
|
||||
<head><title>User Interface</title>
|
||||
<meta http-equiv="Content-Type" content="text/html; charset=iso-8859-1">
|
||||
<meta name="generator" content="TeX4ht (https://tug.org/tex4ht/)">
|
||||
<meta name="originator" content="TeX4ht (https://tug.org/tex4ht/)">
|
||||
@@ -29,385 +29,229 @@ class="cmr-12">up</span></a><span
|
||||
class="cmr-12">] </span></p></div>
|
||||
<h3 class="sectionHead"><span class="titlemark"><span
|
||||
class="cmr-12">5 </span></span> <a
|
||||
id="x17-160005"></a><span
|
||||
class="cmr-12">Getting Started</span></h3>
|
||||
id="x15-140005"></a><span
|
||||
class="cmr-12">User Interface</span></h3>
|
||||
<!--l. 5--><p class="noindent" ><span
|
||||
class="cmr-12">We describe the basics for building and applying AMG4PSBLAS one-level and</span>
|
||||
class="cmr-12">The basic user interface of AMG4PBLAS consists of eight methods. The six methods</span>
|
||||
<span class="obeylines-h"><span class="verb"><span
|
||||
class="cmtt-12">init</span></span></span><span
|
||||
class="cmr-12">, </span><span class="obeylines-h"><span class="verb"><span
|
||||
class="cmtt-12">set</span></span></span><span
|
||||
class="cmr-12">, </span><span class="obeylines-h"><span class="verb"><span
|
||||
class="cmtt-12">build</span></span></span><span
|
||||
class="cmr-12">, </span><span class="obeylines-h"><span class="verb"><span
|
||||
class="cmtt-12">hierarchy_build</span></span></span><span
|
||||
class="cmr-12">, </span><span class="obeylines-h"><span class="verb"><span
|
||||
class="cmtt-12">smoothers_build</span></span></span> <span
|
||||
class="cmr-12">and </span><span class="obeylines-h"><span class="verb"><span
|
||||
class="cmtt-12">apply</span></span></span> <span
|
||||
class="cmr-12">encapsulate all the</span>
|
||||
<span
|
||||
class="cmr-12">multilevel (i.e., AMG) preconditioners with the Krylov solvers included in PSBLAS</span>
|
||||
<span class="cite"><span
|
||||
class="cmr-12">[</span><a
|
||||
href="userhtmlli4.html#XPSBLASGUIDE"><span
|
||||
class="cmr-12">16</span></a><span
|
||||
class="cmr-12">]</span></span><span
|
||||
class="cmr-12">. The following steps are required:</span>
|
||||
<ol class="enumerate1" >
|
||||
<li
|
||||
class="enumerate" id="x17-16002x1"><span
|
||||
class="cmti-12">Declare the preconditioner data structure</span><span
|
||||
class="cmr-12">. It is a derived data type,</span>
|
||||
<span class="obeylines-h"><span class="verb"><span
|
||||
class="cmr-12">functionalities for the setup and the application of any multilevel and one-level</span>
|
||||
<span
|
||||
class="cmr-12">preconditioner implemented in the package. The method </span><span class="obeylines-h"><span class="verb"><span
|
||||
class="cmtt-12">free</span></span></span> <span
|
||||
class="cmr-12">deallocates the</span>
|
||||
<span
|
||||
class="cmr-12">preconditioner data structure, while </span><span class="obeylines-h"><span class="verb"><span
|
||||
class="cmtt-12">descr</span></span></span> <span
|
||||
class="cmr-12">prints a description of the preconditioner</span>
|
||||
<span
|
||||
class="cmr-12">setup by the user. For backward compatibility, methods are also accessible as</span>
|
||||
<span
|
||||
class="cmr-12">stand-alone subroutines.</span>
|
||||
<!--l. 16--><p class="indent" > <span
|
||||
class="cmr-12">For each method, the same user interface is overloaded with respect to the real/</span>
|
||||
<span
|
||||
class="cmr-12">complex case and the single/double precision; arguments with appropriate data types</span>
|
||||
<span
|
||||
class="cmr-12">must be passed to the method, i.e.,</span>
|
||||
<ul class="itemize1">
|
||||
<li class="itemize"><span
|
||||
class="cmr-12">the sparse matrix data structure, containing the matrix to be preconditioned,</span>
|
||||
<span
|
||||
class="cmr-12">must be of type </span><span class="obeylines-h"><span class="verb"><span
|
||||
class="cmtt-12">psb_</span></span></span><span
|
||||
class="cmti-12">x</span><span class="obeylines-h"><span class="verb"><span
|
||||
class="cmtt-12">spmat_type</span></span></span> <span
|
||||
class="cmr-12">with </span><span
|
||||
class="cmti-12">x </span><span
|
||||
class="cmr-12">= </span><span class="obeylines-h"><span class="verb"><span
|
||||
class="cmtt-12">s</span></span></span> <span
|
||||
class="cmr-12">for real single precision, </span><span
|
||||
class="cmti-12">x</span>
|
||||
<span
|
||||
class="cmr-12">= </span><span class="obeylines-h"><span class="verb"><span
|
||||
class="cmtt-12">d</span></span></span> <span
|
||||
class="cmr-12">for real double precision, </span><span
|
||||
class="cmti-12">x </span><span
|
||||
class="cmr-12">= </span><span class="obeylines-h"><span class="verb"><span
|
||||
class="cmtt-12">c</span></span></span> <span
|
||||
class="cmr-12">for complex single precision, </span><span
|
||||
class="cmti-12">x </span><span
|
||||
class="cmr-12">= </span><span class="obeylines-h"><span class="verb"><span
|
||||
class="cmtt-12">z</span></span></span> <span
|
||||
class="cmr-12">for</span>
|
||||
<span
|
||||
class="cmr-12">complex double precision;</span>
|
||||
</li>
|
||||
<li class="itemize"><span
|
||||
class="cmr-12">the preconditioner data structure must be of type </span><span class="obeylines-h"><span class="verb"><span
|
||||
class="cmtt-12">amg_</span></span></span><span
|
||||
class="cmti-12">x</span><span class="obeylines-h"><span class="verb"><span
|
||||
class="cmtt-12">prec_</span></span></span> <span class="obeylines-h"><span class="verb"><span
|
||||
class="cmtt-12">type</span></span></span><span
|
||||
class="cmr-12">, where </span><span
|
||||
class="cmti-12">x </span><span
|
||||
class="cmr-12">may be </span><span class="obeylines-h"><span class="verb"><span
|
||||
class="cmtt-12">prec_type</span></span></span><span
|
||||
class="cmr-12">, with </span><span
|
||||
class="cmti-12">x</span>
|
||||
<span
|
||||
class="cmr-12">= </span><span class="obeylines-h"><span class="verb"><span
|
||||
class="cmtt-12">s</span></span></span><span
|
||||
class="cmr-12">, </span><span class="obeylines-h"><span class="verb"><span
|
||||
class="cmtt-12">d</span></span></span><span
|
||||
class="cmr-12">, </span><span class="obeylines-h"><span class="verb"><span
|
||||
class="cmtt-12">c</span></span></span> <span
|
||||
class="cmr-12">or </span><span class="obeylines-h"><span class="verb"><span
|
||||
class="cmtt-12">c</span></span></span><span
|
||||
class="cmr-12">, </span><span class="obeylines-h"><span class="verb"><span
|
||||
class="cmtt-12">z</span></span></span><span
|
||||
class="cmr-12">, according to the basic data</span>
|
||||
<span
|
||||
class="cmr-12">type of the sparse matrix (</span><span class="obeylines-h"><span class="verb"><span
|
||||
class="cmtt-12">s</span></span></span> <span
|
||||
class="cmr-12">= real single precision; </span><span class="obeylines-h"><span class="verb"><span
|
||||
class="cmtt-12">d</span></span></span> <span
|
||||
class="cmr-12">= real double precision;</span>
|
||||
<span class="obeylines-h"><span class="verb"><span
|
||||
class="cmtt-12">c</span></span></span> <span
|
||||
class="cmr-12">= complex single precision; </span><span class="obeylines-h"><span class="verb"><span
|
||||
class="cmtt-12">z</span></span></span> <span
|
||||
class="cmr-12">= complex double precision). This data</span>
|
||||
<span
|
||||
class="cmr-12">structure is accessed by the user only through the AMG4PSBLAS routines,</span>
|
||||
<span
|
||||
class="cmr-12">following an object-oriented approach.</span>
|
||||
class="cmr-12">, according to the sparse matrix data structure;</span>
|
||||
</li>
|
||||
<li
|
||||
class="enumerate" id="x17-16004x2"><span
|
||||
class="cmti-12">Allocate and initialize the preconditioner data structure, according to a</span>
|
||||
<li class="itemize"><span
|
||||
class="cmr-12">the arrays containing the vectors </span><span
|
||||
class="cmmi-12">v </span><span
|
||||
class="cmr-12">and </span><span
|
||||
class="cmmi-12">w </span><span
|
||||
class="cmr-12">involved in the preconditioner</span>
|
||||
<span
|
||||
class="cmti-12">preconditioner type chosen by the user</span><span
|
||||
class="cmr-12">. This is performed by the routine</span>
|
||||
<span class="obeylines-h"><span class="verb"><span
|
||||
class="cmtt-12">init</span></span></span><span
|
||||
class="cmr-12">, which also sets defaults for each preconditioner type selected by</span>
|
||||
<span
|
||||
class="cmr-12">the user. The preconditioner types and the defaults associated with them</span>
|
||||
<span
|
||||
class="cmr-12">are given in Table</span><span
|
||||
class="cmr-12"> </span><a
|
||||
href="#x17-160151"><span
|
||||
class="cmr-12">1</span><!--tex4ht:ref: tab:precinit --></a><span
|
||||
class="cmr-12">, where the strings used by </span><span class="obeylines-h"><span class="verb"><span
|
||||
class="cmtt-12">init</span></span></span> <span
|
||||
class="cmr-12">to identify the</span>
|
||||
<span
|
||||
class="cmr-12">preconditioner types are also given. Note that these strings are valid also if</span>
|
||||
<span
|
||||
class="cmr-12">uppercase letters are substituted by corresponding lowercase ones.</span>
|
||||
</li>
|
||||
<li
|
||||
class="enumerate" id="x17-16006x3"><span
|
||||
class="cmti-12">Modify the selected preconditioner type, by properly setting preconditioner</span>
|
||||
<span
|
||||
class="cmti-12">parameters. </span><span
|
||||
class="cmr-12">This is performed by the routine </span><span class="obeylines-h"><span class="verb"><span
|
||||
class="cmtt-12">set</span></span></span><span
|
||||
class="cmr-12">. This routine must be</span>
|
||||
<span
|
||||
class="cmr-12">called only if the user wants to modify the default values of the parameters</span>
|
||||
<span
|
||||
class="cmr-12">associated with the selected preconditioner type, to obtain a variant of that</span>
|
||||
<span
|
||||
class="cmr-12">preconditioner. Examples of use of </span><span class="obeylines-h"><span class="verb"><span
|
||||
class="cmtt-12">set</span></span></span> <span
|
||||
class="cmr-12">are given in Section</span><span
|
||||
class="cmr-12"> </span><a
|
||||
href="userhtmlsu9.html#x18-170005.1"><span
|
||||
class="cmr-12">5.1</span><!--tex4ht:ref: sec:examples --></a><span
|
||||
class="cmr-12">; a complete</span>
|
||||
<span
|
||||
class="cmr-12">list of all the preconditioner parameters and their allowed and default values</span>
|
||||
<span
|
||||
class="cmr-12">is provided in Section</span><span
|
||||
class="cmr-12"> </span><a
|
||||
href="userhtmlse6.html#x19-180006"><span
|
||||
class="cmr-12">6</span><!--tex4ht:ref: sec:userinterface --></a><span
|
||||
class="cmr-12">, Tables</span><span
|
||||
class="cmr-12"> </span><a
|
||||
href="userhtmlsu11.html#x21-200092"><span
|
||||
class="cmr-12">2</span><!--tex4ht:ref: tab:p_cycle --></a><span
|
||||
class="cmr-12">-</span><a
|
||||
href="userhtmlsu11.html#x21-200158"><span
|
||||
class="cmr-12">8</span><!--tex4ht:ref: tab:p_smoother_1 --></a><span
|
||||
class="cmr-12">.</span>
|
||||
</li>
|
||||
<li
|
||||
class="enumerate" id="x17-16008x4"><span
|
||||
class="cmti-12">Build the preconditioner for a given matrix</span><span
|
||||
class="cmr-12">. If the selected preconditioner is</span>
|
||||
<span
|
||||
class="cmr-12">multilevel, then two steps must be performed, as specified next.</span>
|
||||
<ol class="enumerate2" >
|
||||
<li
|
||||
class="enumerate" id="x17-16009x0"><span
|
||||
class="cmti-12">Build the AMG hierarchy for a given matrix. </span><span
|
||||
class="cmr-12">This is performed by the</span>
|
||||
<span
|
||||
class="cmr-12">routine </span><span class="obeylines-h"><span class="verb"><span
|
||||
class="cmtt-12">hierarchy_build</span></span></span><span
|
||||
class="cmr-12">.</span>
|
||||
|
||||
|
||||
|
||||
</li>
|
||||
<li
|
||||
class="enumerate" id="x17-16010x0"><span
|
||||
class="cmti-12">Build the preconditioner for a given matrix. </span><span
|
||||
class="cmr-12">This is performed by the</span>
|
||||
<span
|
||||
class="cmr-12">routine </span><span class="obeylines-h"><span class="verb"><span
|
||||
class="cmtt-12">smoothers_build</span></span></span><span
|
||||
class="cmr-12">.</span></li></ol>
|
||||
<!--l. 41--><p class="noindent" ><span
|
||||
class="cmr-12">If the selected preconditioner is one-level, it is built in a single step, performed by</span>
|
||||
<span
|
||||
class="cmr-12">the routine </span><span class="obeylines-h"><span class="verb"><span
|
||||
class="cmtt-12">bld</span></span></span><span
|
||||
class="cmr-12">.</span>
|
||||
</li>
|
||||
<li
|
||||
class="enumerate" id="x17-16012x5"><span
|
||||
class="cmti-12">Apply the preconditioner at each iteration of a Krylov solver. </span><span
|
||||
class="cmr-12">This is performed by</span>
|
||||
<span
|
||||
class="cmr-12">the method </span><span class="obeylines-h"><span class="verb"><span
|
||||
class="cmtt-12">apply</span></span></span><span
|
||||
class="cmr-12">. When using the PSBLAS Krylov solvers, this step is</span>
|
||||
<span
|
||||
class="cmr-12">completely transparent to the user, since </span><span class="obeylines-h"><span class="verb"><span
|
||||
class="cmtt-12">apply</span></span></span> <span
|
||||
class="cmr-12">is called by the PSBLAS routine</span>
|
||||
<span
|
||||
class="cmr-12">implementing the Krylov solver (</span><span class="obeylines-h"><span class="verb"><span
|
||||
class="cmtt-12">psb_krylov</span></span></span><span
|
||||
class="cmr-12">).</span>
|
||||
</li>
|
||||
<li
|
||||
class="enumerate" id="x17-16014x6"><span
|
||||
class="cmti-12">Free the preconditioner data structure</span><span
|
||||
class="cmr-12">. This is performed by the routine </span><span class="obeylines-h"><span class="verb"><span
|
||||
class="cmtt-12">free</span></span></span><span
|
||||
class="cmr-12">.</span>
|
||||
<span
|
||||
class="cmr-12">This step is complementary to step 1 and should be performed when the</span>
|
||||
<span
|
||||
class="cmr-12">preconditioner is no more used.</span></li></ol>
|
||||
<!--l. 52--><p class="indent" > <span
|
||||
class="cmr-12">All the previous routines are available as methods of the preconditioner object. A</span>
|
||||
<span
|
||||
class="cmr-12">detailed description of them is given in Section</span><span
|
||||
class="cmr-12"> </span><a
|
||||
href="userhtmlse6.html#x19-180006"><span
|
||||
class="cmr-12">6</span><!--tex4ht:ref: sec:userinterface --></a><span
|
||||
class="cmr-12">. Examples showing the basic use of</span>
|
||||
<span
|
||||
class="cmr-12">AMG4PSBLAS are reported in Section</span><span
|
||||
class="cmr-12"> </span><a
|
||||
href="userhtmlsu9.html#x18-170005.1"><span
|
||||
class="cmr-12">5.1</span><!--tex4ht:ref: sec:examples --></a><span
|
||||
class="cmr-12">.</span>
|
||||
<div class="table">
|
||||
|
||||
|
||||
|
||||
<!--l. 56--><p class="indent" > <a
|
||||
id="x17-160151"></a><hr class="float"><div class="float"
|
||||
>
|
||||
|
||||
|
||||
|
||||
<div class="center"
|
||||
>
|
||||
<!--l. 57--><p class="noindent" >
|
||||
<div class="tabular"> <table id="TBL-1" class="tabular"
|
||||
cellspacing="0" cellpadding="0"
|
||||
><colgroup id="TBL-1-1g"><col
|
||||
id="TBL-1-1"></colgroup><colgroup id="TBL-1-2g"><col
|
||||
id="TBL-1-2"></colgroup><colgroup id="TBL-1-3g"><col
|
||||
id="TBL-1-3"></colgroup><tr
|
||||
class="hline"><td><hr></td><td><hr></td><td><hr></td></tr><tr
|
||||
style="vertical-align:baseline;" id="TBL-1-1-"><td style="white-space:nowrap; text-align:left;" id="TBL-1-1-1"
|
||||
class="td11"><span
|
||||
class="cmcsc-10x-x-109"><span
|
||||
class="small-caps">t</span><span
|
||||
class="small-caps">y</span><span
|
||||
class="small-caps">p</span><span
|
||||
class="small-caps">e</span> </span></td><td style="white-space:normal; text-align:left;" id="TBL-1-1-2"
|
||||
class="td11"><!--l. 61--><p class="noindent" ><span
|
||||
class="cmcsc-10x-x-109"><span
|
||||
class="small-caps">s</span><span
|
||||
class="small-caps">t</span><span
|
||||
class="small-caps">r</span><span
|
||||
class="small-caps">i</span><span
|
||||
class="small-caps">n</span><span
|
||||
class="small-caps">g</span></span> </td><td style="white-space:normal; text-align:left;" id="TBL-1-1-3"
|
||||
class="td11"><!--l. 61--><p class="noindent" ><span
|
||||
class="cmcsc-10x-x-109"><span
|
||||
class="small-caps">d</span><span
|
||||
class="small-caps">e</span><span
|
||||
class="small-caps">f</span><span
|
||||
class="small-caps">a</span><span
|
||||
class="small-caps">u</span><span
|
||||
class="small-caps">l</span><span
|
||||
class="small-caps">t</span> <span
|
||||
class="small-caps">p</span><span
|
||||
class="small-caps">r</span><span
|
||||
class="small-caps">e</span><span
|
||||
class="small-caps">c</span><span
|
||||
class="small-caps">o</span><span
|
||||
class="small-caps">n</span><span
|
||||
class="small-caps">d</span><span
|
||||
class="small-caps">i</span><span
|
||||
class="small-caps">t</span><span
|
||||
class="small-caps">i</span><span
|
||||
class="small-caps">o</span><span
|
||||
class="small-caps">n</span><span
|
||||
class="small-caps">e</span><span
|
||||
class="small-caps">r</span></span> </td></tr><tr
|
||||
class="hline"><td><hr></td><td><hr></td><td><hr></td></tr><tr
|
||||
style="vertical-align:baseline;" id="TBL-1-2-"><td style="white-space:nowrap; text-align:left;" id="TBL-1-2-1"
|
||||
class="td11">No preconditioner </td><td style="white-space:normal; text-align:left;" id="TBL-1-2-2"
|
||||
class="td11"><!--l. 62--><p class="noindent" ><span class="obeylines-h"><span class="verb"><span
|
||||
class="cmtt-10x-x-109">’NONE’</span></span></span> </td><td style="white-space:normal; text-align:left;" id="TBL-1-2-3"
|
||||
class="td11"><!--l. 62--><p class="noindent" >Considered to use the PSBLAS Krylov solvers
|
||||
with no preconditioner. </td>
|
||||
</tr><tr
|
||||
class="hline"><td><hr></td><td><hr></td><td><hr></td></tr><tr
|
||||
style="vertical-align:baseline;" id="TBL-1-3-"><td style="white-space:nowrap; text-align:left;" id="TBL-1-3-1"
|
||||
class="td11">Diagonal </td><td style="white-space:normal; text-align:left;" id="TBL-1-3-2"
|
||||
class="td11"><!--l. 64--><p class="noindent" ><span class="obeylines-h"><span class="verb"><span
|
||||
class="cmtt-10x-x-109">’DIAG’</span></span></span>,
|
||||
<span class="obeylines-h"><span class="verb"><span
|
||||
class="cmtt-10x-x-109">’JACOBI’</span></span></span>,
|
||||
<span class="obeylines-h"><span class="verb"><span
|
||||
class="cmtt-10x-x-109">’L1-JACOBI’</span></span></span> </td><td style="white-space:normal; text-align:left;" id="TBL-1-3-3"
|
||||
class="td11"><!--l. 64--><p class="noindent" >Diagonal preconditioner. For any zero diagonal
|
||||
entry of the matrix to be preconditioned, the
|
||||
corresponding entry of the preconditioner is set
|
||||
to 1. </td>
|
||||
</tr><tr
|
||||
class="hline"><td><hr></td><td><hr></td><td><hr></td></tr><tr
|
||||
style="vertical-align:baseline;" id="TBL-1-4-"><td style="white-space:nowrap; text-align:left;" id="TBL-1-4-1"
|
||||
class="td11">Gauss-Seidel </td><td style="white-space:normal; text-align:left;" id="TBL-1-4-2"
|
||||
class="td11"><!--l. 67--><p class="noindent" ><span class="obeylines-h"><span class="verb"><span
|
||||
class="cmtt-10x-x-109">’GS’</span></span></span>,
|
||||
<span class="obeylines-h"><span class="verb"><span
|
||||
class="cmtt-10x-x-109">’L1-GS’</span></span></span> </td><td style="white-space:normal; text-align:left;" id="TBL-1-4-3"
|
||||
class="td11"><!--l. 67--><p class="noindent" >Hybrid Gauss-Seidel (forward), that is, global
|
||||
block Jacobi with Gauss-Seidel as local solver. </td>
|
||||
</tr><tr
|
||||
class="hline"><td><hr></td><td><hr></td><td><hr></td></tr><tr
|
||||
style="vertical-align:baseline;" id="TBL-1-5-"><td style="white-space:nowrap; text-align:left;" id="TBL-1-5-1"
|
||||
class="td11">Symmetrized Gauss-Seidel</td><td style="white-space:normal; text-align:left;" id="TBL-1-5-2"
|
||||
class="td11"><!--l. 70--><p class="noindent" ><span class="obeylines-h"><span class="verb"><span
|
||||
class="cmtt-10x-x-109">’FBGS’</span></span></span>,
|
||||
<span class="obeylines-h"><span class="verb"><span
|
||||
class="cmtt-10x-x-109">’L1-FBGS’</span></span></span> </td><td style="white-space:normal; text-align:left;" id="TBL-1-5-3"
|
||||
class="td11"><!--l. 70--><p class="noindent" >Symmetrized hybrid Gauss-Seidel, that is,
|
||||
forward Gauss-Seidel followed by backward
|
||||
Gauss-Seidel. </td>
|
||||
</tr><tr
|
||||
class="hline"><td><hr></td><td><hr></td><td><hr></td></tr><tr
|
||||
style="vertical-align:baseline;" id="TBL-1-6-"><td style="white-space:nowrap; text-align:left;" id="TBL-1-6-1"
|
||||
class="td11">Block Jacobi </td><td style="white-space:normal; text-align:left;" id="TBL-1-6-2"
|
||||
class="td11"><!--l. 73--><p class="noindent" ><span class="obeylines-h"><span class="verb"><span
|
||||
class="cmtt-10x-x-109">’BJAC’</span></span></span>,
|
||||
<span class="obeylines-h"><span class="verb"><span
|
||||
class="cmtt-10x-x-109">’L1-BJAC’</span></span></span> </td><td style="white-space:normal; text-align:left;" id="TBL-1-6-3"
|
||||
class="td11"><!--l. 73--><p class="noindent" >Block-Jacobi with ILU(0) on the local blocks. </td>
|
||||
</tr><tr
|
||||
class="hline"><td><hr></td><td><hr></td><td><hr></td></tr><tr
|
||||
style="vertical-align:baseline;" id="TBL-1-7-"><td style="white-space:nowrap; text-align:left;" id="TBL-1-7-1"
|
||||
class="td11">Additive Schwarz </td><td style="white-space:normal; text-align:left;" id="TBL-1-7-2"
|
||||
class="td11"><!--l. 74--><p class="noindent" ><span class="obeylines-h"><span class="verb"><span
|
||||
class="cmtt-10x-x-109">’AS’</span></span></span> </td><td style="white-space:normal; text-align:left;" id="TBL-1-7-3"
|
||||
class="td11"><!--l. 74--><p class="noindent" >Additive Schwarz (AS), with overlap 1 and
|
||||
ILU(0) on the local blocks. </td>
|
||||
</tr><tr
|
||||
class="hline"><td><hr></td><td><hr></td><td><hr></td></tr><tr
|
||||
style="vertical-align:baseline;" id="TBL-1-8-"><td style="white-space:nowrap; text-align:left;" id="TBL-1-8-1"
|
||||
class="td11">Multilevel </td><td style="white-space:normal; text-align:left;" id="TBL-1-8-2"
|
||||
class="td11"><!--l. 76--><p class="noindent" ><span class="obeylines-h"><span class="verb"><span
|
||||
class="cmtt-10x-x-109">’ML’</span></span></span> </td><td style="white-space:normal; text-align:left;" id="TBL-1-8-3"
|
||||
class="td11"><!--l. 76--><p class="noindent" >V-cycle with one hybrid forward Gauss-Seidel
|
||||
(GS) sweep
|
||||
as pre-smoother and one hybrid backward GS
|
||||
sweep as post-smoother, decoupled smoothed
|
||||
aggregation as coarsening algorithm, and LU
|
||||
(plus triangular solve) as coarsest-level solver.
|
||||
See the default values in Tables <a
|
||||
href="userhtmlsu11.html#x21-200092">2<!--tex4ht:ref: tab:p_cycle --></a>-<a
|
||||
href="userhtmlsu11.html#x21-200158">8<!--tex4ht:ref: tab:p_smoother_1 --></a> for further
|
||||
details of the preconditioner. </td>
|
||||
</tr><tr
|
||||
class="hline"><td><hr></td><td><hr></td><td><hr></td></tr><tr
|
||||
style="vertical-align:baseline;" id="TBL-1-9-"><td style="white-space:nowrap; text-align:left;" id="TBL-1-9-1"
|
||||
class="td11"> </td></tr></table></div>
|
||||
<br /> <div class="caption"
|
||||
><span class="id">Table 1: </span><span
|
||||
class="content">Preconditioner types, corresponding strings and default choices. </span></div><!--tex4ht:label?: x17-160151 -->
|
||||
</div>
|
||||
|
||||
|
||||
|
||||
</div><hr class="endfloat" />
|
||||
</div>
|
||||
<!--l. 91--><p class="indent" > <span
|
||||
class="cmr-12">Note that the module </span><span class="obeylines-h"><span class="verb"><span
|
||||
class="cmtt-12">amg_prec_mod</span></span></span><span
|
||||
class="cmr-12">, containing the definition of the preconditioner</span>
|
||||
<span
|
||||
class="cmr-12">data type and the interfaces to the routines of AMG4PSBLAS, must be used</span>
|
||||
<span
|
||||
class="cmr-12">in any program calling such routines. The modules </span><span class="obeylines-h"><span class="verb"><span
|
||||
class="cmtt-12">psb_base_mod</span></span></span><span
|
||||
class="cmr-12">, for the</span>
|
||||
<span
|
||||
class="cmr-12">sparse matrix and communication descriptor data types, and </span><span class="obeylines-h"><span class="verb"><span
|
||||
class="cmtt-12">psb_krylov_mod</span></span></span><span
|
||||
class="cmr-12">application </span><span
|
||||
class="cmmi-12">w </span><span
|
||||
class="cmr-12">= </span><span
|
||||
class="cmmi-12">B</span><sup><span
|
||||
class="cmsy-8">-</span><span
|
||||
class="cmr-8">1</span></sup><span
|
||||
class="cmmi-12">v </span><span
|
||||
class="cmr-12">must be of type </span><span class="obeylines-h"><span class="verb"><span
|
||||
class="cmtt-12">psb_</span></span></span><span
|
||||
class="cmti-12">x</span><span class="obeylines-h"><span class="verb"><span
|
||||
class="cmtt-12">vect_type</span></span></span> <span
|
||||
class="cmr-12">with </span><span
|
||||
class="cmti-12">x </span><span
|
||||
class="cmr-12">= </span><span class="obeylines-h"><span class="verb"><span
|
||||
class="cmtt-12">s</span></span></span><span
|
||||
class="cmr-12">, </span><span class="obeylines-h"><span class="verb"><span
|
||||
class="cmtt-12">d</span></span></span><span
|
||||
class="cmr-12">, </span><span class="obeylines-h"><span class="verb"><span
|
||||
class="cmtt-12">c</span></span></span><span
|
||||
class="cmr-12">,</span>
|
||||
<span
|
||||
class="cmr-12">for interfacing with the Krylov solvers, must be also used (see Section</span><span
|
||||
<span class="obeylines-h"><span class="verb"><span
|
||||
class="cmtt-12">z</span></span></span><span
|
||||
class="cmr-12">, in a manner completely analogous to the sparse matrix type;</span>
|
||||
</li>
|
||||
<li class="itemize"><span
|
||||
class="cmr-12">real parameters defining the preconditioner must be declared according to</span>
|
||||
<span
|
||||
class="cmr-12">the precision of the sparse matrix and preconditioner data structures (see</span>
|
||||
<span
|
||||
class="cmr-12">Section</span><span
|
||||
class="cmr-12"> </span><a
|
||||
href="userhtmlsu9.html#x18-170005.1"><span
|
||||
class="cmr-12">5.1</span><!--tex4ht:ref: sec:examples --></a><span
|
||||
class="cmr-12">).</span>
|
||||
<br
|
||||
class="newline" />
|
||||
<!--l. 98--><p class="indent" > <span
|
||||
class="cmbx-12">Remark 1. </span><span
|
||||
class="cmr-12">Coarsest-level solvers based on the LU factorization, such as those</span>
|
||||
<span
|
||||
class="cmr-12">implemented in UMFPACK, MUMPS, SuperLU, and SuperLU</span><span
|
||||
class="cmr-12">_Dist, usually lead to</span>
|
||||
<span
|
||||
class="cmr-12">smaller numbers of preconditioned Krylov iterations than inexact solvers, when the</span>
|
||||
<span
|
||||
class="cmr-12">linear system comes from a standard discretization of basic scalar elliptic PDE</span>
|
||||
<span
|
||||
class="cmr-12">problems. However, this does not necessarily correspond to the shortest execution time</span>
|
||||
<span
|
||||
class="cmr-12">on parallel computers.</span>
|
||||
<!--l. 107--><p class="indent" > <span
|
||||
class="cmti-12">DA MODIFICARE PER INSERIRE TIPO DI AGGREGAZIONE</span>
|
||||
href="userhtmlsu8.html#x17-160005.2"><span
|
||||
class="cmr-12">5.2</span><!--tex4ht:ref: sec:precset --></a><span
|
||||
class="cmr-12">).</span></li></ul>
|
||||
<!--l. 39--><p class="noindent" ><span
|
||||
class="cmr-12">A description of each method is given in the remainder of this section.</span>
|
||||
|
||||
|
||||
|
||||
<div class="subsectionTOCS">
|
||||
<span
|
||||
class="cmr-12"> </span><span class="subsectionToc" ><span
|
||||
class="cmr-12">5.1 </span><a
|
||||
href="userhtmlsu9.html#x18-170005.1"><span
|
||||
class="cmr-12">Examples</span></a></span>
|
||||
href="userhtmlsu7.html#x16-150005.1"><span
|
||||
class="cmr-12">Method init</span></a></span>
|
||||
<br /> <span
|
||||
class="cmr-12"> </span><span class="subsectionToc" ><span
|
||||
class="cmr-12">5.2 </span><a
|
||||
href="userhtmlsu8.html#x17-160005.2"><span
|
||||
class="cmr-12">Method set</span></a></span>
|
||||
<br /> <span
|
||||
class="cmr-12"> </span><span class="subsectionToc" ><span
|
||||
class="cmr-12">5.3 </span><a
|
||||
href="userhtmlsu9.html#x18-170005.3"><span
|
||||
class="cmr-12">Method hierarchy</span><span
|
||||
class="cmr-12">_build</span></a></span>
|
||||
<br /> <span
|
||||
class="cmr-12"> </span><span class="subsectionToc" ><span
|
||||
class="cmr-12">5.4 </span><a
|
||||
href="userhtmlsu10.html#x19-180005.4"><span
|
||||
class="cmr-12">Method smoothers</span><span
|
||||
class="cmr-12">_build</span></a></span>
|
||||
<br /> <span
|
||||
class="cmr-12"> </span><span class="subsectionToc" ><span
|
||||
class="cmr-12">5.5 </span><a
|
||||
href="userhtmlsu11.html#x20-190005.5"><span
|
||||
class="cmr-12">Method build</span></a></span>
|
||||
<br /> <span
|
||||
class="cmr-12"> </span><span class="subsectionToc" ><span
|
||||
class="cmr-12">5.6 </span><a
|
||||
href="userhtmlsu12.html#x21-200005.6"><span
|
||||
class="cmr-12">Method apply</span></a></span>
|
||||
<br /> <span
|
||||
class="cmr-12"> </span><span class="subsectionToc" ><span
|
||||
class="cmr-12">5.7 </span><a
|
||||
href="userhtmlsu13.html#x22-210005.7"><span
|
||||
class="cmr-12">Method free</span></a></span>
|
||||
<br /> <span
|
||||
class="cmr-12"> </span><span class="subsectionToc" ><span
|
||||
class="cmr-12">5.8 </span><a
|
||||
href="userhtmlsu14.html#x23-220005.8"><span
|
||||
class="cmr-12">Method descr</span></a></span>
|
||||
<br /> <span
|
||||
class="cmr-12"> </span><span class="subsectionToc" ><span
|
||||
class="cmr-12">5.9 </span><a
|
||||
href="userhtmlsu15.html#x24-230005.9"><span
|
||||
class="cmr-12">Auxiliary Methods</span></a></span>
|
||||
<br /> <span
|
||||
class="cmr-12"> </span><span
|
||||
class="cmr-12"> </span><span class="subsubsectionToc" ><span
|
||||
class="cmr-12">5.9.1 </span><a
|
||||
href="userhtmlsu15.html#x24-240005.9.1"><span
|
||||
class="cmr-12">Method: dump</span></a></span>
|
||||
<br /> <span
|
||||
class="cmr-12"> </span><span
|
||||
class="cmr-12"> </span><span class="subsubsectionToc" ><span
|
||||
class="cmr-12">5.9.2 </span><a
|
||||
href="userhtmlsu15.html#x24-250005.9.2"><span
|
||||
class="cmr-12">Method: clone</span></a></span>
|
||||
<br /> <span
|
||||
class="cmr-12"> </span><span
|
||||
class="cmr-12"> </span><span class="subsubsectionToc" ><span
|
||||
class="cmr-12">5.9.3 </span><a
|
||||
href="userhtmlsu15.html#x24-260005.9.3"><span
|
||||
class="cmr-12">Method: sizeof</span></a></span>
|
||||
<br /> <span
|
||||
class="cmr-12"> </span><span
|
||||
class="cmr-12"> </span><span class="subsubsectionToc" ><span
|
||||
class="cmr-12">5.9.4 </span><a
|
||||
href="userhtmlsu15.html#x24-270005.9.4"><span
|
||||
class="cmr-12">Method: allocate</span><span
|
||||
class="cmr-12">_wrk</span></a></span>
|
||||
<br /> <span
|
||||
class="cmr-12"> </span><span
|
||||
class="cmr-12"> </span><span class="subsubsectionToc" ><span
|
||||
class="cmr-12">5.9.5 </span><a
|
||||
href="userhtmlsu15.html#x24-280005.9.5"><span
|
||||
class="cmr-12">Method: free</span><span
|
||||
class="cmr-12">_wrk</span></a></span>
|
||||
</div>
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
<!--l. 1--><div class="crosslinks"><p class="noindent"><span
|
||||
<!--l. 4--><div class="crosslinks"><p class="noindent"><span
|
||||
class="cmr-12">[</span><a
|
||||
href="userhtmlse6.html" ><span
|
||||
class="cmr-12">next</span></a><span
|
||||
@@ -424,6 +268,6 @@ class="cmr-12">] [</span><a
|
||||
href="userhtml.html#userhtmlse5.html" ><span
|
||||
class="cmr-12">up</span></a><span
|
||||
class="cmr-12">] </span></p></div>
|
||||
<!--l. 1--><p class="indent" > <a
|
||||
<!--l. 4--><p class="indent" > <a
|
||||
id="tailuserhtmlse5.html"></a>
|
||||
</body></html>
|
||||
|
||||
+161
-205
@@ -1,7 +1,7 @@
|
||||
<!DOCTYPE html PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN"
|
||||
"http://www.w3.org/TR/html4/loose.dtd">
|
||||
<html >
|
||||
<head><title>User Interface</title>
|
||||
<head><title>Adding new smoother and solver objects to AMG4PSBLAS</title>
|
||||
<meta http-equiv="Content-Type" content="text/html; charset=iso-8859-1">
|
||||
<meta name="generator" content="TeX4ht (https://tug.org/tex4ht/)">
|
||||
<meta name="originator" content="TeX4ht (https://tug.org/tex4ht/)">
|
||||
@@ -10,7 +10,7 @@
|
||||
<link rel="stylesheet" type="text/css" href="userhtml.css">
|
||||
</head><body
|
||||
>
|
||||
<!--l. 1--><div class="crosslinks"><p class="noindent"><span
|
||||
<!--l. 4--><div class="crosslinks"><p class="noindent"><span
|
||||
class="cmr-12">[</span><a
|
||||
href="userhtmlse7.html" ><span
|
||||
class="cmr-12">next</span></a><span
|
||||
@@ -29,229 +29,185 @@ class="cmr-12">up</span></a><span
|
||||
class="cmr-12">] </span></p></div>
|
||||
<h3 class="sectionHead"><span class="titlemark"><span
|
||||
class="cmr-12">6 </span></span> <a
|
||||
id="x19-180006"></a><span
|
||||
class="cmr-12">User Interface</span></h3>
|
||||
<!--l. 5--><p class="noindent" ><span
|
||||
class="cmr-12">The basic user interface of AMG4PBLAS consists of eight methods. The six methods</span>
|
||||
<span class="obeylines-h"><span class="verb"><span
|
||||
class="cmtt-12">init</span></span></span><span
|
||||
class="cmr-12">, </span><span class="obeylines-h"><span class="verb"><span
|
||||
class="cmtt-12">set</span></span></span><span
|
||||
class="cmr-12">, </span><span class="obeylines-h"><span class="verb"><span
|
||||
class="cmtt-12">build</span></span></span><span
|
||||
class="cmr-12">, </span><span class="obeylines-h"><span class="verb"><span
|
||||
class="cmtt-12">hierarchy_build</span></span></span><span
|
||||
class="cmr-12">, </span><span class="obeylines-h"><span class="verb"><span
|
||||
class="cmtt-12">smoothers_build</span></span></span> <span
|
||||
class="cmr-12">and </span><span class="obeylines-h"><span class="verb"><span
|
||||
class="cmtt-12">apply</span></span></span> <span
|
||||
class="cmr-12">encapsulate all the</span>
|
||||
id="x25-290006"></a><span
|
||||
class="cmr-12">Adding new smoother and solver objects to AMG4PSBLAS</span></h3>
|
||||
<!--l. 6--><p class="noindent" ><span
|
||||
class="cmr-12">Developers can add completely new smoother and/or solver classes derived from the</span>
|
||||
<span
|
||||
class="cmr-12">functionalities for the setup and the application of any multilevel and one-level</span>
|
||||
class="cmr-12">base objects in the library (see Remark</span><span
|
||||
class="cmr-12"> 2 in Section</span><span
|
||||
class="cmr-12"> </span><a
|
||||
href="userhtmlsu8.html#x17-160005.2"><span
|
||||
class="cmr-12">5.2</span><!--tex4ht:ref: sec:precset --></a><span
|
||||
class="cmr-12">), without recompiling the</span>
|
||||
<span
|
||||
class="cmr-12">preconditioner implemented in the package. The method </span><span class="obeylines-h"><span class="verb"><span
|
||||
class="cmtt-12">free</span></span></span> <span
|
||||
class="cmr-12">deallocates the</span>
|
||||
class="cmr-12">library itself.</span>
|
||||
<!--l. 10--><p class="indent" > <span
|
||||
class="cmr-12">To do so, it is necessary first to select the base type to be extended. In our</span>
|
||||
<span
|
||||
class="cmr-12">preconditioner data structure, while </span><span class="obeylines-h"><span class="verb"><span
|
||||
class="cmtt-12">descr</span></span></span> <span
|
||||
class="cmr-12">prints a description of the preconditioner</span>
|
||||
class="cmr-12">experience, it is quite likely that the new application needs only the definition of a</span>
|
||||
<span
|
||||
class="cmr-12">setup by the user. For backward compatibility, methods are also accessible as</span>
|
||||
class="cmr-12">“solver” object, which is almost always acting only on the local part of the distributed</span>
|
||||
<span
|
||||
class="cmr-12">stand-alone subroutines.</span>
|
||||
<!--l. 16--><p class="indent" > <span
|
||||
class="cmr-12">For each method, the same user interface is overloaded with respect to the real/</span>
|
||||
class="cmr-12">matrix. The parallel actions required to connect the various solver objects are most</span>
|
||||
<span
|
||||
class="cmr-12">complex case and the single/double precision; arguments with appropriate data types</span>
|
||||
class="cmr-12">often already provided by the block-Jacobi or the additive Schwarz smoothers. To</span>
|
||||
<span
|
||||
class="cmr-12">must be passed to the method, i.e.,</span>
|
||||
class="cmr-12">define a new solver, the developer will then have to define its components and</span>
|
||||
<span
|
||||
class="cmr-12">methods, perhaps taking one of the predefined solvers as a starting point, if</span>
|
||||
<span
|
||||
class="cmr-12">possible.</span>
|
||||
<!--l. 20--><p class="indent" > <span
|
||||
class="cmr-12">Once the new smoother/solver class has been developed, to use it in the context of</span>
|
||||
<span
|
||||
class="cmr-12">the multilevel preconditioners it is necessary to:</span>
|
||||
<ul class="itemize1">
|
||||
<li class="itemize"><span
|
||||
class="cmr-12">the sparse matrix data structure, containing the matrix to be preconditioned,</span>
|
||||
<span
|
||||
class="cmr-12">must be of type </span><span class="obeylines-h"><span class="verb"><span
|
||||
class="cmtt-12">psb_</span></span></span><span
|
||||
class="cmti-12">x</span><span class="obeylines-h"><span class="verb"><span
|
||||
class="cmtt-12">spmat_type</span></span></span> <span
|
||||
class="cmr-12">with </span><span
|
||||
class="cmti-12">x </span><span
|
||||
class="cmr-12">= </span><span class="obeylines-h"><span class="verb"><span
|
||||
class="cmtt-12">s</span></span></span> <span
|
||||
class="cmr-12">for real single precision, </span><span
|
||||
class="cmti-12">x</span>
|
||||
<span
|
||||
class="cmr-12">= </span><span class="obeylines-h"><span class="verb"><span
|
||||
class="cmtt-12">d</span></span></span> <span
|
||||
class="cmr-12">for real double precision, </span><span
|
||||
class="cmti-12">x </span><span
|
||||
class="cmr-12">= </span><span class="obeylines-h"><span class="verb"><span
|
||||
class="cmtt-12">c</span></span></span> <span
|
||||
class="cmr-12">for complex single precision, </span><span
|
||||
class="cmti-12">x </span><span
|
||||
class="cmr-12">= </span><span class="obeylines-h"><span class="verb"><span
|
||||
class="cmtt-12">z</span></span></span> <span
|
||||
class="cmr-12">for</span>
|
||||
<span
|
||||
class="cmr-12">complex double precision;</span>
|
||||
class="cmr-12">declare in the application program a variable of the new type;</span>
|
||||
</li>
|
||||
<li class="itemize"><span
|
||||
class="cmr-12">the preconditioner data structure must be of type </span><span class="obeylines-h"><span class="verb"><span
|
||||
class="cmtt-12">amg_</span></span></span><span
|
||||
class="cmti-12">x</span><span class="obeylines-h"><span class="verb"><span
|
||||
class="cmtt-12">prec_type</span></span></span><span
|
||||
class="cmr-12">, with </span><span
|
||||
class="cmti-12">x</span>
|
||||
<span
|
||||
class="cmr-12">= </span><span class="obeylines-h"><span class="verb"><span
|
||||
class="cmtt-12">s</span></span></span><span
|
||||
class="cmr-12">, </span><span class="obeylines-h"><span class="verb"><span
|
||||
class="cmtt-12">d</span></span></span><span
|
||||
class="cmr-12">, </span><span class="obeylines-h"><span class="verb"><span
|
||||
class="cmtt-12">c</span></span></span><span
|
||||
class="cmr-12">, </span><span class="obeylines-h"><span class="verb"><span
|
||||
class="cmtt-12">z</span></span></span><span
|
||||
class="cmr-12">, according to the sparse matrix data structure;</span>
|
||||
class="cmr-12">pass that variable as the argument to the </span><span class="obeylines-h"><span class="verb"><span
|
||||
class="cmtt-12">set</span></span></span> <span
|
||||
class="cmr-12">routine as in the following:</span>
|
||||
<div class="center"
|
||||
>
|
||||
<!--l. 26--><p class="noindent" >
|
||||
<!--l. 27--><p class="noindent" ><span class="obeylines-h"><span class="verb"><span
|
||||
class="cmtt-12">call</span><span
|
||||
class="cmtt-12"> p%set(smoother,info</span><span
|
||||
class="cmtt-12"> [,ilev,ilmax,pos])</span></span></span><br />
|
||||
<span class="obeylines-h"><span class="verb"><span
|
||||
class="cmtt-12">call</span><span
|
||||
class="cmtt-12"> p%set(solver,info</span><span
|
||||
class="cmtt-12"> [,ilev,ilmax,pos])</span></span></span></div>
|
||||
</li>
|
||||
<li class="itemize"><span
|
||||
class="cmr-12">the arrays containing the vectors </span><span
|
||||
class="cmmi-12">v </span><span
|
||||
class="cmr-12">and </span><span
|
||||
class="cmmi-12">w </span><span
|
||||
class="cmr-12">involved in the preconditioner</span>
|
||||
class="cmr-12">link the code implementing the various methods into the application</span>
|
||||
<span
|
||||
class="cmr-12">application </span><span
|
||||
class="cmmi-12">w </span><span
|
||||
class="cmr-12">= </span><span
|
||||
class="cmmi-12">B</span><sup><span
|
||||
class="cmsy-8">-</span><span
|
||||
class="cmr-8">1</span></sup><span
|
||||
class="cmmi-12">v </span><span
|
||||
class="cmr-12">must be of type </span><span class="obeylines-h"><span class="verb"><span
|
||||
class="cmtt-12">psb_</span></span></span><span
|
||||
class="cmti-12">x</span><span class="obeylines-h"><span class="verb"><span
|
||||
class="cmtt-12">vect_type</span></span></span> <span
|
||||
class="cmr-12">with </span><span
|
||||
class="cmti-12">x </span><span
|
||||
class="cmr-12">= </span><span class="obeylines-h"><span class="verb"><span
|
||||
class="cmtt-12">s</span></span></span><span
|
||||
class="cmr-12">, </span><span class="obeylines-h"><span class="verb"><span
|
||||
class="cmtt-12">d</span></span></span><span
|
||||
class="cmr-12">, </span><span class="obeylines-h"><span class="verb"><span
|
||||
class="cmtt-12">c</span></span></span><span
|
||||
class="cmr-12">,</span>
|
||||
<span class="obeylines-h"><span class="verb"><span
|
||||
class="cmtt-12">z</span></span></span><span
|
||||
class="cmr-12">, in a manner completely analogous to the sparse matrix type;</span>
|
||||
</li>
|
||||
<li class="itemize"><span
|
||||
class="cmr-12">real parameters defining the preconditioner must be declared according to</span>
|
||||
<span
|
||||
class="cmr-12">the precision of the sparse matrix and preconditioner data structures (see</span>
|
||||
<span
|
||||
class="cmr-12">Section</span><span
|
||||
class="cmr-12">executable.</span></li></ul>
|
||||
<!--l. 32--><p class="noindent" ><span
|
||||
class="cmr-12">The new solver object is then dynamically included in the preconditioner structure,</span>
|
||||
<span
|
||||
class="cmr-12">and acts as a </span><span
|
||||
class="cmti-12">mold </span><span
|
||||
class="cmr-12">to which the preconditioner will conform, even though</span>
|
||||
<span
|
||||
class="cmr-12">the AMG4PSBLAS library has not been modified to account for this new</span>
|
||||
<span
|
||||
class="cmr-12">development.</span>
|
||||
|
||||
|
||||
|
||||
<!--l. 37--><p class="indent" > <span
|
||||
class="cmr-12">It is possible to define new values for the keyword </span><span class="obeylines-h"><span class="verb"><span
|
||||
class="cmtt-12">WHAT</span></span></span> <span
|
||||
class="cmr-12">in the </span><span class="obeylines-h"><span class="verb"><span
|
||||
class="cmtt-12">set</span></span></span> <span
|
||||
class="cmr-12">routine; if the</span>
|
||||
<span
|
||||
class="cmr-12">library code does not recognize a keyword, it passes it down the composition hierarchy</span>
|
||||
<span
|
||||
class="cmr-12">(levels containing smoothers containing in turn solvers), so that it can be eventually</span>
|
||||
<span
|
||||
class="cmr-12">caught by the new solver. By the same token, any keyword/value pair that does not</span>
|
||||
<span
|
||||
class="cmr-12">pertain to a given smoother should be passed down to the contained solver, and</span>
|
||||
<span
|
||||
class="cmr-12">any keyword/value pair that does not pertain to a given solver is by default</span>
|
||||
<span
|
||||
class="cmr-12">ignored.</span>
|
||||
<!--l. 46--><p class="indent" > <span
|
||||
class="cmr-12">An example is provided in the source code distribution under the folder</span>
|
||||
<span class="obeylines-h"><span class="verb"><span
|
||||
class="cmtt-12">tests/newslv</span></span></span><span
|
||||
class="cmr-12">. In this example we are implementing a new incomplete factorization</span>
|
||||
<span
|
||||
class="cmr-12">variant (which is simply the ILU(0) factorization under a new name). Because of the</span>
|
||||
<span
|
||||
class="cmr-12">specifics of this case, it is possible to reuse the basic structure of the ILU solver, with</span>
|
||||
<span
|
||||
class="cmr-12">its L/D/U components and the methods needed to apply the solver; only a few</span>
|
||||
<span
|
||||
class="cmr-12">methods, such as the description and most importantly the build, need to be</span>
|
||||
<span
|
||||
class="cmr-12">ovverridden (rewritten).</span>
|
||||
<!--l. 55--><p class="indent" > <span
|
||||
class="cmr-12">The interfaces for the calls shown above are defined using</span>
|
||||
<div class="center"
|
||||
>
|
||||
<!--l. 56--><p class="noindent" >
|
||||
<div class="tabular"> <table id="TBL-21" class="tabular"
|
||||
cellspacing="0" cellpadding="0"
|
||||
><colgroup id="TBL-21-1g"><col
|
||||
id="TBL-21-1"><col
|
||||
id="TBL-21-2"></colgroup><tr
|
||||
style="vertical-align:baseline;" id="TBL-21-1-"><td style="white-space:normal; text-align:left;" id="TBL-21-1-1"
|
||||
class="td11"><!--l. 58--><p class="noindent" ><span class="obeylines-h"><span class="verb"><span
|
||||
class="cmtt-12">smoother</span></span></span> </td><td style="white-space:normal; text-align:left;" id="TBL-21-1-2"
|
||||
class="td11"><!--l. 58--><p class="noindent" ><span class="obeylines-h"><span class="verb"><span
|
||||
class="cmtt-12">class(amg_x_base_smoother_type)</span></span></span> </td>
|
||||
</tr><tr
|
||||
style="vertical-align:baseline;" id="TBL-21-2-"><td style="white-space:normal; text-align:left;" id="TBL-21-2-1"
|
||||
class="td11"><!--l. 59--><p class="noindent" > </td><td style="white-space:normal; text-align:left;" id="TBL-21-2-2"
|
||||
class="td11"><!--l. 59--><p class="noindent" ><span
|
||||
class="cmr-12">The user-defined new smoother to be employed in the</span>
|
||||
<span
|
||||
class="cmr-12">preconditioner.</span> </td>
|
||||
</tr><tr
|
||||
style="vertical-align:baseline;" id="TBL-21-3-"><td style="white-space:normal; text-align:left;" id="TBL-21-3-1"
|
||||
class="td11"><!--l. 61--><p class="noindent" ><span class="obeylines-h"><span class="verb"><span
|
||||
class="cmtt-12">solver</span></span></span> </td><td style="white-space:normal; text-align:left;" id="TBL-21-3-2"
|
||||
class="td11"><!--l. 61--><p class="noindent" ><span class="obeylines-h"><span class="verb"><span
|
||||
class="cmtt-12">class(amg_x_base_solver_type)</span></span></span> </td>
|
||||
</tr><tr
|
||||
style="vertical-align:baseline;" id="TBL-21-4-"><td style="white-space:normal; text-align:left;" id="TBL-21-4-1"
|
||||
class="td11"><!--l. 62--><p class="noindent" > </td><td style="white-space:normal; text-align:left;" id="TBL-21-4-2"
|
||||
class="td11"><!--l. 62--><p class="noindent" ><span
|
||||
class="cmr-12">The user-defined new solver to be employed in the preconditioner.</span></td></tr></table></div></div>
|
||||
<!--l. 66--><p class="noindent" ><span
|
||||
class="cmr-12">The other arguments are defined in the way described in Sec.</span><span
|
||||
class="cmr-12"> </span><a
|
||||
href="userhtmlsu11.html#x21-200006.2"><span
|
||||
class="cmr-12">6.2</span><!--tex4ht:ref: sec:precset --></a><span
|
||||
class="cmr-12">).</span></li></ul>
|
||||
<!--l. 39--><p class="noindent" ><span
|
||||
class="cmr-12">A description of each method is given in the remainder of this section.</span>
|
||||
href="userhtmlsu8.html#x17-160005.2"><span
|
||||
class="cmr-12">5.2</span><!--tex4ht:ref: sec:precset --></a><span
|
||||
class="cmr-12">. As an example, in the</span>
|
||||
<span class="obeylines-h"><span class="verb"><span
|
||||
class="cmtt-12">tests/newslv</span></span></span> <span
|
||||
class="cmr-12">code we define a new object of type </span><span class="obeylines-h"><span class="verb"><span
|
||||
class="cmtt-12">amg_d_tlu_solver_type</span></span></span><span
|
||||
class="cmr-12">, and we</span>
|
||||
<span
|
||||
class="cmr-12">pass it as follows:</span>
|
||||
|
||||
|
||||
|
||||
<div class="subsectionTOCS">
|
||||
<span
|
||||
class="cmr-12"> </span><span class="subsectionToc" ><span
|
||||
class="cmr-12">6.1 </span><a
|
||||
href="userhtmlsu10.html#x20-190006.1"><span
|
||||
class="cmr-12">Method init</span></a></span>
|
||||
<br /> <span
|
||||
class="cmr-12"> </span><span class="subsectionToc" ><span
|
||||
class="cmr-12">6.2 </span><a
|
||||
href="userhtmlsu11.html#x21-200006.2"><span
|
||||
class="cmr-12">Method set</span></a></span>
|
||||
<br /> <span
|
||||
class="cmr-12"> </span><span class="subsectionToc" ><span
|
||||
class="cmr-12">6.3 </span><a
|
||||
href="userhtmlsu12.html#x22-210006.3"><span
|
||||
class="cmr-12">Method hierarchy</span><span
|
||||
class="cmr-12">_build</span></a></span>
|
||||
<br /> <span
|
||||
class="cmr-12"> </span><span class="subsectionToc" ><span
|
||||
class="cmr-12">6.4 </span><a
|
||||
href="userhtmlsu13.html#x23-220006.4"><span
|
||||
class="cmr-12">Method smoothers</span><span
|
||||
class="cmr-12">_build</span></a></span>
|
||||
<br /> <span
|
||||
class="cmr-12"> </span><span class="subsectionToc" ><span
|
||||
class="cmr-12">6.5 </span><a
|
||||
href="userhtmlsu14.html#x24-230006.5"><span
|
||||
class="cmr-12">Method build</span></a></span>
|
||||
<br /> <span
|
||||
class="cmr-12"> </span><span class="subsectionToc" ><span
|
||||
class="cmr-12">6.6 </span><a
|
||||
href="userhtmlsu15.html#x25-240006.6"><span
|
||||
class="cmr-12">Method apply</span></a></span>
|
||||
<br /> <span
|
||||
class="cmr-12"> </span><span class="subsectionToc" ><span
|
||||
class="cmr-12">6.7 </span><a
|
||||
href="userhtmlsu16.html#x26-250006.7"><span
|
||||
class="cmr-12">Method free</span></a></span>
|
||||
<br /> <span
|
||||
class="cmr-12"> </span><span class="subsectionToc" ><span
|
||||
class="cmr-12">6.8 </span><a
|
||||
href="userhtmlsu17.html#x27-260006.8"><span
|
||||
class="cmr-12">Method descr</span></a></span>
|
||||
<br /> <span
|
||||
class="cmr-12"> </span><span class="subsectionToc" ><span
|
||||
class="cmr-12">6.9 </span><a
|
||||
href="userhtmlsu18.html#x28-270006.9"><span
|
||||
class="cmr-12">Auxiliary Methods</span></a></span>
|
||||
<br /> <span
|
||||
class="cmr-12"> </span><span
|
||||
class="cmr-12"> </span><span class="subsubsectionToc" ><span
|
||||
class="cmr-12">6.9.1 </span><a
|
||||
href="userhtmlsu18.html#x28-280006.9.1"><span
|
||||
class="cmr-12">Method: dump</span></a></span>
|
||||
<br /> <span
|
||||
class="cmr-12"> </span><span
|
||||
class="cmr-12"> </span><span class="subsubsectionToc" ><span
|
||||
class="cmr-12">6.9.2 </span><a
|
||||
href="userhtmlsu18.html#x28-290006.9.2"><span
|
||||
class="cmr-12">Method: clone</span></a></span>
|
||||
<br /> <span
|
||||
class="cmr-12"> </span><span
|
||||
class="cmr-12"> </span><span class="subsubsectionToc" ><span
|
||||
class="cmr-12">6.9.3 </span><a
|
||||
href="userhtmlsu18.html#x28-300006.9.3"><span
|
||||
class="cmr-12">Method: sizeof</span></a></span>
|
||||
<br /> <span
|
||||
class="cmr-12"> </span><span
|
||||
class="cmr-12"> </span><span class="subsubsectionToc" ><span
|
||||
class="cmr-12">6.9.4 </span><a
|
||||
href="userhtmlsu18.html#x28-310006.9.4"><span
|
||||
class="cmr-12">Method: allocate</span><span
|
||||
class="cmr-12">_wrk</span></a></span>
|
||||
<br /> <span
|
||||
class="cmr-12"> </span><span
|
||||
class="cmr-12"> </span><span class="subsubsectionToc" ><span
|
||||
class="cmr-12">6.9.5 </span><a
|
||||
href="userhtmlsu18.html#x28-320006.9.5"><span
|
||||
class="cmr-12">Method: free</span><span
|
||||
class="cmr-12">_wrk</span></a></span>
|
||||
</div>
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
<pre class="verbatim" id="verbatim-10">
|
||||
  ! sparse matrix and preconditioner
|
||||
  type(psb_dspmat_type) :: a
|
||||
  type(amg_dprec_type)  :: prec
|
||||
  type(amg_d_tlu_solver_type) :: tlusv
|
||||
......
|
||||
  !
|
||||
  !  prepare the preconditioner: an ML with defaults, but with TLU solver at
|
||||
  !  intermediate levels. All other parameters are at default values.
|
||||
  !
|
||||
  call prec%init(’ML’,       info)
|
||||
  call prec%hierarchy_build(a,desc_a,info)
|
||||
  nlv = prec%get_nlevs()
|
||||
  call prec%set(tlusv,   info,ilev=1,ilmax=max(1,nlv-1))
|
||||
  call prec%smoothers_build(a,desc_a,info)
|
||||
</pre>
|
||||
<!--l. 88--><p class="nopar" >
|
||||
|
||||
|
||||
|
||||
<!--l. 4--><div class="crosslinks"><p class="noindent"><span
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
<!--l. 1--><div class="crosslinks"><p class="noindent"><span
|
||||
class="cmr-12">[</span><a
|
||||
href="userhtmlse7.html" ><span
|
||||
class="cmr-12">next</span></a><span
|
||||
@@ -268,6 +224,6 @@ class="cmr-12">] [</span><a
|
||||
href="userhtml.html#userhtmlse6.html" ><span
|
||||
class="cmr-12">up</span></a><span
|
||||
class="cmr-12">] </span></p></div>
|
||||
<!--l. 4--><p class="indent" > <a
|
||||
<!--l. 1--><p class="indent" > <a
|
||||
id="tailuserhtmlse6.html"></a>
|
||||
</body></html>
|
||||
|
||||
+22
-158
@@ -1,7 +1,7 @@
|
||||
<!DOCTYPE html PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN"
|
||||
"http://www.w3.org/TR/html4/loose.dtd">
|
||||
<html >
|
||||
<head><title>Adding new smoother and solver objects to AMG4PSBLAS</title>
|
||||
<head><title>Error Handling</title>
|
||||
<meta http-equiv="Content-Type" content="text/html; charset=iso-8859-1">
|
||||
<meta name="generator" content="TeX4ht (https://tug.org/tex4ht/)">
|
||||
<meta name="originator" content="TeX4ht (https://tug.org/tex4ht/)">
|
||||
@@ -10,7 +10,7 @@
|
||||
<link rel="stylesheet" type="text/css" href="userhtml.css">
|
||||
</head><body
|
||||
>
|
||||
<!--l. 4--><div class="crosslinks"><p class="noindent"><span
|
||||
<!--l. 1--><div class="crosslinks"><p class="noindent"><span
|
||||
class="cmr-12">[</span><a
|
||||
href="userhtmlse8.html" ><span
|
||||
class="cmr-12">next</span></a><span
|
||||
@@ -29,175 +29,39 @@ class="cmr-12">up</span></a><span
|
||||
class="cmr-12">] </span></p></div>
|
||||
<h3 class="sectionHead"><span class="titlemark"><span
|
||||
class="cmr-12">7 </span></span> <a
|
||||
id="x29-330007"></a><span
|
||||
class="cmr-12">Adding new smoother and solver objects to AMG4PSBLAS</span></h3>
|
||||
<!--l. 6--><p class="noindent" ><span
|
||||
class="cmr-12">Developers can add completely new smoother and/or solver classes derived from the</span>
|
||||
id="x26-300007"></a><span
|
||||
class="cmr-12">Error Handling</span></h3>
|
||||
<!--l. 5--><p class="noindent" ><span
|
||||
class="cmr-12">The error handling in AMG4PSBLAS is based on the PSBLAS error handling. Error</span>
|
||||
<span
|
||||
class="cmr-12">base objects in the library (see Remark</span><span
|
||||
class="cmr-12"> 2 in Section</span><span
|
||||
class="cmr-12"> </span><a
|
||||
href="userhtmlsu11.html#x21-200006.2"><span
|
||||
class="cmr-12">6.2</span><!--tex4ht:ref: sec:precset --></a><span
|
||||
class="cmr-12">), without recompiling the</span>
|
||||
class="cmr-12">conditions are signaled via an integer argument </span><span class="obeylines-h"><span class="verb"><span
|
||||
class="cmtt-12">info</span></span></span><span
|
||||
class="cmr-12">; whenever an error condition is</span>
|
||||
<span
|
||||
class="cmr-12">library itself.</span>
|
||||
<!--l. 10--><p class="indent" > <span
|
||||
class="cmr-12">To do so, it is necessary first to select the base type to be extended. In our</span>
|
||||
class="cmr-12">detected, an error trace stack is built by the library up to the top-level, user-callable</span>
|
||||
<span
|
||||
class="cmr-12">experience, it is quite likely that the new application needs only the definition of a</span>
|
||||
class="cmr-12">routine. This routine will then decide, according to the user preferences, whether</span>
|
||||
<span
|
||||
class="cmr-12">“solver” object, which is almost always acting only on the local part of the distributed</span>
|
||||
class="cmr-12">the error should be handled by terminating the program or by returning the</span>
|
||||
<span
|
||||
class="cmr-12">matrix. The parallel actions required to connect the various solver objects are most</span>
|
||||
class="cmr-12">error condition to the user code, which will then take action, and whether</span>
|
||||
<span
|
||||
class="cmr-12">often already provided by the block-Jacobi or the additive Schwarz smoothers. To</span>
|
||||
class="cmr-12">an error message should be printed. These options may be set by using the</span>
|
||||
<span
|
||||
class="cmr-12">define a new solver, the developer will then have to define its components and</span>
|
||||
<span
|
||||
class="cmr-12">methods, perhaps taking one of the predefined solvers as a starting point, if</span>
|
||||
<span
|
||||
class="cmr-12">possible.</span>
|
||||
<!--l. 20--><p class="indent" > <span
|
||||
class="cmr-12">Once the new smoother/solver class has been developed, to use it in the context of</span>
|
||||
<span
|
||||
class="cmr-12">the multilevel preconditioners it is necessary to:</span>
|
||||
<ul class="itemize1">
|
||||
<li class="itemize"><span
|
||||
class="cmr-12">declare in the application program a variable of the new type;</span>
|
||||
</li>
|
||||
<li class="itemize"><span
|
||||
class="cmr-12">pass that variable as the argument to the </span><span class="obeylines-h"><span class="verb"><span
|
||||
class="cmtt-12">set</span></span></span> <span
|
||||
class="cmr-12">routine as in the following:</span>
|
||||
<div class="center"
|
||||
>
|
||||
<!--l. 26--><p class="noindent" >
|
||||
<!--l. 27--><p class="noindent" ><span class="obeylines-h"><span class="verb"><span
|
||||
class="cmtt-12">call</span><span
|
||||
class="cmtt-12"> p%set(smoother,info</span><span
|
||||
class="cmtt-12"> [,ilev,ilmax,pos])</span></span></span><br />
|
||||
<span class="obeylines-h"><span class="verb"><span
|
||||
class="cmtt-12">call</span><span
|
||||
class="cmtt-12"> p%set(solver,info</span><span
|
||||
class="cmtt-12"> [,ilev,ilmax,pos])</span></span></span></div>
|
||||
</li>
|
||||
<li class="itemize"><span
|
||||
class="cmr-12">link the code implementing the various methods into the application</span>
|
||||
<span
|
||||
class="cmr-12">executable.</span></li></ul>
|
||||
<!--l. 32--><p class="noindent" ><span
|
||||
class="cmr-12">The new solver object is then dynamically included in the preconditioner structure,</span>
|
||||
<span
|
||||
class="cmr-12">and acts as a </span><span
|
||||
class="cmti-12">mold </span><span
|
||||
class="cmr-12">to which the preconditioner will conform, even though</span>
|
||||
<span
|
||||
class="cmr-12">the AMG4PSBLAS library has not been modified to account for this new</span>
|
||||
<span
|
||||
class="cmr-12">development.</span>
|
||||
class="cmr-12">PSBLAS error handling routines; for further details see the PSBLAS User’s Guide</span>
|
||||
<span class="cite"><span
|
||||
class="cmr-12">[</span><a
|
||||
href="userhtmlli4.html#XPSBLASGUIDE"><span
|
||||
class="cmr-12">16</span></a><span
|
||||
class="cmr-12">]</span></span><span
|
||||
class="cmr-12">.</span>
|
||||
|
||||
|
||||
|
||||
<!--l. 37--><p class="indent" > <span
|
||||
class="cmr-12">It is possible to define new values for the keyword </span><span class="obeylines-h"><span class="verb"><span
|
||||
class="cmtt-12">WHAT</span></span></span> <span
|
||||
class="cmr-12">in the </span><span class="obeylines-h"><span class="verb"><span
|
||||
class="cmtt-12">set</span></span></span> <span
|
||||
class="cmr-12">routine; if the</span>
|
||||
<span
|
||||
class="cmr-12">library code does not recognize a keyword, it passes it down the composition hierarchy</span>
|
||||
<span
|
||||
class="cmr-12">(levels containing smoothers containing in turn solvers), so that it can be eventually</span>
|
||||
<span
|
||||
class="cmr-12">caught by the new solver. By the same token, any keyword/value pair that does not</span>
|
||||
<span
|
||||
class="cmr-12">pertain to a given smoother should be passed down to the contained solver, and</span>
|
||||
<span
|
||||
class="cmr-12">any keyword/value pair that does not pertain to a given solver is by default</span>
|
||||
<span
|
||||
class="cmr-12">ignored.</span>
|
||||
<!--l. 46--><p class="indent" > <span
|
||||
class="cmr-12">An example is provided in the source code distribution under the folder</span>
|
||||
<span class="obeylines-h"><span class="verb"><span
|
||||
class="cmtt-12">tests/newslv</span></span></span><span
|
||||
class="cmr-12">. In this example we are implementing a new incomplete factorization</span>
|
||||
<span
|
||||
class="cmr-12">variant (which is simply the ILU(0) factorization under a new name). Because of the</span>
|
||||
<span
|
||||
class="cmr-12">specifics of this case, it is possible to reuse the basic structure of the ILU solver, with</span>
|
||||
<span
|
||||
class="cmr-12">its L/D/U components and the methods needed to apply the solver; only a few</span>
|
||||
<span
|
||||
class="cmr-12">methods, such as the description and most importantly the build, need to be</span>
|
||||
<span
|
||||
class="cmr-12">ovverridden (rewritten).</span>
|
||||
<!--l. 55--><p class="indent" > <span
|
||||
class="cmr-12">The interfaces for the calls shown above are defined using</span>
|
||||
<div class="center"
|
||||
>
|
||||
<!--l. 56--><p class="noindent" >
|
||||
<div class="tabular"> <table id="TBL-21" class="tabular"
|
||||
cellspacing="0" cellpadding="0"
|
||||
><colgroup id="TBL-21-1g"><col
|
||||
id="TBL-21-1"><col
|
||||
id="TBL-21-2"></colgroup><tr
|
||||
style="vertical-align:baseline;" id="TBL-21-1-"><td style="white-space:normal; text-align:left;" id="TBL-21-1-1"
|
||||
class="td11"><!--l. 58--><p class="noindent" ><span class="obeylines-h"><span class="verb"><span
|
||||
class="cmtt-12">smoother</span></span></span> </td><td style="white-space:normal; text-align:left;" id="TBL-21-1-2"
|
||||
class="td11"><!--l. 58--><p class="noindent" ><span class="obeylines-h"><span class="verb"><span
|
||||
class="cmtt-12">class(amg_x_base_smoother_type)</span></span></span> </td>
|
||||
</tr><tr
|
||||
style="vertical-align:baseline;" id="TBL-21-2-"><td style="white-space:normal; text-align:left;" id="TBL-21-2-1"
|
||||
class="td11"><!--l. 59--><p class="noindent" > </td><td style="white-space:normal; text-align:left;" id="TBL-21-2-2"
|
||||
class="td11"><!--l. 59--><p class="noindent" ><span
|
||||
class="cmr-12">The user-defined new smoother to be employed in the</span>
|
||||
<span
|
||||
class="cmr-12">preconditioner.</span> </td>
|
||||
</tr><tr
|
||||
style="vertical-align:baseline;" id="TBL-21-3-"><td style="white-space:normal; text-align:left;" id="TBL-21-3-1"
|
||||
class="td11"><!--l. 61--><p class="noindent" ><span class="obeylines-h"><span class="verb"><span
|
||||
class="cmtt-12">solver</span></span></span> </td><td style="white-space:normal; text-align:left;" id="TBL-21-3-2"
|
||||
class="td11"><!--l. 61--><p class="noindent" ><span class="obeylines-h"><span class="verb"><span
|
||||
class="cmtt-12">class(amg_x_base_solver_type)</span></span></span> </td>
|
||||
</tr><tr
|
||||
style="vertical-align:baseline;" id="TBL-21-4-"><td style="white-space:normal; text-align:left;" id="TBL-21-4-1"
|
||||
class="td11"><!--l. 62--><p class="noindent" > </td><td style="white-space:normal; text-align:left;" id="TBL-21-4-2"
|
||||
class="td11"><!--l. 62--><p class="noindent" ><span
|
||||
class="cmr-12">The user-defined new solver to be employed in the preconditioner.</span></td></tr></table></div></div>
|
||||
<!--l. 66--><p class="noindent" ><span
|
||||
class="cmr-12">The other arguments are defined in the way described in Sec.</span><span
|
||||
class="cmr-12"> </span><a
|
||||
href="userhtmlsu11.html#x21-200006.2"><span
|
||||
class="cmr-12">6.2</span><!--tex4ht:ref: sec:precset --></a><span
|
||||
class="cmr-12">. As an example, in the</span>
|
||||
<span class="obeylines-h"><span class="verb"><span
|
||||
class="cmtt-12">tests/newslv</span></span></span> <span
|
||||
class="cmr-12">code we define a new object of type </span><span class="obeylines-h"><span class="verb"><span
|
||||
class="cmtt-12">amg_d_tlu_solver_type</span></span></span><span
|
||||
class="cmr-12">, and we</span>
|
||||
<span
|
||||
class="cmr-12">pass it as follows:</span>
|
||||
|
||||
|
||||
|
||||
<pre class="verbatim" id="verbatim-10">
|
||||
  ! sparse matrix and preconditioner
|
||||
  type(psb_dspmat_type) :: a
|
||||
  type(amg_dprec_type)  :: prec
|
||||
  type(amg_d_tlu_solver_type) :: tlusv
|
||||
......
|
||||
  !
|
||||
  !  prepare the preconditioner: an ML with defaults, but with TLU solver at
|
||||
  !  intermediate levels. All other parameters are at default values.
|
||||
  !
|
||||
  call prec%init(’ML’,       info)
|
||||
  call prec%hierarchy_build(a,desc_a,info)
|
||||
  nlv = prec%get_nlevs()
|
||||
  call prec%set(tlusv,   info,ilev=1,ilmax=max(1,nlv-1))
|
||||
  call prec%smoothers_build(a,desc_a,info)
|
||||
</pre>
|
||||
<!--l. 88--><p class="nopar" >
|
||||
<!--l. 138--><p class="indent" >
|
||||
|
||||
|
||||
|
||||
|
||||
+102
-43
@@ -1,7 +1,7 @@
|
||||
<!DOCTYPE html PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN"
|
||||
"http://www.w3.org/TR/html4/loose.dtd">
|
||||
<html >
|
||||
<head><title>Error Handling</title>
|
||||
<head><title>License</title>
|
||||
<meta http-equiv="Content-Type" content="text/html; charset=iso-8859-1">
|
||||
<meta name="generator" content="TeX4ht (https://tug.org/tex4ht/)">
|
||||
<meta name="originator" content="TeX4ht (https://tug.org/tex4ht/)">
|
||||
@@ -12,7 +12,7 @@
|
||||
>
|
||||
<!--l. 1--><div class="crosslinks"><p class="noindent"><span
|
||||
class="cmr-12">[</span><a
|
||||
href="userhtmlse9.html" ><span
|
||||
href="userhtmlli4.html" ><span
|
||||
class="cmr-12">next</span></a><span
|
||||
class="cmr-12">] [</span><a
|
||||
href="userhtmlse7.html" ><span
|
||||
@@ -28,48 +28,107 @@ href="userhtml.html#userhtmlse8.html" ><span
|
||||
class="cmr-12">up</span></a><span
|
||||
class="cmr-12">] </span></p></div>
|
||||
<h3 class="sectionHead"><span class="titlemark"><span
|
||||
class="cmr-12">8 </span></span> <a
|
||||
id="x30-340008"></a><span
|
||||
class="cmr-12">Error Handling</span></h3>
|
||||
<!--l. 5--><p class="noindent" ><span
|
||||
class="cmr-12">The error handling in AMG4PSBLAS is based on the PSBLAS error handling. Error</span>
|
||||
class="cmr-12">A </span></span> <a
|
||||
id="x27-31000A"></a><span
|
||||
class="cmr-12">License</span></h3>
|
||||
<!--l. 6--><p class="noindent" ><span
|
||||
class="cmr-12">AMG4PSBLAS is freely distributable under the following copyright terms:</span>
|
||||
|
||||
|
||||
|
||||
<pre class="verbatim" id="verbatim-11">
|
||||
                           AMG4PSBLAS  version 1.0
|
||||
              Algebraic MultiGrid Preconditioners Package
|
||||
             based on PSBLAS (Parallel Sparse BLAS version 3.7)
|
||||
  (C) Copyright 2021
|
||||
  Pasqua D’Ambra         IAC-CNR, IT
|
||||
  Fabio Durastante       University of Pisa and IAC-CNR, IT
|
||||
  Salvatore Filippone    University of Rome Tor-Vergata and IAC-CNR, IT
|
||||
  Redistribution and use in source and binary forms, with or without
|
||||
  modification, are permitted provided that the following conditions
|
||||
  are met:
|
||||
    1. Redistributions of source code must retain the above copyright
|
||||
       notice, this list of conditions and the following disclaimer.
|
||||
    2. Redistributions in binary form must reproduce the above copyright
|
||||
       notice, this list of conditions, and the following disclaimer in the
|
||||
       documentation and/or other materials provided with the distribution.
|
||||
    3. The name of the MLD2P4 group or the names of its contributors may
|
||||
       not be used to endorse or promote products derived from this
|
||||
       software without specific written permission.
|
||||
  THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
|
||||
  ‘‘AS IS’’ AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED
|
||||
  TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR
|
||||
  PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE MLD2P4 GROUP OR ITS CONTRIBUTORS
|
||||
  BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR
|
||||
  CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF
|
||||
  SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS
|
||||
  INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN
|
||||
  CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
|
||||
  ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
|
||||
  POSSIBILITY OF SUCH DAMAGE.
|
||||
</pre>
|
||||
<!--l. 44--><p class="nopar" >
|
||||
|
||||
|
||||
|
||||
<!--l. 47--><p class="indent" > <span
|
||||
class="cmr-12">AMG4PSBLAS is an evolution of MLD2P4, whose license we reproduce here to</span>
|
||||
<span
|
||||
class="cmr-12">conditions are signaled via an integer argument </span><span class="obeylines-h"><span class="verb"><span
|
||||
class="cmtt-12">info</span></span></span><span
|
||||
class="cmr-12">; whenever an error condition is</span>
|
||||
<span
|
||||
class="cmr-12">detected, an error trace stack is built by the library up to the top-level, user-callable</span>
|
||||
<span
|
||||
class="cmr-12">routine. This routine will then decide, according to the user preferences, whether</span>
|
||||
<span
|
||||
class="cmr-12">the error should be handled by terminating the program or by returning the</span>
|
||||
<span
|
||||
class="cmr-12">error condition to the user code, which will then take action, and whether</span>
|
||||
<span
|
||||
class="cmr-12">an error message should be printed. These options may be set by using the</span>
|
||||
<span
|
||||
class="cmr-12">PSBLAS error handling routines; for further details see the PSBLAS User’s Guide</span>
|
||||
<span class="cite"><span
|
||||
class="cmr-12">abide by its terms:</span>
|
||||
|
||||
|
||||
|
||||
<pre class="verbatim" id="verbatim-12">
|
||||
                           MLD2P4  version 2.2
|
||||
  MultiLevel Domain Decomposition Parallel Preconditioners Package
|
||||
             based on PSBLAS (Parallel Sparse BLAS version 3.5)
|
||||
  (C) Copyright 2008-2018
|
||||
      Salvatore Filippone
|
||||
      Pasqua D’Ambra
|
||||
      Daniela di Serafino
|
||||
  Redistribution and use in source and binary forms, with or without
|
||||
  modification, are permitted provided that the following conditions
|
||||
  are met:
|
||||
    1. Redistributions of source code must retain the above copyright
|
||||
       notice, this list of conditions and the following disclaimer.
|
||||
    2. Redistributions in binary form must reproduce the above copyright
|
||||
       notice, this list of conditions, and the following disclaimer in the
|
||||
       documentation and/or other materials provided with the distribution.
|
||||
    3. The name of the MLD2P4 group or the names of its contributors may
|
||||
       not be used to endorse or promote products derived from this
|
||||
       software without specific written permission.
|
||||
  THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
|
||||
  ‘‘AS IS’’ AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED
|
||||
  TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR
|
||||
  PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE MLD2P4 GROUP OR ITS CONTRIBUTORS
|
||||
  BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR
|
||||
  CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF
|
||||
  SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS
|
||||
  INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN
|
||||
  CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
|
||||
  ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
|
||||
  POSSIBILITY OF SUCH DAMAGE.
|
||||
</pre>
|
||||
<!--l. 87--><p class="nopar" >
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
<!--l. 141--><p class="indent" >
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
<!--l. 2--><div class="crosslinks"><p class="noindent"><span
|
||||
class="cmr-12">[</span><a
|
||||
href="userhtmlli4.html#XPSBLASGUIDE"><span
|
||||
class="cmr-12">16</span></a><span
|
||||
class="cmr-12">]</span></span><span
|
||||
class="cmr-12">.</span>
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
<!--l. 1--><div class="crosslinks"><p class="noindent"><span
|
||||
class="cmr-12">[</span><a
|
||||
href="userhtmlse9.html" ><span
|
||||
href="userhtmlli4.html" ><span
|
||||
class="cmr-12">next</span></a><span
|
||||
class="cmr-12">] [</span><a
|
||||
href="userhtmlse7.html" ><span
|
||||
@@ -84,6 +143,6 @@ class="cmr-12">] [</span><a
|
||||
href="userhtml.html#userhtmlse8.html" ><span
|
||||
class="cmr-12">up</span></a><span
|
||||
class="cmr-12">] </span></p></div>
|
||||
<!--l. 1--><p class="indent" > <a
|
||||
<!--l. 2--><p class="indent" > <a
|
||||
id="tailuserhtmlse8.html"></a>
|
||||
</body></html>
|
||||
|
||||
+166
-65
@@ -1,7 +1,7 @@
|
||||
<!DOCTYPE html PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN"
|
||||
"http://www.w3.org/TR/html4/loose.dtd">
|
||||
<html >
|
||||
<head><title>Method init</title>
|
||||
<head><title>Method smoothers_build</title>
|
||||
<meta http-equiv="Content-Type" content="text/html; charset=iso-8859-1">
|
||||
<meta name="generator" content="TeX4ht (https://tug.org/tex4ht/)">
|
||||
<meta name="originator" content="TeX4ht (https://tug.org/tex4ht/)">
|
||||
@@ -10,92 +10,187 @@
|
||||
<link rel="stylesheet" type="text/css" href="userhtml.css">
|
||||
</head><body
|
||||
>
|
||||
<!--l. 43--><div class="crosslinks"><p class="noindent"><span
|
||||
<!--l. 603--><div class="crosslinks"><p class="noindent"><span
|
||||
class="cmr-12">[</span><a
|
||||
href="userhtmlsu11.html" ><span
|
||||
class="cmr-12">next</span></a><span
|
||||
class="cmr-12">] [</span><a
|
||||
href="userhtmlsu9.html" ><span
|
||||
class="cmr-12">prev</span></a><span
|
||||
class="cmr-12">] [</span><a
|
||||
href="userhtmlsu9.html#tailuserhtmlsu9.html" ><span
|
||||
class="cmr-12">prev-tail</span></a><span
|
||||
class="cmr-12">] [</span><a
|
||||
href="#tailuserhtmlsu10.html"><span
|
||||
class="cmr-12">tail</span></a><span
|
||||
class="cmr-12">] [</span><a
|
||||
href="userhtmlse6.html#userhtmlsu10.html" ><span
|
||||
href="userhtmlse5.html#userhtmlsu10.html" ><span
|
||||
class="cmr-12">up</span></a><span
|
||||
class="cmr-12">] </span></p></div>
|
||||
<h4 class="subsectionHead"><span class="titlemark"><span
|
||||
class="cmr-12">6.1 </span></span> <a
|
||||
id="x20-190006.1"></a><span
|
||||
class="cmr-12">Method init</span></h4>
|
||||
class="cmr-12">5.4 </span></span> <a
|
||||
id="x19-180005.4"></a><span
|
||||
class="cmr-12">Method smoothers</span><span
|
||||
class="cmr-12">_build</span></h4>
|
||||
<div class="center"
|
||||
>
|
||||
<!--l. 45--><p class="noindent" >
|
||||
<!--l. 46--><p class="noindent" ><span class="obeylines-h"><span class="verb"><span
|
||||
<!--l. 606--><p class="noindent" >
|
||||
<!--l. 607--><p class="noindent" ><span class="obeylines-h"><span class="verb"><span
|
||||
class="cmtt-12">call</span><span
|
||||
class="cmtt-12"> p%init(icontx,ptype,info)</span></span></span></div>
|
||||
<!--l. 49--><p class="noindent" ><span
|
||||
class="cmr-12">This method allocates and initializes the preconditioner </span><span class="obeylines-h"><span class="verb"><span
|
||||
class="cmtt-12">p</span></span></span><span
|
||||
class="cmr-12">, according to the</span>
|
||||
class="cmtt-12"> p%smoothers_build(a,desc_a,p,info[,amold,vmold,imold])</span></span></span><br />
|
||||
</div>
|
||||
<!--l. 610--><p class="noindent" ><span
|
||||
class="cmr-12">This method builds the smoothers and the coarsest-level solvers for the multilevel</span>
|
||||
<span
|
||||
class="cmr-12">preconditioner type chosen by the user.</span>
|
||||
<!--l. 53--><p class="noindent" ><span
|
||||
class="cmbx-12">Arguments</span>
|
||||
<div class="tabular"> <table id="TBL-2" class="tabular"
|
||||
cellspacing="0" cellpadding="0"
|
||||
><colgroup id="TBL-2-1g"><col
|
||||
id="TBL-2-1"><col
|
||||
id="TBL-2-2"></colgroup><tr
|
||||
style="vertical-align:baseline;" id="TBL-2-1-"><td style="white-space:normal; text-align:left;" id="TBL-2-1-1"
|
||||
class="td11"><!--l. 57--><p class="noindent" ><span class="obeylines-h"><span class="verb"><span
|
||||
class="cmtt-12">icontxt</span></span></span> </td> <td style="white-space:normal; text-align:left;" id="TBL-2-1-2"
|
||||
class="td11"><!--l. 57--><p class="noindent" ><span class="obeylines-h"><span class="verb"><span
|
||||
class="cmtt-12">integer,</span><span
|
||||
class="cmtt-12"> intent(in)</span></span></span><span
|
||||
class="cmr-12">.</span> </td>
|
||||
</tr><tr
|
||||
style="vertical-align:baseline;" id="TBL-2-2-"><td style="white-space:normal; text-align:left;" id="TBL-2-2-1"
|
||||
class="td11"><!--l. 58--><p class="noindent" > </td><td style="white-space:normal; text-align:left;" id="TBL-2-2-2"
|
||||
class="td11"><!--l. 58--><p class="noindent" ><span
|
||||
class="cmr-12">The communication context.</span> </td></tr><tr
|
||||
style="vertical-align:baseline;" id="TBL-2-3-"><td style="white-space:normal; text-align:left;" id="TBL-2-3-1"
|
||||
class="td11"><!--l. 59--><p class="noindent" ><span class="obeylines-h"><span class="verb"><span
|
||||
class="cmtt-12">ptype</span></span></span> </td> <td style="white-space:normal; text-align:left;" id="TBL-2-3-2"
|
||||
class="td11"><!--l. 59--><p class="noindent" ><span class="obeylines-h"><span class="verb"><span
|
||||
class="cmtt-12">character(len=*),</span><span
|
||||
class="cmtt-12"> intent(in)</span></span></span><span
|
||||
class="cmr-12">.</span></td>
|
||||
</tr><tr
|
||||
style="vertical-align:baseline;" id="TBL-2-4-"><td style="white-space:normal; text-align:left;" id="TBL-2-4-1"
|
||||
class="td11"><!--l. 60--><p class="noindent" > </td><td style="white-space:normal; text-align:left;" id="TBL-2-4-2"
|
||||
class="td11"><!--l. 60--><p class="noindent" ><span
|
||||
class="cmr-12">The type of preconditioner. Its values are specified in Table</span><span
|
||||
class="cmr-12">preconditioner </span><span class="obeylines-h"><span class="verb"><span
|
||||
class="cmtt-12">p</span></span></span><span
|
||||
class="cmr-12">, according to the requirements made by the user through the methods</span>
|
||||
<span class="obeylines-h"><span class="verb"><span
|
||||
class="cmtt-12">init</span></span></span> <span
|
||||
class="cmr-12">and </span><span class="obeylines-h"><span class="verb"><span
|
||||
class="cmtt-12">set</span></span></span><span
|
||||
class="cmr-12">, and based on the aggregation hierarchy produced by a previous call to</span>
|
||||
<span class="obeylines-h"><span class="verb"><span
|
||||
class="cmtt-12">hierarchy_build</span></span></span> <span
|
||||
class="cmr-12">(see Section</span><span
|
||||
class="cmr-12"> </span><a
|
||||
href="userhtmlse5.html#x17-160151"><span
|
||||
class="cmr-12">1</span><!--tex4ht:ref: tab:precinit --></a><span
|
||||
class="cmr-12">.</span> </td>
|
||||
href="userhtmlsu9.html#x18-170005.3"><span
|
||||
class="cmr-12">5.3</span><!--tex4ht:ref: sec:hier_bld --></a><span
|
||||
class="cmr-12">).</span>
|
||||
<!--l. 617--><p class="noindent" ><span
|
||||
class="cmbx-12">Arguments</span>
|
||||
<div class="tabular"> <table id="TBL-12" class="tabular"
|
||||
cellspacing="0" cellpadding="0"
|
||||
><colgroup id="TBL-12-1g"><col
|
||||
id="TBL-12-1"><col
|
||||
id="TBL-12-2"></colgroup><tr
|
||||
style="vertical-align:baseline;" id="TBL-12-1-"><td style="white-space:normal; text-align:left;" id="TBL-12-1-1"
|
||||
class="td11"><!--l. 620--><p class="noindent" ><span class="obeylines-h"><span class="verb"><span
|
||||
class="cmtt-12">a</span></span></span> </td><td style="white-space:normal; text-align:left;" id="TBL-12-1-2"
|
||||
class="td11"><!--l. 620--><p class="noindent" ><span class="obeylines-h"><span class="verb"><span
|
||||
class="cmtt-12">type(psb_</span></span></span><span
|
||||
class="cmti-12">x</span><span class="obeylines-h"><span class="verb"><span
|
||||
class="cmtt-12">spmat_type),</span><span
|
||||
class="cmtt-12"> intent(in)</span></span></span><span
|
||||
class="cmr-12">.</span> </td>
|
||||
</tr><tr
|
||||
style="vertical-align:baseline;" id="TBL-2-5-"><td style="white-space:normal; text-align:left;" id="TBL-2-5-1"
|
||||
class="td11"><!--l. 62--><p class="noindent" > </td><td style="white-space:normal; text-align:left;" id="TBL-2-5-2"
|
||||
class="td11"><!--l. 62--><p class="noindent" ><span
|
||||
class="cmr-12">Note that the strings are case insensitive.</span> </td>
|
||||
style="vertical-align:baseline;" id="TBL-12-2-"><td style="white-space:normal; text-align:left;" id="TBL-12-2-1"
|
||||
class="td11"><!--l. 621--><p class="noindent" > </td><td style="white-space:normal; text-align:left;" id="TBL-12-2-2"
|
||||
class="td11"><!--l. 621--><p class="noindent" ><span
|
||||
class="cmr-12">The sparse matrix structure containing the local part of the matrix</span>
|
||||
<span
|
||||
class="cmr-12">to be preconditioned. Note that </span><span
|
||||
class="cmti-12">x </span><span
|
||||
class="cmr-12">must be chosen according to the</span>
|
||||
<span
|
||||
class="cmr-12">real/complex, single/double precision version of AMG4PSBLAS</span>
|
||||
<span
|
||||
class="cmr-12">under use. See the PSBLAS User’s Guide for details </span><span class="cite"><span
|
||||
class="cmr-12">[</span><a
|
||||
href="userhtmlli4.html#XPSBLASGUIDE"><span
|
||||
class="cmr-12">16</span></a><span
|
||||
class="cmr-12">]</span></span><span
|
||||
class="cmr-12">.</span> </td>
|
||||
</tr><tr
|
||||
style="vertical-align:baseline;" id="TBL-2-6-"><td style="white-space:normal; text-align:left;" id="TBL-2-6-1"
|
||||
class="td11"><!--l. 63--><p class="noindent" ><span class="obeylines-h"><span class="verb"><span
|
||||
class="cmtt-12">info</span></span></span> </td><td style="white-space:normal; text-align:left;" id="TBL-2-6-2"
|
||||
class="td11"><!--l. 63--><p class="noindent" ><span class="obeylines-h"><span class="verb"><span
|
||||
style="vertical-align:baseline;" id="TBL-12-3-"><td style="white-space:normal; text-align:left;" id="TBL-12-3-1"
|
||||
class="td11"><!--l. 625--><p class="noindent" ><span class="obeylines-h"><span class="verb"><span
|
||||
class="cmtt-12">desc_a</span></span></span></td><td style="white-space:normal; text-align:left;" id="TBL-12-3-2"
|
||||
class="td11"><!--l. 625--><p class="noindent" ><span class="obeylines-h"><span class="verb"><span
|
||||
class="cmtt-12">type(psb_desc_type),</span><span
|
||||
class="cmtt-12"> intent(in)</span></span></span><span
|
||||
class="cmr-12">.</span> </td>
|
||||
</tr><tr
|
||||
style="vertical-align:baseline;" id="TBL-12-4-"><td style="white-space:normal; text-align:left;" id="TBL-12-4-1"
|
||||
class="td11"><!--l. 626--><p class="noindent" > </td><td style="white-space:normal; text-align:left;" id="TBL-12-4-2"
|
||||
class="td11"><!--l. 626--><p class="noindent" ><span
|
||||
class="cmr-12">The communication descriptor of </span><span class="obeylines-h"><span class="verb"><span
|
||||
class="cmtt-12">a</span></span></span><span
|
||||
class="cmr-12">. See the PSBLAS User’s Guide</span>
|
||||
<span
|
||||
class="cmr-12">for details </span><span class="cite"><span
|
||||
class="cmr-12">[</span><a
|
||||
href="userhtmlli4.html#XPSBLASGUIDE"><span
|
||||
class="cmr-12">16</span></a><span
|
||||
class="cmr-12">]</span></span><span
|
||||
class="cmr-12">.</span> </td>
|
||||
</tr><tr
|
||||
style="vertical-align:baseline;" id="TBL-12-5-"><td style="white-space:normal; text-align:left;" id="TBL-12-5-1"
|
||||
class="td11"><!--l. 628--><p class="noindent" ><span class="obeylines-h"><span class="verb"><span
|
||||
class="cmtt-12">info</span></span></span> </td><td style="white-space:normal; text-align:left;" id="TBL-12-5-2"
|
||||
class="td11"><!--l. 628--><p class="noindent" ><span class="obeylines-h"><span class="verb"><span
|
||||
class="cmtt-12">integer,</span><span
|
||||
class="cmtt-12"> intent(out)</span></span></span><span
|
||||
class="cmr-12">.</span> </td>
|
||||
</tr><tr
|
||||
style="vertical-align:baseline;" id="TBL-2-7-"><td style="white-space:normal; text-align:left;" id="TBL-2-7-1"
|
||||
class="td11"><!--l. 64--><p class="noindent" > </td><td style="white-space:normal; text-align:left;" id="TBL-2-7-2"
|
||||
class="td11"><!--l. 64--><p class="noindent" ><span
|
||||
style="vertical-align:baseline;" id="TBL-12-6-"><td style="white-space:normal; text-align:left;" id="TBL-12-6-1"
|
||||
class="td11"><!--l. 629--><p class="noindent" > </td><td style="white-space:normal; text-align:left;" id="TBL-12-6-2"
|
||||
class="td11"><!--l. 629--><p class="noindent" ><span
|
||||
class="cmr-12">Error code. If no error, 0 is returned. See Section</span><span
|
||||
class="cmr-12"> </span><a
|
||||
href="userhtmlse8.html#x30-340008"><span
|
||||
class="cmr-12">8</span><!--tex4ht:ref: sec:errors --></a> <span
|
||||
href="userhtmlse7.html#x26-300007"><span
|
||||
class="cmr-12">7</span><!--tex4ht:ref: sec:errors --></a> <span
|
||||
class="cmr-12">for details.</span> </td>
|
||||
</tr><tr
|
||||
style="vertical-align:baseline;" id="TBL-2-8-"><td style="white-space:normal; text-align:left;" id="TBL-2-8-1"
|
||||
style="vertical-align:baseline;" id="TBL-12-7-"><td style="white-space:normal; text-align:left;" id="TBL-12-7-1"
|
||||
class="td11"><!--l. 630--><p class="noindent" ><span class="obeylines-h"><span class="verb"><span
|
||||
class="cmtt-12">amold</span></span></span> </td><td style="white-space:normal; text-align:left;" id="TBL-12-7-2"
|
||||
class="td11"><!--l. 630--><p class="noindent" ><span class="obeylines-h"><span class="verb"><span
|
||||
class="cmtt-12">class(psb_</span></span></span><span
|
||||
class="cmti-12">x</span><span class="obeylines-h"><span class="verb"><span
|
||||
class="cmtt-12">_base_sparse_mat),</span><span
|
||||
class="cmtt-12"> intent(in),</span><span
|
||||
class="cmtt-12"> optional</span></span></span><span
|
||||
class="cmr-12">.</span> </td>
|
||||
</tr><tr
|
||||
style="vertical-align:baseline;" id="TBL-12-8-"><td style="white-space:normal; text-align:left;" id="TBL-12-8-1"
|
||||
class="td11"><!--l. 631--><p class="noindent" > </td><td style="white-space:normal; text-align:left;" id="TBL-12-8-2"
|
||||
class="td11"><!--l. 631--><p class="noindent" ><span
|
||||
class="cmr-12">The desired dynamic type for internal matrix components; this</span>
|
||||
<span
|
||||
class="cmr-12">allows e.g. running on GPUs; it needs not be the same on all</span>
|
||||
<span
|
||||
class="cmr-12">processes. See the PSBLAS User’s Guide for details </span><span class="cite"><span
|
||||
class="cmr-12">[</span><a
|
||||
href="userhtmlli4.html#XPSBLASGUIDE"><span
|
||||
class="cmr-12">16</span></a><span
|
||||
class="cmr-12">]</span></span><span
|
||||
class="cmr-12">.</span> </td>
|
||||
</tr><tr
|
||||
style="vertical-align:baseline;" id="TBL-12-9-"><td style="white-space:normal; text-align:left;" id="TBL-12-9-1"
|
||||
class="td11"><!--l. 635--><p class="noindent" ><span class="obeylines-h"><span class="verb"><span
|
||||
class="cmtt-12">vmold</span></span></span> </td><td style="white-space:normal; text-align:left;" id="TBL-12-9-2"
|
||||
class="td11"><!--l. 635--><p class="noindent" ><span class="obeylines-h"><span class="verb"><span
|
||||
class="cmtt-12">class(psb_</span></span></span><span
|
||||
class="cmti-12">x</span><span class="obeylines-h"><span class="verb"><span
|
||||
class="cmtt-12">_base_vect_type),</span><span
|
||||
class="cmtt-12"> intent(in),</span><span
|
||||
class="cmtt-12"> optional</span></span></span><span
|
||||
class="cmr-12">.</span> </td>
|
||||
</tr><tr
|
||||
style="vertical-align:baseline;" id="TBL-12-10-"><td style="white-space:normal; text-align:left;" id="TBL-12-10-1"
|
||||
class="td11"><!--l. 636--><p class="noindent" > </td><td style="white-space:normal; text-align:left;" id="TBL-12-10-2"
|
||||
class="td11"><!--l. 636--><p class="noindent" ><span
|
||||
class="cmr-12">The desired dynamic type for internal vector components; this</span>
|
||||
<span
|
||||
class="cmr-12">allows e.g. running on GPUs.</span> </td>
|
||||
</tr><tr
|
||||
style="vertical-align:baseline;" id="TBL-12-11-"><td style="white-space:normal; text-align:left;" id="TBL-12-11-1"
|
||||
class="td11"><!--l. 638--><p class="noindent" ><span class="obeylines-h"><span class="verb"><span
|
||||
class="cmtt-12">imold</span></span></span> </td><td style="white-space:normal; text-align:left;" id="TBL-12-11-2"
|
||||
class="td11"><!--l. 638--><p class="noindent" ><span class="obeylines-h"><span class="verb"><span
|
||||
class="cmtt-12">class(psb_i_base_vect_type),</span><span
|
||||
class="cmtt-12"> intent(in),</span><span
|
||||
class="cmtt-12"> optional</span></span></span><span
|
||||
class="cmr-12">.</span> </td>
|
||||
</tr><tr
|
||||
style="vertical-align:baseline;" id="TBL-12-12-"><td style="white-space:normal; text-align:left;" id="TBL-12-12-1"
|
||||
class="td11"><!--l. 639--><p class="noindent" > </td><td style="white-space:normal; text-align:left;" id="TBL-12-12-2"
|
||||
class="td11"><!--l. 639--><p class="noindent" ><span
|
||||
class="cmr-12">The desired dynamic type for internal integer vector components;</span>
|
||||
<span
|
||||
class="cmr-12">this allows e.g. running on GPUs.</span> </td>
|
||||
</tr><tr
|
||||
style="vertical-align:baseline;" id="TBL-12-13-"><td style="white-space:normal; text-align:left;" id="TBL-12-13-1"
|
||||
class="td11"> </td> </tr></table></div>
|
||||
|
||||
|
||||
@@ -103,17 +198,23 @@ class="td11"> </td> </tr></table></div>
|
||||
|
||||
|
||||
|
||||
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|
||||
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|
||||
class="cmr-12">[</span><a
|
||||
href="userhtmlsu11.html" ><span
|
||||
class="cmr-12">next</span></a><span
|
||||
class="cmr-12">] [</span><a
|
||||
href="userhtmlsu9.html" ><span
|
||||
class="cmr-12">prev</span></a><span
|
||||
class="cmr-12">] [</span><a
|
||||
href="userhtmlsu9.html#tailuserhtmlsu9.html" ><span
|
||||
class="cmr-12">prev-tail</span></a><span
|
||||
class="cmr-12">] [</span><a
|
||||
href="userhtmlsu10.html" ><span
|
||||
class="cmr-12">front</span></a><span
|
||||
class="cmr-12">] [</span><a
|
||||
href="userhtmlse6.html#userhtmlsu10.html" ><span
|
||||
href="userhtmlse5.html#userhtmlsu10.html" ><span
|
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class="cmr-12">up</span></a><span
|
||||
class="cmr-12">] </span></p></div>
|
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|
||||
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|
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id="tailuserhtmlsu10.html"></a>
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</body></html>
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"http://www.w3.org/TR/html4/loose.dtd">
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<html >
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<head><title>Method hierarchy_build</title>
|
||||
<head><title>Method apply</title>
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||||
<meta http-equiv="Content-Type" content="text/html; charset=iso-8859-1">
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||||
<meta name="generator" content="TeX4ht (https://tug.org/tex4ht/)">
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|
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<link rel="stylesheet" type="text/css" href="userhtml.css">
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</head><body
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>
|
||||
<!--l. 572--><div class="crosslinks"><p class="noindent"><span
|
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<!--l. 693--><div class="crosslinks"><p class="noindent"><span
|
||||
class="cmr-12">[</span><a
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href="userhtmlsu13.html" ><span
|
||||
class="cmr-12">next</span></a><span
|
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@@ -24,108 +24,247 @@ class="cmr-12">] [</span><a
|
||||
href="#tailuserhtmlsu12.html"><span
|
||||
class="cmr-12">tail</span></a><span
|
||||
class="cmr-12">] [</span><a
|
||||
href="userhtmlse6.html#userhtmlsu12.html" ><span
|
||||
href="userhtmlse5.html#userhtmlsu12.html" ><span
|
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class="cmr-12">up</span></a><span
|
||||
class="cmr-12">] </span></p></div>
|
||||
<h4 class="subsectionHead"><span class="titlemark"><span
|
||||
class="cmr-12">6.3 </span></span> <a
|
||||
id="x22-210006.3"></a><span
|
||||
class="cmr-12">Method hierarchy</span><span
|
||||
class="cmr-12">_build</span></h4>
|
||||
class="cmr-12">5.6 </span></span> <a
|
||||
id="x21-200005.6"></a><span
|
||||
class="cmr-12">Method apply</span></h4>
|
||||
<div class="center"
|
||||
>
|
||||
<!--l. 574--><p class="noindent" >
|
||||
<!--l. 575--><p class="noindent" ><span class="obeylines-h"><span class="verb"><span
|
||||
<!--l. 695--><p class="noindent" >
|
||||
<!--l. 696--><p class="noindent" ><span class="obeylines-h"><span class="verb"><span
|
||||
class="cmtt-12">call</span><span
|
||||
class="cmtt-12"> p%hierarchy_build(a,desc_a,info)</span></span></span><br />
|
||||
class="cmtt-12"> p%apply(x,y,desc_a,info</span><span
|
||||
class="cmtt-12"> [,trans,work])</span></span></span><br />
|
||||
</div>
|
||||
<!--l. 578--><p class="noindent" ><span
|
||||
class="cmr-12">This method builds the hierarchy of matrices and restriction/prolongation operators for</span>
|
||||
<!--l. 699--><p class="noindent" ><span
|
||||
class="cmr-12">This method computes </span><span
|
||||
class="cmmi-12">y </span><span
|
||||
class="cmr-12">= </span><span
|
||||
class="cmmi-12">op</span><span
|
||||
class="cmr-12">(</span><span
|
||||
class="cmmi-12">B</span><sup><span
|
||||
class="cmsy-8">-</span><span
|
||||
class="cmr-8">1</span></sup><span
|
||||
class="cmr-12">) </span><span
|
||||
class="cmmi-12">x</span><span
|
||||
class="cmr-12">, where </span><span
|
||||
class="cmmi-12">B </span><span
|
||||
class="cmr-12">is a previously built preconditioner,</span>
|
||||
<span
|
||||
class="cmr-12">the multilevel preconditioner </span><span class="obeylines-h"><span class="verb"><span
|
||||
class="cmr-12">stored into </span><span class="obeylines-h"><span class="verb"><span
|
||||
class="cmtt-12">p</span></span></span><span
|
||||
class="cmr-12">, according to the requirements made by the user</span>
|
||||
class="cmr-12">, and </span><span
|
||||
class="cmmi-12">op </span><span
|
||||
class="cmr-12">denotes the preconditioner itself or its transpose, according to the</span>
|
||||
<span
|
||||
class="cmr-12">through the methods </span><span class="obeylines-h"><span class="verb"><span
|
||||
class="cmtt-12">init</span></span></span> <span
|
||||
class="cmr-12">and </span><span class="obeylines-h"><span class="verb"><span
|
||||
class="cmtt-12">set</span></span></span><span
|
||||
class="cmr-12">.</span>
|
||||
<!--l. 583--><p class="noindent" ><span
|
||||
class="cmr-12">value of </span><span class="obeylines-h"><span class="verb"><span
|
||||
class="cmtt-12">trans</span></span></span><span
|
||||
class="cmr-12">. Note that, when AMG4PSBLAS is used with a Krylov solver from</span>
|
||||
<span
|
||||
class="cmr-12">PSBLAS, </span><span class="obeylines-h"><span class="verb"><span
|
||||
class="cmtt-12">p%apply</span></span></span> <span
|
||||
class="cmr-12">is called within the PSBLAS method </span><span class="obeylines-h"><span class="verb"><span
|
||||
class="cmtt-12">psb_krylov</span></span></span> <span
|
||||
class="cmr-12">and hence it is</span>
|
||||
<span
|
||||
class="cmr-12">completely transparent to the user.</span>
|
||||
<!--l. 708--><p class="noindent" ><span
|
||||
class="cmbx-12">Arguments</span>
|
||||
<div class="tabular"> <table id="TBL-11" class="tabular"
|
||||
<div class="tabular"> <table id="TBL-14" class="tabular"
|
||||
cellspacing="0" cellpadding="0"
|
||||
><colgroup id="TBL-11-1g"><col
|
||||
id="TBL-11-1"><col
|
||||
id="TBL-11-2"></colgroup><tr
|
||||
style="vertical-align:baseline;" id="TBL-11-1-"><td style="white-space:normal; text-align:left;" id="TBL-11-1-1"
|
||||
class="td11"><!--l. 586--><p class="noindent" ><span class="obeylines-h"><span class="verb"><span
|
||||
class="cmtt-12">a</span></span></span> </td><td style="white-space:normal; text-align:left;" id="TBL-11-1-2"
|
||||
class="td11"><!--l. 586--><p class="noindent" ><span class="obeylines-h"><span class="verb"><span
|
||||
class="cmtt-12">type(psb_</span></span></span><span
|
||||
class="cmti-12">x</span><span class="obeylines-h"><span class="verb"><span
|
||||
class="cmtt-12">spmat_type),</span><span
|
||||
><colgroup id="TBL-14-1g"><col
|
||||
id="TBL-14-1"><col
|
||||
id="TBL-14-2"></colgroup><tr
|
||||
style="vertical-align:baseline;" id="TBL-14-1-"><td style="white-space:normal; text-align:left;" id="TBL-14-1-1"
|
||||
class="td11"><!--l. 711--><p class="noindent" ><span class="obeylines-h"><span class="verb"><span
|
||||
class="cmtt-12">x</span></span></span> </td><td style="white-space:normal; text-align:left;" id="TBL-14-1-2"
|
||||
class="td11"><!--l. 711--><p class="noindent" ><span
|
||||
class="cmti-12">type</span><span class="obeylines-h"><span class="verb"><span
|
||||
class="cmtt-12">(</span></span></span><span
|
||||
class="cmti-12">kind</span><span
|
||||
class="cmti-12">_parameter</span><span class="obeylines-h"><span class="verb"><span
|
||||
class="cmtt-12">),</span><span
|
||||
class="cmtt-12"> dimension(:),</span><span
|
||||
class="cmtt-12"> intent(in)</span></span></span><span
|
||||
class="cmr-12">.</span> </td>
|
||||
class="cmr-12">.</span> </td>
|
||||
</tr><tr
|
||||
style="vertical-align:baseline;" id="TBL-11-2-"><td style="white-space:normal; text-align:left;" id="TBL-11-2-1"
|
||||
class="td11"><!--l. 587--><p class="noindent" > </td><td style="white-space:normal; text-align:left;" id="TBL-11-2-2"
|
||||
class="td11"><!--l. 587--><p class="noindent" ><span
|
||||
class="cmr-12">The sparse matrix structure containing the local part of the matrix</span>
|
||||
style="vertical-align:baseline;" id="TBL-14-2-"><td style="white-space:normal; text-align:left;" id="TBL-14-2-1"
|
||||
class="td11"><!--l. 712--><p class="noindent" > </td><td style="white-space:normal; text-align:left;" id="TBL-14-2-2"
|
||||
class="td11"><!--l. 712--><p class="noindent" ><span
|
||||
class="cmr-12">The local part of the vector </span><span
|
||||
class="cmmi-12">x</span><span
|
||||
class="cmr-12">. Note that </span><span
|
||||
class="cmti-12">type </span><span
|
||||
class="cmr-12">and </span><span
|
||||
class="cmti-12">kind</span><span
|
||||
class="cmti-12">_parameter</span>
|
||||
<span
|
||||
class="cmr-12">to be preconditioned. Note that </span><span
|
||||
class="cmti-12">x </span><span
|
||||
class="cmr-12">must be chosen according to the</span>
|
||||
class="cmr-12">must be chosen according to the real/complex, single/double</span>
|
||||
<span
|
||||
class="cmr-12">real/complex, single/double precision version of AMG4PSBLAS</span>
|
||||
<span
|
||||
class="cmr-12">under use. See the PSBLAS User’s Guide for details </span><span class="cite"><span
|
||||
class="cmr-12">[</span><a
|
||||
href="userhtmlli4.html#XPSBLASGUIDE"><span
|
||||
class="cmr-12">16</span></a><span
|
||||
class="cmr-12">]</span></span><span
|
||||
class="cmr-12">.</span> </td>
|
||||
class="cmr-12">precision version of AMG4PSBLAS under use.</span> </td>
|
||||
</tr><tr
|
||||
style="vertical-align:baseline;" id="TBL-11-3-"><td style="white-space:normal; text-align:left;" id="TBL-11-3-1"
|
||||
class="td11"><!--l. 592--><p class="noindent" ><span class="obeylines-h"><span class="verb"><span
|
||||
class="cmtt-12">desc_a</span></span></span></td><td style="white-space:normal; text-align:left;" id="TBL-11-3-2"
|
||||
class="td11"><!--l. 592--><p class="noindent" ><span class="obeylines-h"><span class="verb"><span
|
||||
style="vertical-align:baseline;" id="TBL-14-3-"><td style="white-space:normal; text-align:left;" id="TBL-14-3-1"
|
||||
class="td11"><!--l. 715--><p class="noindent" ><span class="obeylines-h"><span class="verb"><span
|
||||
class="cmtt-12">y</span></span></span> </td><td style="white-space:normal; text-align:left;" id="TBL-14-3-2"
|
||||
class="td11"><!--l. 715--><p class="noindent" ><span
|
||||
class="cmti-12">type</span><span class="obeylines-h"><span class="verb"><span
|
||||
class="cmtt-12">(</span></span></span><span
|
||||
class="cmti-12">kind</span><span
|
||||
class="cmti-12">_parameter</span><span class="obeylines-h"><span class="verb"><span
|
||||
class="cmtt-12">),</span><span
|
||||
class="cmtt-12"> dimension(:),</span><span
|
||||
class="cmtt-12"> intent(out)</span></span></span><span
|
||||
class="cmr-12">.</span> </td>
|
||||
</tr><tr
|
||||
style="vertical-align:baseline;" id="TBL-14-4-"><td style="white-space:normal; text-align:left;" id="TBL-14-4-1"
|
||||
class="td11"><!--l. 716--><p class="noindent" > </td><td style="white-space:normal; text-align:left;" id="TBL-14-4-2"
|
||||
class="td11"><!--l. 716--><p class="noindent" ><span
|
||||
class="cmr-12">The local part of the vector </span><span
|
||||
class="cmmi-12">y</span><span
|
||||
class="cmr-12">. Note that </span><span
|
||||
class="cmti-12">type </span><span
|
||||
class="cmr-12">and </span><span
|
||||
class="cmti-12">kind</span><span
|
||||
class="cmti-12">_parameter</span>
|
||||
<span
|
||||
class="cmr-12">must be chosen according to the real/complex, single/double</span>
|
||||
<span
|
||||
class="cmr-12">precision version of AMG4PSBLAS under use.</span> </td>
|
||||
</tr><tr
|
||||
style="vertical-align:baseline;" id="TBL-14-5-"><td style="white-space:normal; text-align:left;" id="TBL-14-5-1"
|
||||
class="td11"><!--l. 719--><p class="noindent" ><span class="obeylines-h"><span class="verb"><span
|
||||
class="cmtt-12">desc_a</span></span></span></td><td style="white-space:normal; text-align:left;" id="TBL-14-5-2"
|
||||
class="td11"><!--l. 719--><p class="noindent" ><span class="obeylines-h"><span class="verb"><span
|
||||
class="cmtt-12">type(psb_desc_type),</span><span
|
||||
class="cmtt-12"> intent(in)</span></span></span><span
|
||||
class="cmr-12">.</span> </td>
|
||||
</tr><tr
|
||||
style="vertical-align:baseline;" id="TBL-11-4-"><td style="white-space:normal; text-align:left;" id="TBL-11-4-1"
|
||||
class="td11"><!--l. 593--><p class="noindent" > </td><td style="white-space:normal; text-align:left;" id="TBL-11-4-2"
|
||||
class="td11"><!--l. 593--><p class="noindent" ><span
|
||||
class="cmr-12">The communication descriptor of </span><span class="obeylines-h"><span class="verb"><span
|
||||
class="cmtt-12">a</span></span></span><span
|
||||
class="cmr-12">. See the PSBLAS User’s Guide</span>
|
||||
style="vertical-align:baseline;" id="TBL-14-6-"><td style="white-space:normal; text-align:left;" id="TBL-14-6-1"
|
||||
class="td11"><!--l. 720--><p class="noindent" > </td><td style="white-space:normal; text-align:left;" id="TBL-14-6-2"
|
||||
class="td11"><!--l. 720--><p class="noindent" ><span
|
||||
class="cmr-12">The communication descriptor associated to the matrix to be</span>
|
||||
<span
|
||||
class="cmr-12">for details </span><span class="cite"><span
|
||||
class="cmr-12">[</span><a
|
||||
href="userhtmlli4.html#XPSBLASGUIDE"><span
|
||||
class="cmr-12">16</span></a><span
|
||||
class="cmr-12">]</span></span><span
|
||||
class="cmr-12">.</span> </td>
|
||||
class="cmr-12">preconditioned.</span> </td>
|
||||
</tr><tr
|
||||
style="vertical-align:baseline;" id="TBL-11-5-"><td style="white-space:normal; text-align:left;" id="TBL-11-5-1"
|
||||
class="td11"><!--l. 596--><p class="noindent" ><span class="obeylines-h"><span class="verb"><span
|
||||
class="cmtt-12">info</span></span></span> </td><td style="white-space:normal; text-align:left;" id="TBL-11-5-2"
|
||||
class="td11"><!--l. 596--><p class="noindent" ><span class="obeylines-h"><span class="verb"><span
|
||||
style="vertical-align:baseline;" id="TBL-14-7-"><td style="white-space:normal; text-align:left;" id="TBL-14-7-1"
|
||||
class="td11"><!--l. 722--><p class="noindent" ><span class="obeylines-h"><span class="verb"><span
|
||||
class="cmtt-12">info</span></span></span> </td><td style="white-space:normal; text-align:left;" id="TBL-14-7-2"
|
||||
class="td11"><!--l. 722--><p class="noindent" ><span class="obeylines-h"><span class="verb"><span
|
||||
class="cmtt-12">integer,</span><span
|
||||
class="cmtt-12"> intent(out)</span></span></span><span
|
||||
class="cmr-12">.</span> </td>
|
||||
</tr><tr
|
||||
style="vertical-align:baseline;" id="TBL-11-6-"><td style="white-space:normal; text-align:left;" id="TBL-11-6-1"
|
||||
class="td11"><!--l. 597--><p class="noindent" > </td><td style="white-space:normal; text-align:left;" id="TBL-11-6-2"
|
||||
class="td11"><!--l. 597--><p class="noindent" ><span
|
||||
style="vertical-align:baseline;" id="TBL-14-8-"><td style="white-space:normal; text-align:left;" id="TBL-14-8-1"
|
||||
class="td11"><!--l. 723--><p class="noindent" > </td><td style="white-space:normal; text-align:left;" id="TBL-14-8-2"
|
||||
class="td11"><!--l. 723--><p class="noindent" ><span
|
||||
class="cmr-12">Error code. If no error, 0 is returned. See Section</span><span
|
||||
class="cmr-12"> </span><a
|
||||
href="userhtmlse8.html#x30-340008"><span
|
||||
class="cmr-12">8</span><!--tex4ht:ref: sec:errors --></a> <span
|
||||
href="userhtmlse7.html#x26-300007"><span
|
||||
class="cmr-12">7</span><!--tex4ht:ref: sec:errors --></a> <span
|
||||
class="cmr-12">for details.</span> </td>
|
||||
</tr><tr
|
||||
style="vertical-align:baseline;" id="TBL-11-7-"><td style="white-space:normal; text-align:left;" id="TBL-11-7-1"
|
||||
style="vertical-align:baseline;" id="TBL-14-9-"><td style="white-space:normal; text-align:left;" id="TBL-14-9-1"
|
||||
class="td11"><!--l. 724--><p class="noindent" ><span class="obeylines-h"><span class="verb"><span
|
||||
class="cmtt-12">trans</span></span></span> </td><td style="white-space:normal; text-align:left;" id="TBL-14-9-2"
|
||||
class="td11"><!--l. 724--><p class="noindent" ><span class="obeylines-h"><span class="verb"><span
|
||||
class="cmtt-12">character(len=1),</span><span
|
||||
class="cmtt-12"> optional,</span><span
|
||||
class="cmtt-12"> intent(in).</span></span></span> </td>
|
||||
</tr><tr
|
||||
style="vertical-align:baseline;" id="TBL-14-10-"><td style="white-space:normal; text-align:left;" id="TBL-14-10-1"
|
||||
class="td11"><!--l. 725--><p class="noindent" > </td><td style="white-space:normal; text-align:left;" id="TBL-14-10-2"
|
||||
class="td11"><!--l. 725--><p class="noindent" ><span
|
||||
class="cmr-12">If </span><span class="obeylines-h"><span class="verb"><span
|
||||
class="cmtt-12">trans</span></span></span> <span
|
||||
class="cmr-12">= </span><span class="obeylines-h"><span class="verb"><span
|
||||
class="cmtt-12">’N’,’n’</span></span></span> <span
|
||||
class="cmr-12">then </span><span
|
||||
class="cmmi-12">op</span><span
|
||||
class="cmr-12">(</span><span
|
||||
class="cmmi-12">B</span><sup><span
|
||||
class="cmsy-8">-</span><span
|
||||
class="cmr-8">1</span></sup><span
|
||||
class="cmr-12">) = </span><span
|
||||
class="cmmi-12">B</span><sup><span
|
||||
class="cmsy-8">-</span><span
|
||||
class="cmr-8">1</span></sup><span
|
||||
class="cmr-12">; if </span><span class="obeylines-h"><span class="verb"><span
|
||||
class="cmtt-12">trans</span></span></span> <span
|
||||
class="cmr-12">= </span><span class="obeylines-h"><span class="verb"><span
|
||||
class="cmtt-12">’T’,’t’</span></span></span>
|
||||
<span
|
||||
class="cmr-12">then </span><span
|
||||
class="cmmi-12">op</span><span
|
||||
class="cmr-12">(</span><span
|
||||
class="cmmi-12">B</span><sup><span
|
||||
class="cmsy-8">-</span><span
|
||||
class="cmr-8">1</span></sup><span
|
||||
class="cmr-12">) = </span><span
|
||||
class="cmmi-12">B</span><sup><span
|
||||
class="cmsy-8">-</span><span
|
||||
class="cmmi-8">T</span> </sup> <span
|
||||
class="cmr-12">(transpose of </span><span
|
||||
class="cmmi-12">B</span><sup><span
|
||||
class="cmsy-8">-</span><span
|
||||
class="cmr-8">1</span></sup><span
|
||||
class="cmr-12">); if </span><span class="obeylines-h"><span class="verb"><span
|
||||
class="cmtt-12">trans</span></span></span> <span
|
||||
class="cmr-12">= </span><span class="obeylines-h"><span class="verb"><span
|
||||
class="cmtt-12">’C’,’c’</span></span></span> <span
|
||||
class="cmr-12">then</span>
|
||||
<span
|
||||
class="cmmi-12">op</span><span
|
||||
class="cmr-12">(</span><span
|
||||
class="cmmi-12">B</span><sup><span
|
||||
class="cmsy-8">-</span><span
|
||||
class="cmr-8">1</span></sup><span
|
||||
class="cmr-12">) = </span><span
|
||||
class="cmmi-12">B</span><sup><span
|
||||
class="cmsy-8">-</span><span
|
||||
class="cmmi-8">C</span></sup> <span
|
||||
class="cmr-12">(conjugate transpose of </span><span
|
||||
class="cmmi-12">B</span><sup><span
|
||||
class="cmsy-8">-</span><span
|
||||
class="cmr-8">1</span></sup><span
|
||||
class="cmr-12">).</span> </td>
|
||||
</tr><tr
|
||||
style="vertical-align:baseline;" id="TBL-14-11-"><td style="white-space:normal; text-align:left;" id="TBL-14-11-1"
|
||||
class="td11"><!--l. 729--><p class="noindent" ><span class="obeylines-h"><span class="verb"><span
|
||||
class="cmtt-12">work</span></span></span> </td><td style="white-space:normal; text-align:left;" id="TBL-14-11-2"
|
||||
class="td11"><!--l. 729--><p class="noindent" ><span
|
||||
class="cmti-12">type</span><span class="obeylines-h"><span class="verb"><span
|
||||
class="cmtt-12">(</span></span></span><span
|
||||
class="cmti-12">kind</span><span
|
||||
class="cmti-12">_parameter</span><span class="obeylines-h"><span class="verb"><span
|
||||
class="cmtt-12">),</span><span
|
||||
class="cmtt-12"> dimension(:),</span><span
|
||||
class="cmtt-12"> optional,</span><span
|
||||
class="cmtt-12"> target</span></span></span><span
|
||||
class="cmr-12">.</span> </td>
|
||||
</tr><tr
|
||||
style="vertical-align:baseline;" id="TBL-14-12-"><td style="white-space:normal; text-align:left;" id="TBL-14-12-1"
|
||||
class="td11"><!--l. 730--><p class="noindent" > </td><td style="white-space:normal; text-align:left;" id="TBL-14-12-2"
|
||||
class="td11"><!--l. 730--><p class="noindent" ><span
|
||||
class="cmr-12">Workspace. Its size should be at least </span><span class="obeylines-h"><span class="verb"><span
|
||||
class="cmtt-12">4</span><span
|
||||
class="cmtt-12"> *</span><span
|
||||
class="cmtt-12"> psb_cd_get_local_</span></span></span>
|
||||
<span class="obeylines-h"><span class="verb"><span
|
||||
class="cmtt-12">cols(desc_a)</span></span></span> <span
|
||||
class="cmr-12">(see the PSBLAS User’s Guide). Note that </span><span
|
||||
class="cmti-12">type</span>
|
||||
<span
|
||||
class="cmr-12">and </span><span
|
||||
class="cmti-12">kind</span><span
|
||||
class="cmti-12">_parameter </span><span
|
||||
class="cmr-12">must be chosen according to the real/complex,</span>
|
||||
<span
|
||||
class="cmr-12">single/double precision version of AMG4PSBLAS under use.</span> </td>
|
||||
</tr><tr
|
||||
style="vertical-align:baseline;" id="TBL-14-13-"><td style="white-space:normal; text-align:left;" id="TBL-14-13-1"
|
||||
class="td11"> </td> </tr></table></div>
|
||||
|
||||
|
||||
@@ -133,7 +272,7 @@ class="td11"> </td> </tr></table></div>
|
||||
|
||||
|
||||
|
||||
<!--l. 603--><div class="crosslinks"><p class="noindent"><span
|
||||
<!--l. 739--><div class="crosslinks"><p class="noindent"><span
|
||||
class="cmr-12">[</span><a
|
||||
href="userhtmlsu13.html" ><span
|
||||
class="cmr-12">next</span></a><span
|
||||
@@ -147,9 +286,9 @@ class="cmr-12">] [</span><a
|
||||
href="userhtmlsu12.html" ><span
|
||||
class="cmr-12">front</span></a><span
|
||||
class="cmr-12">] [</span><a
|
||||
href="userhtmlse6.html#userhtmlsu12.html" ><span
|
||||
href="userhtmlse5.html#userhtmlsu12.html" ><span
|
||||
class="cmr-12">up</span></a><span
|
||||
class="cmr-12">] </span></p></div>
|
||||
<!--l. 603--><p class="indent" > <a
|
||||
<!--l. 739--><p class="indent" > <a
|
||||
id="tailuserhtmlsu12.html"></a>
|
||||
</body></html>
|
||||
|
||||
+33
-155
@@ -1,7 +1,7 @@
|
||||
<!DOCTYPE html PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN"
|
||||
"http://www.w3.org/TR/html4/loose.dtd">
|
||||
<html >
|
||||
<head><title>Method smoothers_build</title>
|
||||
<head><title>Method free</title>
|
||||
<meta http-equiv="Content-Type" content="text/html; charset=iso-8859-1">
|
||||
<meta name="generator" content="TeX4ht (https://tug.org/tex4ht/)">
|
||||
<meta name="originator" content="TeX4ht (https://tug.org/tex4ht/)">
|
||||
@@ -10,7 +10,7 @@
|
||||
<link rel="stylesheet" type="text/css" href="userhtml.css">
|
||||
</head><body
|
||||
>
|
||||
<!--l. 603--><div class="crosslinks"><p class="noindent"><span
|
||||
<!--l. 739--><div class="crosslinks"><p class="noindent"><span
|
||||
class="cmr-12">[</span><a
|
||||
href="userhtmlsu14.html" ><span
|
||||
class="cmr-12">next</span></a><span
|
||||
@@ -24,173 +24,51 @@ class="cmr-12">] [</span><a
|
||||
href="#tailuserhtmlsu13.html"><span
|
||||
class="cmr-12">tail</span></a><span
|
||||
class="cmr-12">] [</span><a
|
||||
href="userhtmlse6.html#userhtmlsu13.html" ><span
|
||||
href="userhtmlse5.html#userhtmlsu13.html" ><span
|
||||
class="cmr-12">up</span></a><span
|
||||
class="cmr-12">] </span></p></div>
|
||||
<h4 class="subsectionHead"><span class="titlemark"><span
|
||||
class="cmr-12">6.4 </span></span> <a
|
||||
id="x23-220006.4"></a><span
|
||||
class="cmr-12">Method smoothers</span><span
|
||||
class="cmr-12">_build</span></h4>
|
||||
class="cmr-12">5.7 </span></span> <a
|
||||
id="x22-210005.7"></a><span
|
||||
class="cmr-12">Method free</span></h4>
|
||||
<div class="center"
|
||||
>
|
||||
<!--l. 606--><p class="noindent" >
|
||||
<!--l. 607--><p class="noindent" ><span class="obeylines-h"><span class="verb"><span
|
||||
<!--l. 741--><p class="noindent" >
|
||||
<!--l. 742--><p class="noindent" ><span class="obeylines-h"><span class="verb"><span
|
||||
class="cmtt-12">call</span><span
|
||||
class="cmtt-12"> p%smoothers_build(a,desc_a,p,info[,amold,vmold,imold])</span></span></span><br />
|
||||
class="cmtt-12"> p%free(p,info)</span></span></span><br />
|
||||
</div>
|
||||
<!--l. 610--><p class="noindent" ><span
|
||||
class="cmr-12">This method builds the smoothers and the coarsest-level solvers for the multilevel</span>
|
||||
<span
|
||||
class="cmr-12">preconditioner </span><span class="obeylines-h"><span class="verb"><span
|
||||
<!--l. 745--><p class="noindent" ><span
|
||||
class="cmr-12">This method deallocates the preconditioner data structure </span><span class="obeylines-h"><span class="verb"><span
|
||||
class="cmtt-12">p</span></span></span><span
|
||||
class="cmr-12">, according to the requirements made by the user through the methods</span>
|
||||
<span class="obeylines-h"><span class="verb"><span
|
||||
class="cmtt-12">init</span></span></span> <span
|
||||
class="cmr-12">and </span><span class="obeylines-h"><span class="verb"><span
|
||||
class="cmtt-12">set</span></span></span><span
|
||||
class="cmr-12">, and based on the aggregation hierarchy produced by a previous call to</span>
|
||||
<span class="obeylines-h"><span class="verb"><span
|
||||
class="cmtt-12">hierarchy_build</span></span></span> <span
|
||||
class="cmr-12">(see Section</span><span
|
||||
class="cmr-12"> </span><a
|
||||
href="userhtmlsu12.html#x22-210006.3"><span
|
||||
class="cmr-12">6.3</span><!--tex4ht:ref: sec:hier_bld --></a><span
|
||||
class="cmr-12">).</span>
|
||||
<!--l. 617--><p class="noindent" ><span
|
||||
class="cmr-12">.</span>
|
||||
<!--l. 748--><p class="noindent" ><span
|
||||
class="cmbx-12">Arguments</span>
|
||||
<div class="tabular"> <table id="TBL-12" class="tabular"
|
||||
<div class="tabular"> <table id="TBL-15" class="tabular"
|
||||
cellspacing="0" cellpadding="0"
|
||||
><colgroup id="TBL-12-1g"><col
|
||||
id="TBL-12-1"><col
|
||||
id="TBL-12-2"></colgroup><tr
|
||||
style="vertical-align:baseline;" id="TBL-12-1-"><td style="white-space:normal; text-align:left;" id="TBL-12-1-1"
|
||||
class="td11"><!--l. 620--><p class="noindent" ><span class="obeylines-h"><span class="verb"><span
|
||||
class="cmtt-12">a</span></span></span> </td><td style="white-space:normal; text-align:left;" id="TBL-12-1-2"
|
||||
class="td11"><!--l. 620--><p class="noindent" ><span class="obeylines-h"><span class="verb"><span
|
||||
class="cmtt-12">type(psb_</span></span></span><span
|
||||
class="cmti-12">x</span><span class="obeylines-h"><span class="verb"><span
|
||||
class="cmtt-12">spmat_type),</span><span
|
||||
class="cmtt-12"> intent(in)</span></span></span><span
|
||||
class="cmr-12">.</span> </td>
|
||||
</tr><tr
|
||||
style="vertical-align:baseline;" id="TBL-12-2-"><td style="white-space:normal; text-align:left;" id="TBL-12-2-1"
|
||||
class="td11"><!--l. 621--><p class="noindent" > </td><td style="white-space:normal; text-align:left;" id="TBL-12-2-2"
|
||||
class="td11"><!--l. 621--><p class="noindent" ><span
|
||||
class="cmr-12">The sparse matrix structure containing the local part of the matrix</span>
|
||||
<span
|
||||
class="cmr-12">to be preconditioned. Note that </span><span
|
||||
class="cmti-12">x </span><span
|
||||
class="cmr-12">must be chosen according to the</span>
|
||||
<span
|
||||
class="cmr-12">real/complex, single/double precision version of AMG4PSBLAS</span>
|
||||
<span
|
||||
class="cmr-12">under use. See the PSBLAS User’s Guide for details </span><span class="cite"><span
|
||||
class="cmr-12">[</span><a
|
||||
href="userhtmlli4.html#XPSBLASGUIDE"><span
|
||||
class="cmr-12">16</span></a><span
|
||||
class="cmr-12">]</span></span><span
|
||||
class="cmr-12">.</span> </td>
|
||||
</tr><tr
|
||||
style="vertical-align:baseline;" id="TBL-12-3-"><td style="white-space:normal; text-align:left;" id="TBL-12-3-1"
|
||||
class="td11"><!--l. 625--><p class="noindent" ><span class="obeylines-h"><span class="verb"><span
|
||||
class="cmtt-12">desc_a</span></span></span></td><td style="white-space:normal; text-align:left;" id="TBL-12-3-2"
|
||||
class="td11"><!--l. 625--><p class="noindent" ><span class="obeylines-h"><span class="verb"><span
|
||||
class="cmtt-12">type(psb_desc_type),</span><span
|
||||
class="cmtt-12"> intent(in)</span></span></span><span
|
||||
class="cmr-12">.</span> </td>
|
||||
</tr><tr
|
||||
style="vertical-align:baseline;" id="TBL-12-4-"><td style="white-space:normal; text-align:left;" id="TBL-12-4-1"
|
||||
class="td11"><!--l. 626--><p class="noindent" > </td><td style="white-space:normal; text-align:left;" id="TBL-12-4-2"
|
||||
class="td11"><!--l. 626--><p class="noindent" ><span
|
||||
class="cmr-12">The communication descriptor of </span><span class="obeylines-h"><span class="verb"><span
|
||||
class="cmtt-12">a</span></span></span><span
|
||||
class="cmr-12">. See the PSBLAS User’s Guide</span>
|
||||
<span
|
||||
class="cmr-12">for details </span><span class="cite"><span
|
||||
class="cmr-12">[</span><a
|
||||
href="userhtmlli4.html#XPSBLASGUIDE"><span
|
||||
class="cmr-12">16</span></a><span
|
||||
class="cmr-12">]</span></span><span
|
||||
class="cmr-12">.</span> </td>
|
||||
</tr><tr
|
||||
style="vertical-align:baseline;" id="TBL-12-5-"><td style="white-space:normal; text-align:left;" id="TBL-12-5-1"
|
||||
class="td11"><!--l. 628--><p class="noindent" ><span class="obeylines-h"><span class="verb"><span
|
||||
class="cmtt-12">info</span></span></span> </td><td style="white-space:normal; text-align:left;" id="TBL-12-5-2"
|
||||
class="td11"><!--l. 628--><p class="noindent" ><span class="obeylines-h"><span class="verb"><span
|
||||
><colgroup id="TBL-15-1g"><col
|
||||
id="TBL-15-1"><col
|
||||
id="TBL-15-2"></colgroup><tr
|
||||
style="vertical-align:baseline;" id="TBL-15-1-"><td style="white-space:normal; text-align:left;" id="TBL-15-1-1"
|
||||
class="td11"><!--l. 751--><p class="noindent" ><span class="obeylines-h"><span class="verb"><span
|
||||
class="cmtt-12">info</span></span></span> </td><td style="white-space:normal; text-align:left;" id="TBL-15-1-2"
|
||||
class="td11"><!--l. 751--><p class="noindent" ><span class="obeylines-h"><span class="verb"><span
|
||||
class="cmtt-12">integer,</span><span
|
||||
class="cmtt-12"> intent(out)</span></span></span><span
|
||||
class="cmr-12">.</span> </td>
|
||||
class="cmr-12">.</span> </td>
|
||||
</tr><tr
|
||||
style="vertical-align:baseline;" id="TBL-12-6-"><td style="white-space:normal; text-align:left;" id="TBL-12-6-1"
|
||||
class="td11"><!--l. 629--><p class="noindent" > </td><td style="white-space:normal; text-align:left;" id="TBL-12-6-2"
|
||||
class="td11"><!--l. 629--><p class="noindent" ><span
|
||||
style="vertical-align:baseline;" id="TBL-15-2-"><td style="white-space:normal; text-align:left;" id="TBL-15-2-1"
|
||||
class="td11"><!--l. 752--><p class="noindent" > </td><td style="white-space:normal; text-align:left;" id="TBL-15-2-2"
|
||||
class="td11"><!--l. 752--><p class="noindent" ><span
|
||||
class="cmr-12">Error code. If no error, 0 is returned. See Section</span><span
|
||||
class="cmr-12"> </span><a
|
||||
href="userhtmlse8.html#x30-340008"><span
|
||||
class="cmr-12">8</span><!--tex4ht:ref: sec:errors --></a> <span
|
||||
class="cmr-12">for details.</span> </td>
|
||||
</tr><tr
|
||||
style="vertical-align:baseline;" id="TBL-12-7-"><td style="white-space:normal; text-align:left;" id="TBL-12-7-1"
|
||||
class="td11"><!--l. 630--><p class="noindent" ><span class="obeylines-h"><span class="verb"><span
|
||||
class="cmtt-12">amold</span></span></span> </td><td style="white-space:normal; text-align:left;" id="TBL-12-7-2"
|
||||
class="td11"><!--l. 630--><p class="noindent" ><span class="obeylines-h"><span class="verb"><span
|
||||
class="cmtt-12">class(psb_</span></span></span><span
|
||||
class="cmti-12">x</span><span class="obeylines-h"><span class="verb"><span
|
||||
class="cmtt-12">_base_sparse_mat),</span><span
|
||||
class="cmtt-12"> intent(in),</span><span
|
||||
class="cmtt-12"> optional</span></span></span><span
|
||||
class="cmr-12">.</span> </td>
|
||||
</tr><tr
|
||||
style="vertical-align:baseline;" id="TBL-12-8-"><td style="white-space:normal; text-align:left;" id="TBL-12-8-1"
|
||||
class="td11"><!--l. 631--><p class="noindent" > </td><td style="white-space:normal; text-align:left;" id="TBL-12-8-2"
|
||||
class="td11"><!--l. 631--><p class="noindent" ><span
|
||||
class="cmr-12">The desired dynamic type for internal matrix components; this</span>
|
||||
href="userhtmlse7.html#x26-300007"><span
|
||||
class="cmr-12">7</span><!--tex4ht:ref: sec:errors --></a> <span
|
||||
class="cmr-12">for</span>
|
||||
<span
|
||||
class="cmr-12">allows e.g. running on GPUs; it needs not be the same on all</span>
|
||||
<span
|
||||
class="cmr-12">processes. See the PSBLAS User’s Guide for details </span><span class="cite"><span
|
||||
class="cmr-12">[</span><a
|
||||
href="userhtmlli4.html#XPSBLASGUIDE"><span
|
||||
class="cmr-12">16</span></a><span
|
||||
class="cmr-12">]</span></span><span
|
||||
class="cmr-12">.</span> </td>
|
||||
class="cmr-12">details.</span> </td>
|
||||
</tr><tr
|
||||
style="vertical-align:baseline;" id="TBL-12-9-"><td style="white-space:normal; text-align:left;" id="TBL-12-9-1"
|
||||
class="td11"><!--l. 635--><p class="noindent" ><span class="obeylines-h"><span class="verb"><span
|
||||
class="cmtt-12">vmold</span></span></span> </td><td style="white-space:normal; text-align:left;" id="TBL-12-9-2"
|
||||
class="td11"><!--l. 635--><p class="noindent" ><span class="obeylines-h"><span class="verb"><span
|
||||
class="cmtt-12">class(psb_</span></span></span><span
|
||||
class="cmti-12">x</span><span class="obeylines-h"><span class="verb"><span
|
||||
class="cmtt-12">_base_vect_type),</span><span
|
||||
class="cmtt-12"> intent(in),</span><span
|
||||
class="cmtt-12"> optional</span></span></span><span
|
||||
class="cmr-12">.</span> </td>
|
||||
</tr><tr
|
||||
style="vertical-align:baseline;" id="TBL-12-10-"><td style="white-space:normal; text-align:left;" id="TBL-12-10-1"
|
||||
class="td11"><!--l. 636--><p class="noindent" > </td><td style="white-space:normal; text-align:left;" id="TBL-12-10-2"
|
||||
class="td11"><!--l. 636--><p class="noindent" ><span
|
||||
class="cmr-12">The desired dynamic type for internal vector components; this</span>
|
||||
<span
|
||||
class="cmr-12">allows e.g. running on GPUs.</span> </td>
|
||||
</tr><tr
|
||||
style="vertical-align:baseline;" id="TBL-12-11-"><td style="white-space:normal; text-align:left;" id="TBL-12-11-1"
|
||||
class="td11"><!--l. 638--><p class="noindent" ><span class="obeylines-h"><span class="verb"><span
|
||||
class="cmtt-12">imold</span></span></span> </td><td style="white-space:normal; text-align:left;" id="TBL-12-11-2"
|
||||
class="td11"><!--l. 638--><p class="noindent" ><span class="obeylines-h"><span class="verb"><span
|
||||
class="cmtt-12">class(psb_i_base_vect_type),</span><span
|
||||
class="cmtt-12"> intent(in),</span><span
|
||||
class="cmtt-12"> optional</span></span></span><span
|
||||
class="cmr-12">.</span> </td>
|
||||
</tr><tr
|
||||
style="vertical-align:baseline;" id="TBL-12-12-"><td style="white-space:normal; text-align:left;" id="TBL-12-12-1"
|
||||
class="td11"><!--l. 639--><p class="noindent" > </td><td style="white-space:normal; text-align:left;" id="TBL-12-12-2"
|
||||
class="td11"><!--l. 639--><p class="noindent" ><span
|
||||
class="cmr-12">The desired dynamic type for internal integer vector components;</span>
|
||||
<span
|
||||
class="cmr-12">this allows e.g. running on GPUs.</span> </td>
|
||||
</tr><tr
|
||||
style="vertical-align:baseline;" id="TBL-12-13-"><td style="white-space:normal; text-align:left;" id="TBL-12-13-1"
|
||||
style="vertical-align:baseline;" id="TBL-15-3-"><td style="white-space:normal; text-align:left;" id="TBL-15-3-1"
|
||||
class="td11"> </td> </tr></table></div>
|
||||
|
||||
|
||||
@@ -198,7 +76,7 @@ class="td11"> </td> </tr></table></div>
|
||||
|
||||
|
||||
|
||||
<!--l. 645--><div class="crosslinks"><p class="noindent"><span
|
||||
<!--l. 758--><div class="crosslinks"><p class="noindent"><span
|
||||
class="cmr-12">[</span><a
|
||||
href="userhtmlsu14.html" ><span
|
||||
class="cmr-12">next</span></a><span
|
||||
@@ -212,9 +90,9 @@ class="cmr-12">] [</span><a
|
||||
href="userhtmlsu13.html" ><span
|
||||
class="cmr-12">front</span></a><span
|
||||
class="cmr-12">] [</span><a
|
||||
href="userhtmlse6.html#userhtmlsu13.html" ><span
|
||||
href="userhtmlse5.html#userhtmlsu13.html" ><span
|
||||
class="cmr-12">up</span></a><span
|
||||
class="cmr-12">] </span></p></div>
|
||||
<!--l. 645--><p class="indent" > <a
|
||||
<!--l. 758--><p class="indent" > <a
|
||||
id="tailuserhtmlsu13.html"></a>
|
||||
</body></html>
|
||||
|
||||
+48
-160
@@ -1,7 +1,7 @@
|
||||
<!DOCTYPE html PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN"
|
||||
"http://www.w3.org/TR/html4/loose.dtd">
|
||||
<html >
|
||||
<head><title>Method build</title>
|
||||
<head><title>Method descr</title>
|
||||
<meta http-equiv="Content-Type" content="text/html; charset=iso-8859-1">
|
||||
<meta name="generator" content="TeX4ht (https://tug.org/tex4ht/)">
|
||||
<meta name="originator" content="TeX4ht (https://tug.org/tex4ht/)">
|
||||
@@ -10,7 +10,7 @@
|
||||
<link rel="stylesheet" type="text/css" href="userhtml.css">
|
||||
</head><body
|
||||
>
|
||||
<!--l. 645--><div class="crosslinks"><p class="noindent"><span
|
||||
<!--l. 758--><div class="crosslinks"><p class="noindent"><span
|
||||
class="cmr-12">[</span><a
|
||||
href="userhtmlsu15.html" ><span
|
||||
class="cmr-12">next</span></a><span
|
||||
@@ -24,193 +24,81 @@ class="cmr-12">] [</span><a
|
||||
href="#tailuserhtmlsu14.html"><span
|
||||
class="cmr-12">tail</span></a><span
|
||||
class="cmr-12">] [</span><a
|
||||
href="userhtmlse6.html#userhtmlsu14.html" ><span
|
||||
href="userhtmlse5.html#userhtmlsu14.html" ><span
|
||||
class="cmr-12">up</span></a><span
|
||||
class="cmr-12">] </span></p></div>
|
||||
<h4 class="subsectionHead"><span class="titlemark"><span
|
||||
class="cmr-12">6.5 </span></span> <a
|
||||
id="x24-230006.5"></a><span
|
||||
class="cmr-12">Method build</span></h4>
|
||||
class="cmr-12">5.8 </span></span> <a
|
||||
id="x23-220005.8"></a><span
|
||||
class="cmr-12">Method descr</span></h4>
|
||||
<div class="center"
|
||||
>
|
||||
<!--l. 647--><p class="noindent" >
|
||||
<!--l. 648--><p class="noindent" ><span class="obeylines-h"><span class="verb"><span
|
||||
<!--l. 760--><p class="noindent" >
|
||||
<!--l. 761--><p class="noindent" ><span class="obeylines-h"><span class="verb"><span
|
||||
class="cmtt-12">call</span><span
|
||||
class="cmtt-12"> p%build(a,desc_a,info[,amold,vmold,imold])</span></span></span><br />
|
||||
class="cmtt-12"> p%descr(info,</span><span
|
||||
class="cmtt-12"> [iout])</span></span></span><br />
|
||||
</div>
|
||||
<!--l. 651--><p class="noindent" ><span
|
||||
class="cmr-12">This method builds the preconditioner </span><span class="obeylines-h"><span class="verb"><span
|
||||
<!--l. 764--><p class="noindent" ><span
|
||||
class="cmr-12">This method prints a description of the preconditioner </span><span class="obeylines-h"><span class="verb"><span
|
||||
class="cmtt-12">p</span></span></span> <span
|
||||
class="cmr-12">according to the requirements made by the</span>
|
||||
class="cmr-12">to the standard output or to a</span>
|
||||
<span
|
||||
class="cmr-12">user through the methods </span><span class="obeylines-h"><span class="verb"><span
|
||||
class="cmtt-12">init</span></span></span> <span
|
||||
class="cmr-12">file. It must be called after </span><span class="obeylines-h"><span class="verb"><span
|
||||
class="cmtt-12">hierachy_build</span></span></span> <span
|
||||
class="cmr-12">and </span><span class="obeylines-h"><span class="verb"><span
|
||||
class="cmtt-12">set</span></span></span> <span
|
||||
class="cmr-12">(see Sections</span><span
|
||||
class="cmr-12"> </span><a
|
||||
href="userhtmlsu12.html#x22-210006.3"><span
|
||||
class="cmr-12">6.3</span><!--tex4ht:ref: sec:hier_bld --></a> <span
|
||||
class="cmr-12">and</span><span
|
||||
class="cmr-12"> </span><a
|
||||
href="userhtmlsu13.html#x23-220006.4"><span
|
||||
class="cmr-12">6.4</span><!--tex4ht:ref: sec:smooth_bld --></a> <span
|
||||
class="cmr-12">for multilevel</span>
|
||||
<span
|
||||
class="cmr-12">preconditioners). It is mostly provided for backward compatibility; indeed, it is</span>
|
||||
<span
|
||||
class="cmr-12">internally implemented by invoking the two previous methods </span><span class="obeylines-h"><span class="verb"><span
|
||||
class="cmtt-12">hierarchy_build</span></span></span> <span
|
||||
class="cmr-12">and</span>
|
||||
<span class="obeylines-h"><span class="verb"><span
|
||||
class="cmtt-12">smoothers_build</span></span></span><span
|
||||
class="cmr-12">, whose nomenclature would however be somewhat unnatural when</span>
|
||||
class="cmr-12">, or </span><span class="obeylines-h"><span class="verb"><span
|
||||
class="cmtt-12">build</span></span></span><span
|
||||
class="cmr-12">, have</span>
|
||||
<span
|
||||
class="cmr-12">dealing with simple one-level preconditioners.</span>
|
||||
<!--l. 661--><p class="noindent" ><span
|
||||
class="cmr-12">been called.</span>
|
||||
<!--l. 769--><p class="noindent" ><span
|
||||
class="cmbx-12">Arguments</span>
|
||||
<div class="tabular"> <table id="TBL-13" class="tabular"
|
||||
<div class="tabular"> <table id="TBL-16" class="tabular"
|
||||
cellspacing="0" cellpadding="0"
|
||||
><colgroup id="TBL-13-1g"><col
|
||||
id="TBL-13-1"><col
|
||||
id="TBL-13-2"></colgroup><tr
|
||||
style="vertical-align:baseline;" id="TBL-13-1-"><td style="white-space:normal; text-align:left;" id="TBL-13-1-1"
|
||||
class="td11"><!--l. 664--><p class="noindent" ><span class="obeylines-h"><span class="verb"><span
|
||||
class="cmtt-12">a</span></span></span> </td><td style="white-space:normal; text-align:left;" id="TBL-13-1-2"
|
||||
class="td11"><!--l. 664--><p class="noindent" ><span class="obeylines-h"><span class="verb"><span
|
||||
class="cmtt-12">type(psb_</span></span></span><span
|
||||
class="cmti-12">x</span><span class="obeylines-h"><span class="verb"><span
|
||||
class="cmtt-12">spmat_type),</span><span
|
||||
class="cmtt-12"> intent(in)</span></span></span><span
|
||||
class="cmr-12">.</span> </td>
|
||||
</tr><tr
|
||||
style="vertical-align:baseline;" id="TBL-13-2-"><td style="white-space:normal; text-align:left;" id="TBL-13-2-1"
|
||||
class="td11"><!--l. 665--><p class="noindent" > </td><td style="white-space:normal; text-align:left;" id="TBL-13-2-2"
|
||||
class="td11"><!--l. 665--><p class="noindent" ><span
|
||||
class="cmr-12">The sparse matrix structure containing the local part of the matrix</span>
|
||||
<span
|
||||
class="cmr-12">to be preconditioned. Note that </span><span
|
||||
class="cmti-12">x </span><span
|
||||
class="cmr-12">must be chosen according to the</span>
|
||||
<span
|
||||
class="cmr-12">real/complex, single/double precision version of AMG4PSBLAS</span>
|
||||
<span
|
||||
class="cmr-12">under use. See the PSBLAS User’s Guide for details </span><span class="cite"><span
|
||||
class="cmr-12">[</span><a
|
||||
href="userhtmlli4.html#XPSBLASGUIDE"><span
|
||||
class="cmr-12">16</span></a><span
|
||||
class="cmr-12">]</span></span><span
|
||||
class="cmr-12">.</span> </td>
|
||||
</tr><tr
|
||||
style="vertical-align:baseline;" id="TBL-13-3-"><td style="white-space:normal; text-align:left;" id="TBL-13-3-1"
|
||||
class="td11"><!--l. 669--><p class="noindent" ><span class="obeylines-h"><span class="verb"><span
|
||||
class="cmtt-12">desc_a</span></span></span></td><td style="white-space:normal; text-align:left;" id="TBL-13-3-2"
|
||||
class="td11"><!--l. 669--><p class="noindent" ><span class="obeylines-h"><span class="verb"><span
|
||||
class="cmtt-12">type(psb_desc_type),</span><span
|
||||
class="cmtt-12"> intent(in)</span></span></span><span
|
||||
class="cmr-12">.</span> </td>
|
||||
</tr><tr
|
||||
style="vertical-align:baseline;" id="TBL-13-4-"><td style="white-space:normal; text-align:left;" id="TBL-13-4-1"
|
||||
class="td11"><!--l. 670--><p class="noindent" > </td><td style="white-space:normal; text-align:left;" id="TBL-13-4-2"
|
||||
class="td11"><!--l. 670--><p class="noindent" ><span
|
||||
class="cmr-12">The communication descriptor of </span><span class="obeylines-h"><span class="verb"><span
|
||||
class="cmtt-12">a</span></span></span><span
|
||||
class="cmr-12">. See the PSBLAS User’s Guide</span>
|
||||
<span
|
||||
class="cmr-12">for details </span><span class="cite"><span
|
||||
class="cmr-12">[</span><a
|
||||
href="userhtmlli4.html#XPSBLASGUIDE"><span
|
||||
class="cmr-12">16</span></a><span
|
||||
class="cmr-12">]</span></span><span
|
||||
class="cmr-12">.</span> </td>
|
||||
</tr><tr
|
||||
style="vertical-align:baseline;" id="TBL-13-5-"><td style="white-space:normal; text-align:left;" id="TBL-13-5-1"
|
||||
class="td11"><!--l. 672--><p class="noindent" ><span class="obeylines-h"><span class="verb"><span
|
||||
class="cmtt-12">info</span></span></span> </td><td style="white-space:normal; text-align:left;" id="TBL-13-5-2"
|
||||
class="td11"><!--l. 672--><p class="noindent" ><span class="obeylines-h"><span class="verb"><span
|
||||
><colgroup id="TBL-16-1g"><col
|
||||
id="TBL-16-1"><col
|
||||
id="TBL-16-2"></colgroup><tr
|
||||
style="vertical-align:baseline;" id="TBL-16-1-"><td style="white-space:normal; text-align:left;" id="TBL-16-1-1"
|
||||
class="td11"><!--l. 772--><p class="noindent" ><span class="obeylines-h"><span class="verb"><span
|
||||
class="cmtt-12">info</span></span></span> </td><td style="white-space:normal; text-align:left;" id="TBL-16-1-2"
|
||||
class="td11"><!--l. 772--><p class="noindent" ><span class="obeylines-h"><span class="verb"><span
|
||||
class="cmtt-12">integer,</span><span
|
||||
class="cmtt-12"> intent(out)</span></span></span><span
|
||||
class="cmr-12">.</span> </td>
|
||||
</tr><tr
|
||||
style="vertical-align:baseline;" id="TBL-13-6-"><td style="white-space:normal; text-align:left;" id="TBL-13-6-1"
|
||||
class="td11"><!--l. 673--><p class="noindent" > </td><td style="white-space:normal; text-align:left;" id="TBL-13-6-2"
|
||||
class="td11"><!--l. 673--><p class="noindent" ><span
|
||||
style="vertical-align:baseline;" id="TBL-16-2-"><td style="white-space:normal; text-align:left;" id="TBL-16-2-1"
|
||||
class="td11"><!--l. 773--><p class="noindent" > </td><td style="white-space:normal; text-align:left;" id="TBL-16-2-2"
|
||||
class="td11"><!--l. 773--><p class="noindent" ><span
|
||||
class="cmr-12">Error code. If no error, 0 is returned. See Section</span><span
|
||||
class="cmr-12"> </span><a
|
||||
href="userhtmlse8.html#x30-340008"><span
|
||||
class="cmr-12">8</span><!--tex4ht:ref: sec:errors --></a> <span
|
||||
href="userhtmlse7.html#x26-300007"><span
|
||||
class="cmr-12">7</span><!--tex4ht:ref: sec:errors --></a> <span
|
||||
class="cmr-12">for details.</span> </td>
|
||||
</tr><tr
|
||||
style="vertical-align:baseline;" id="TBL-13-7-"><td style="white-space:normal; text-align:left;" id="TBL-13-7-1"
|
||||
class="td11"><!--l. 674--><p class="noindent" ><span class="obeylines-h"><span class="verb"><span
|
||||
class="cmtt-12">amold</span></span></span> </td><td style="white-space:normal; text-align:left;" id="TBL-13-7-2"
|
||||
class="td11"><!--l. 674--><p class="noindent" ><span class="obeylines-h"><span class="verb"><span
|
||||
class="cmtt-12">class(psb_</span></span></span><span
|
||||
class="cmti-12">x</span><span class="obeylines-h"><span class="verb"><span
|
||||
class="cmtt-12">_base_sparse_mat),</span><span
|
||||
style="vertical-align:baseline;" id="TBL-16-3-"><td style="white-space:normal; text-align:left;" id="TBL-16-3-1"
|
||||
class="td11"><!--l. 774--><p class="noindent" ><span class="obeylines-h"><span class="verb"><span
|
||||
class="cmtt-12">iout</span></span></span> </td><td style="white-space:normal; text-align:left;" id="TBL-16-3-2"
|
||||
class="td11"><!--l. 774--><p class="noindent" ><span class="obeylines-h"><span class="verb"><span
|
||||
class="cmtt-12">integer,</span><span
|
||||
class="cmtt-12"> intent(in),</span><span
|
||||
class="cmtt-12"> optional</span></span></span><span
|
||||
class="cmr-12">.</span> </td>
|
||||
class="cmr-12">.</span> </td>
|
||||
</tr><tr
|
||||
style="vertical-align:baseline;" id="TBL-13-8-"><td style="white-space:normal; text-align:left;" id="TBL-13-8-1"
|
||||
class="td11"><!--l. 675--><p class="noindent" > </td><td style="white-space:normal; text-align:left;" id="TBL-13-8-2"
|
||||
class="td11"><!--l. 675--><p class="noindent" ><span
|
||||
class="cmr-12">The desired dynamic type for internal matrix components; this</span>
|
||||
style="vertical-align:baseline;" id="TBL-16-4-"><td style="white-space:normal; text-align:left;" id="TBL-16-4-1"
|
||||
class="td11"><!--l. 775--><p class="noindent" > </td><td style="white-space:normal; text-align:left;" id="TBL-16-4-2"
|
||||
class="td11"><!--l. 775--><p class="noindent" ><span
|
||||
class="cmr-12">The id of the file where the preconditioner description will be</span>
|
||||
<span
|
||||
class="cmr-12">allows e.g. running on GPUs; it needs not be the same on all</span>
|
||||
<span
|
||||
class="cmr-12">processes. See the PSBLAS User’s Guide for details </span><span class="cite"><span
|
||||
class="cmr-12">[</span><a
|
||||
href="userhtmlli4.html#XPSBLASGUIDE"><span
|
||||
class="cmr-12">16</span></a><span
|
||||
class="cmr-12">]</span></span><span
|
||||
class="cmr-12">.</span> </td>
|
||||
class="cmr-12">printed; the default is the standard output.</span> </td>
|
||||
</tr><tr
|
||||
style="vertical-align:baseline;" id="TBL-13-9-"><td style="white-space:normal; text-align:left;" id="TBL-13-9-1"
|
||||
class="td11"><!--l. 679--><p class="noindent" ><span class="obeylines-h"><span class="verb"><span
|
||||
class="cmtt-12">vmold</span></span></span> </td><td style="white-space:normal; text-align:left;" id="TBL-13-9-2"
|
||||
class="td11"><!--l. 679--><p class="noindent" ><span class="obeylines-h"><span class="verb"><span
|
||||
class="cmtt-12">class(psb_</span></span></span><span
|
||||
class="cmti-12">x</span><span class="obeylines-h"><span class="verb"><span
|
||||
class="cmtt-12">_base_vect_type),</span><span
|
||||
class="cmtt-12"> intent(in),</span><span
|
||||
class="cmtt-12"> optional</span></span></span><span
|
||||
class="cmr-12">.</span> </td>
|
||||
</tr><tr
|
||||
style="vertical-align:baseline;" id="TBL-13-10-"><td style="white-space:normal; text-align:left;" id="TBL-13-10-1"
|
||||
class="td11"><!--l. 680--><p class="noindent" > </td><td style="white-space:normal; text-align:left;" id="TBL-13-10-2"
|
||||
class="td11"><!--l. 680--><p class="noindent" ><span
|
||||
class="cmr-12">The desired dynamic type for internal vector components; this</span>
|
||||
<span
|
||||
class="cmr-12">allows e.g. running on GPUs.</span> </td>
|
||||
</tr><tr
|
||||
style="vertical-align:baseline;" id="TBL-13-11-"><td style="white-space:normal; text-align:left;" id="TBL-13-11-1"
|
||||
class="td11"><!--l. 682--><p class="noindent" ><span class="obeylines-h"><span class="verb"><span
|
||||
class="cmtt-12">imold</span></span></span> </td><td style="white-space:normal; text-align:left;" id="TBL-13-11-2"
|
||||
class="td11"><!--l. 682--><p class="noindent" ><span class="obeylines-h"><span class="verb"><span
|
||||
class="cmtt-12">class(psb_i_base_vect_type),</span><span
|
||||
class="cmtt-12"> intent(in),</span><span
|
||||
class="cmtt-12"> optional</span></span></span><span
|
||||
class="cmr-12">.</span> </td>
|
||||
</tr><tr
|
||||
style="vertical-align:baseline;" id="TBL-13-12-"><td style="white-space:normal; text-align:left;" id="TBL-13-12-1"
|
||||
class="td11"><!--l. 683--><p class="noindent" > </td><td style="white-space:normal; text-align:left;" id="TBL-13-12-2"
|
||||
class="td11"><!--l. 683--><p class="noindent" ><span
|
||||
class="cmr-12">The desired dynamic type for internal integer vector components;</span>
|
||||
<span
|
||||
class="cmr-12">this allows e.g. running on GPUs.</span> </td>
|
||||
</tr><tr
|
||||
style="vertical-align:baseline;" id="TBL-13-13-"><td style="white-space:normal; text-align:left;" id="TBL-13-13-1"
|
||||
style="vertical-align:baseline;" id="TBL-16-5-"><td style="white-space:normal; text-align:left;" id="TBL-16-5-1"
|
||||
class="td11"> </td> </tr></table></div>
|
||||
<!--l. 688--><p class="noindent" ><span
|
||||
class="cmr-12">The method can be used to build multilevel preconditioners too.</span>
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
<!--l. 693--><div class="crosslinks"><p class="noindent"><span
|
||||
<!--l. 780--><div class="crosslinks"><p class="noindent"><span
|
||||
class="cmr-12">[</span><a
|
||||
href="userhtmlsu15.html" ><span
|
||||
class="cmr-12">next</span></a><span
|
||||
@@ -224,9 +112,9 @@ class="cmr-12">] [</span><a
|
||||
href="userhtmlsu14.html" ><span
|
||||
class="cmr-12">front</span></a><span
|
||||
class="cmr-12">] [</span><a
|
||||
href="userhtmlse6.html#userhtmlsu14.html" ><span
|
||||
href="userhtmlse5.html#userhtmlsu14.html" ><span
|
||||
class="cmr-12">up</span></a><span
|
||||
class="cmr-12">] </span></p></div>
|
||||
<!--l. 693--><p class="indent" > <a
|
||||
<!--l. 780--><p class="indent" > <a
|
||||
id="tailuserhtmlsu14.html"></a>
|
||||
</body></html>
|
||||
|
||||
+273
-231
@@ -1,7 +1,7 @@
|
||||
<!DOCTYPE html PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN"
|
||||
"http://www.w3.org/TR/html4/loose.dtd">
|
||||
<html >
|
||||
<head><title>Method apply</title>
|
||||
<head><title>Auxiliary Methods</title>
|
||||
<meta http-equiv="Content-Type" content="text/html; charset=iso-8859-1">
|
||||
<meta name="generator" content="TeX4ht (https://tug.org/tex4ht/)">
|
||||
<meta name="originator" content="TeX4ht (https://tug.org/tex4ht/)">
|
||||
@@ -10,11 +10,8 @@
|
||||
<link rel="stylesheet" type="text/css" href="userhtml.css">
|
||||
</head><body
|
||||
>
|
||||
<!--l. 693--><div class="crosslinks"><p class="noindent"><span
|
||||
<!--l. 780--><div class="crosslinks"><p class="noindent"><span
|
||||
class="cmr-12">[</span><a
|
||||
href="userhtmlsu16.html" ><span
|
||||
class="cmr-12">next</span></a><span
|
||||
class="cmr-12">] [</span><a
|
||||
href="userhtmlsu14.html" ><span
|
||||
class="cmr-12">prev</span></a><span
|
||||
class="cmr-12">] [</span><a
|
||||
@@ -24,247 +21,292 @@ class="cmr-12">] [</span><a
|
||||
href="#tailuserhtmlsu15.html"><span
|
||||
class="cmr-12">tail</span></a><span
|
||||
class="cmr-12">] [</span><a
|
||||
href="userhtmlse6.html#userhtmlsu15.html" ><span
|
||||
href="userhtmlse5.html#userhtmlsu15.html" ><span
|
||||
class="cmr-12">up</span></a><span
|
||||
class="cmr-12">] </span></p></div>
|
||||
<h4 class="subsectionHead"><span class="titlemark"><span
|
||||
class="cmr-12">6.6 </span></span> <a
|
||||
id="x25-240006.6"></a><span
|
||||
class="cmr-12">Method apply</span></h4>
|
||||
class="cmr-12">5.9 </span></span> <a
|
||||
id="x24-230005.9"></a><span
|
||||
class="cmr-12">Auxiliary Methods</span></h4>
|
||||
<!--l. 781--><p class="noindent" ><span
|
||||
class="cmr-12">Various functionalities are implemented as additional methods of the preconditioner</span>
|
||||
<span
|
||||
class="cmr-12">object.</span>
|
||||
<!--l. 784--><p class="noindent" >
|
||||
<h5 class="subsubsectionHead"><span class="titlemark"><span
|
||||
class="cmr-12">5.9.1 </span></span> <a
|
||||
id="x24-240005.9.1"></a><span
|
||||
class="cmr-12">Method: dump</span></h5>
|
||||
<div class="center"
|
||||
>
|
||||
<!--l. 695--><p class="noindent" >
|
||||
<!--l. 696--><p class="noindent" ><span class="obeylines-h"><span class="verb"><span
|
||||
<!--l. 786--><p class="noindent" >
|
||||
<!--l. 787--><p class="noindent" ><span class="obeylines-h"><span class="verb"><span
|
||||
class="cmtt-12">call</span><span
|
||||
class="cmtt-12"> p%apply(x,y,desc_a,info</span><span
|
||||
class="cmtt-12"> [,trans,work])</span></span></span><br />
|
||||
class="cmtt-12"> p%dump(info[,istart,iend,prefix,head,ac,rp,smoother,solver,global_num])</span></span></span><br />
|
||||
</div>
|
||||
<!--l. 699--><p class="noindent" ><span
|
||||
class="cmr-12">This method computes </span><span
|
||||
class="cmmi-12">y </span><span
|
||||
class="cmr-12">= </span><span
|
||||
class="cmmi-12">op</span><span
|
||||
class="cmr-12">(</span><span
|
||||
class="cmmi-12">B</span><sup><span
|
||||
class="cmsy-8">-</span><span
|
||||
class="cmr-8">1</span></sup><span
|
||||
class="cmr-12">) </span><span
|
||||
class="cmmi-12">x</span><span
|
||||
class="cmr-12">, where </span><span
|
||||
class="cmmi-12">B </span><span
|
||||
class="cmr-12">is a previously built preconditioner,</span>
|
||||
<span
|
||||
class="cmr-12">stored into </span><span class="obeylines-h"><span class="verb"><span
|
||||
class="cmtt-12">p</span></span></span><span
|
||||
class="cmr-12">, and </span><span
|
||||
class="cmmi-12">op </span><span
|
||||
class="cmr-12">denotes the preconditioner itself or its transpose, according to the</span>
|
||||
<span
|
||||
class="cmr-12">value of </span><span class="obeylines-h"><span class="verb"><span
|
||||
class="cmtt-12">trans</span></span></span><span
|
||||
class="cmr-12">. Note that, when AMG4PSBLAS is used with a Krylov solver from</span>
|
||||
<span
|
||||
class="cmr-12">PSBLAS, </span><span class="obeylines-h"><span class="verb"><span
|
||||
class="cmtt-12">p%apply</span></span></span> <span
|
||||
class="cmr-12">is called within the PSBLAS method </span><span class="obeylines-h"><span class="verb"><span
|
||||
class="cmtt-12">psb_krylov</span></span></span> <span
|
||||
class="cmr-12">and hence it is</span>
|
||||
<span
|
||||
class="cmr-12">completely transparent to the user.</span>
|
||||
<!--l. 708--><p class="noindent" ><span
|
||||
<!--l. 790--><p class="noindent" ><span
|
||||
class="cmr-12">Dump on file.</span>
|
||||
<!--l. 793--><p class="noindent" ><span
|
||||
class="cmbx-12">Arguments</span>
|
||||
<div class="tabular"> <table id="TBL-14" class="tabular"
|
||||
<div class="tabular"> <table id="TBL-17" class="tabular"
|
||||
cellspacing="0" cellpadding="0"
|
||||
><colgroup id="TBL-14-1g"><col
|
||||
id="TBL-14-1"><col
|
||||
id="TBL-14-2"></colgroup><tr
|
||||
style="vertical-align:baseline;" id="TBL-14-1-"><td style="white-space:normal; text-align:left;" id="TBL-14-1-1"
|
||||
class="td11"><!--l. 711--><p class="noindent" ><span class="obeylines-h"><span class="verb"><span
|
||||
class="cmtt-12">x</span></span></span> </td><td style="white-space:normal; text-align:left;" id="TBL-14-1-2"
|
||||
class="td11"><!--l. 711--><p class="noindent" ><span
|
||||
class="cmti-12">type</span><span class="obeylines-h"><span class="verb"><span
|
||||
class="cmtt-12">(</span></span></span><span
|
||||
class="cmti-12">kind</span><span
|
||||
class="cmti-12">_parameter</span><span class="obeylines-h"><span class="verb"><span
|
||||
class="cmtt-12">),</span><span
|
||||
class="cmtt-12"> dimension(:),</span><span
|
||||
class="cmtt-12"> intent(in)</span></span></span><span
|
||||
class="cmr-12">.</span> </td>
|
||||
</tr><tr
|
||||
style="vertical-align:baseline;" id="TBL-14-2-"><td style="white-space:normal; text-align:left;" id="TBL-14-2-1"
|
||||
class="td11"><!--l. 712--><p class="noindent" > </td><td style="white-space:normal; text-align:left;" id="TBL-14-2-2"
|
||||
class="td11"><!--l. 712--><p class="noindent" ><span
|
||||
class="cmr-12">The local part of the vector </span><span
|
||||
class="cmmi-12">x</span><span
|
||||
class="cmr-12">. Note that </span><span
|
||||
class="cmti-12">type </span><span
|
||||
class="cmr-12">and </span><span
|
||||
class="cmti-12">kind</span><span
|
||||
class="cmti-12">_parameter</span>
|
||||
<span
|
||||
class="cmr-12">must be chosen according to the real/complex, single/double</span>
|
||||
<span
|
||||
class="cmr-12">precision version of AMG4PSBLAS under use.</span> </td>
|
||||
</tr><tr
|
||||
style="vertical-align:baseline;" id="TBL-14-3-"><td style="white-space:normal; text-align:left;" id="TBL-14-3-1"
|
||||
class="td11"><!--l. 715--><p class="noindent" ><span class="obeylines-h"><span class="verb"><span
|
||||
class="cmtt-12">y</span></span></span> </td><td style="white-space:normal; text-align:left;" id="TBL-14-3-2"
|
||||
class="td11"><!--l. 715--><p class="noindent" ><span
|
||||
class="cmti-12">type</span><span class="obeylines-h"><span class="verb"><span
|
||||
class="cmtt-12">(</span></span></span><span
|
||||
class="cmti-12">kind</span><span
|
||||
class="cmti-12">_parameter</span><span class="obeylines-h"><span class="verb"><span
|
||||
class="cmtt-12">),</span><span
|
||||
class="cmtt-12"> dimension(:),</span><span
|
||||
class="cmtt-12"> intent(out)</span></span></span><span
|
||||
class="cmr-12">.</span> </td>
|
||||
</tr><tr
|
||||
style="vertical-align:baseline;" id="TBL-14-4-"><td style="white-space:normal; text-align:left;" id="TBL-14-4-1"
|
||||
class="td11"><!--l. 716--><p class="noindent" > </td><td style="white-space:normal; text-align:left;" id="TBL-14-4-2"
|
||||
class="td11"><!--l. 716--><p class="noindent" ><span
|
||||
class="cmr-12">The local part of the vector </span><span
|
||||
class="cmmi-12">y</span><span
|
||||
class="cmr-12">. Note that </span><span
|
||||
class="cmti-12">type </span><span
|
||||
class="cmr-12">and </span><span
|
||||
class="cmti-12">kind</span><span
|
||||
class="cmti-12">_parameter</span>
|
||||
<span
|
||||
class="cmr-12">must be chosen according to the real/complex, single/double</span>
|
||||
<span
|
||||
class="cmr-12">precision version of AMG4PSBLAS under use.</span> </td>
|
||||
</tr><tr
|
||||
style="vertical-align:baseline;" id="TBL-14-5-"><td style="white-space:normal; text-align:left;" id="TBL-14-5-1"
|
||||
class="td11"><!--l. 719--><p class="noindent" ><span class="obeylines-h"><span class="verb"><span
|
||||
class="cmtt-12">desc_a</span></span></span></td><td style="white-space:normal; text-align:left;" id="TBL-14-5-2"
|
||||
class="td11"><!--l. 719--><p class="noindent" ><span class="obeylines-h"><span class="verb"><span
|
||||
class="cmtt-12">type(psb_desc_type),</span><span
|
||||
class="cmtt-12"> intent(in)</span></span></span><span
|
||||
class="cmr-12">.</span> </td>
|
||||
</tr><tr
|
||||
style="vertical-align:baseline;" id="TBL-14-6-"><td style="white-space:normal; text-align:left;" id="TBL-14-6-1"
|
||||
class="td11"><!--l. 720--><p class="noindent" > </td><td style="white-space:normal; text-align:left;" id="TBL-14-6-2"
|
||||
class="td11"><!--l. 720--><p class="noindent" ><span
|
||||
class="cmr-12">The communication descriptor associated to the matrix to be</span>
|
||||
<span
|
||||
class="cmr-12">preconditioned.</span> </td>
|
||||
</tr><tr
|
||||
style="vertical-align:baseline;" id="TBL-14-7-"><td style="white-space:normal; text-align:left;" id="TBL-14-7-1"
|
||||
class="td11"><!--l. 722--><p class="noindent" ><span class="obeylines-h"><span class="verb"><span
|
||||
class="cmtt-12">info</span></span></span> </td><td style="white-space:normal; text-align:left;" id="TBL-14-7-2"
|
||||
class="td11"><!--l. 722--><p class="noindent" ><span class="obeylines-h"><span class="verb"><span
|
||||
><colgroup id="TBL-17-1g"><col
|
||||
id="TBL-17-1"><col
|
||||
id="TBL-17-2"></colgroup><tr
|
||||
style="vertical-align:baseline;" id="TBL-17-1-"><td style="white-space:normal; text-align:left;" id="TBL-17-1-1"
|
||||
class="td11"><!--l. 796--><p class="noindent" ><span class="obeylines-h"><span class="verb"><span
|
||||
class="cmtt-12">info</span></span></span> </td><td style="white-space:normal; text-align:left;" id="TBL-17-1-2"
|
||||
class="td11"><!--l. 796--><p class="noindent" ><span class="obeylines-h"><span class="verb"><span
|
||||
class="cmtt-12">integer,</span><span
|
||||
class="cmtt-12"> intent(out)</span></span></span><span
|
||||
class="cmr-12">.</span> </td>
|
||||
</tr><tr
|
||||
style="vertical-align:baseline;" id="TBL-14-8-"><td style="white-space:normal; text-align:left;" id="TBL-14-8-1"
|
||||
class="td11"><!--l. 723--><p class="noindent" > </td><td style="white-space:normal; text-align:left;" id="TBL-14-8-2"
|
||||
class="td11"><!--l. 723--><p class="noindent" ><span
|
||||
style="vertical-align:baseline;" id="TBL-17-2-"><td style="white-space:normal; text-align:left;" id="TBL-17-2-1"
|
||||
class="td11"><!--l. 797--><p class="noindent" > </td><td style="white-space:normal; text-align:left;" id="TBL-17-2-2"
|
||||
class="td11"><!--l. 797--><p class="noindent" ><span
|
||||
class="cmr-12">Error code. If no error, 0 is returned. See Section</span><span
|
||||
class="cmr-12"> </span><a
|
||||
href="userhtmlse8.html#x30-340008"><span
|
||||
class="cmr-12">8</span><!--tex4ht:ref: sec:errors --></a> <span
|
||||
href="userhtmlse7.html#x26-300007"><span
|
||||
class="cmr-12">7</span><!--tex4ht:ref: sec:errors --></a> <span
|
||||
class="cmr-12">for details.</span> </td>
|
||||
</tr><tr
|
||||
style="vertical-align:baseline;" id="TBL-14-9-"><td style="white-space:normal; text-align:left;" id="TBL-14-9-1"
|
||||
class="td11"><!--l. 724--><p class="noindent" ><span class="obeylines-h"><span class="verb"><span
|
||||
class="cmtt-12">trans</span></span></span> </td><td style="white-space:normal; text-align:left;" id="TBL-14-9-2"
|
||||
class="td11"><!--l. 724--><p class="noindent" ><span class="obeylines-h"><span class="verb"><span
|
||||
class="cmtt-12">character(len=1),</span><span
|
||||
class="cmtt-12"> optional,</span><span
|
||||
class="cmtt-12"> intent(in).</span></span></span> </td>
|
||||
</tr><tr
|
||||
style="vertical-align:baseline;" id="TBL-14-10-"><td style="white-space:normal; text-align:left;" id="TBL-14-10-1"
|
||||
class="td11"><!--l. 725--><p class="noindent" > </td><td style="white-space:normal; text-align:left;" id="TBL-14-10-2"
|
||||
class="td11"><!--l. 725--><p class="noindent" ><span
|
||||
class="cmr-12">If </span><span class="obeylines-h"><span class="verb"><span
|
||||
class="cmtt-12">trans</span></span></span> <span
|
||||
class="cmr-12">= </span><span class="obeylines-h"><span class="verb"><span
|
||||
class="cmtt-12">’N’,’n’</span></span></span> <span
|
||||
class="cmr-12">then </span><span
|
||||
class="cmmi-12">op</span><span
|
||||
class="cmr-12">(</span><span
|
||||
class="cmmi-12">B</span><sup><span
|
||||
class="cmsy-8">-</span><span
|
||||
class="cmr-8">1</span></sup><span
|
||||
class="cmr-12">) = </span><span
|
||||
class="cmmi-12">B</span><sup><span
|
||||
class="cmsy-8">-</span><span
|
||||
class="cmr-8">1</span></sup><span
|
||||
class="cmr-12">; if </span><span class="obeylines-h"><span class="verb"><span
|
||||
class="cmtt-12">trans</span></span></span> <span
|
||||
class="cmr-12">= </span><span class="obeylines-h"><span class="verb"><span
|
||||
class="cmtt-12">’T’,’t’</span></span></span>
|
||||
<span
|
||||
class="cmr-12">then </span><span
|
||||
class="cmmi-12">op</span><span
|
||||
class="cmr-12">(</span><span
|
||||
class="cmmi-12">B</span><sup><span
|
||||
class="cmsy-8">-</span><span
|
||||
class="cmr-8">1</span></sup><span
|
||||
class="cmr-12">) = </span><span
|
||||
class="cmmi-12">B</span><sup><span
|
||||
class="cmsy-8">-</span><span
|
||||
class="cmmi-8">T</span> </sup> <span
|
||||
class="cmr-12">(transpose of </span><span
|
||||
class="cmmi-12">B</span><sup><span
|
||||
class="cmsy-8">-</span><span
|
||||
class="cmr-8">1</span></sup><span
|
||||
class="cmr-12">); if </span><span class="obeylines-h"><span class="verb"><span
|
||||
class="cmtt-12">trans</span></span></span> <span
|
||||
class="cmr-12">= </span><span class="obeylines-h"><span class="verb"><span
|
||||
class="cmtt-12">’C’,’c’</span></span></span> <span
|
||||
class="cmr-12">then</span>
|
||||
<span
|
||||
class="cmmi-12">op</span><span
|
||||
class="cmr-12">(</span><span
|
||||
class="cmmi-12">B</span><sup><span
|
||||
class="cmsy-8">-</span><span
|
||||
class="cmr-8">1</span></sup><span
|
||||
class="cmr-12">) = </span><span
|
||||
class="cmmi-12">B</span><sup><span
|
||||
class="cmsy-8">-</span><span
|
||||
class="cmmi-8">C</span></sup> <span
|
||||
class="cmr-12">(conjugate transpose of </span><span
|
||||
class="cmmi-12">B</span><sup><span
|
||||
class="cmsy-8">-</span><span
|
||||
class="cmr-8">1</span></sup><span
|
||||
class="cmr-12">).</span> </td>
|
||||
</tr><tr
|
||||
style="vertical-align:baseline;" id="TBL-14-11-"><td style="white-space:normal; text-align:left;" id="TBL-14-11-1"
|
||||
class="td11"><!--l. 729--><p class="noindent" ><span class="obeylines-h"><span class="verb"><span
|
||||
class="cmtt-12">work</span></span></span> </td><td style="white-space:normal; text-align:left;" id="TBL-14-11-2"
|
||||
class="td11"><!--l. 729--><p class="noindent" ><span
|
||||
class="cmti-12">type</span><span class="obeylines-h"><span class="verb"><span
|
||||
class="cmtt-12">(</span></span></span><span
|
||||
class="cmti-12">kind</span><span
|
||||
class="cmti-12">_parameter</span><span class="obeylines-h"><span class="verb"><span
|
||||
class="cmtt-12">),</span><span
|
||||
class="cmtt-12"> dimension(:),</span><span
|
||||
class="cmtt-12"> optional,</span><span
|
||||
class="cmtt-12"> target</span></span></span><span
|
||||
style="vertical-align:baseline;" id="TBL-17-3-"><td style="white-space:normal; text-align:left;" id="TBL-17-3-1"
|
||||
class="td11"><!--l. 798--><p class="noindent" ><span class="obeylines-h"><span class="verb"><span
|
||||
class="cmtt-12">amold</span></span></span> </td><td style="white-space:normal; text-align:left;" id="TBL-17-3-2"
|
||||
class="td11"><!--l. 798--><p class="noindent" ><span class="obeylines-h"><span class="verb"><span
|
||||
class="cmtt-12">class(psb_</span></span></span><span
|
||||
class="cmti-12">x</span><span class="obeylines-h"><span class="verb"><span
|
||||
class="cmtt-12">_base_sparse_mat),</span><span
|
||||
class="cmtt-12"> intent(in),</span><span
|
||||
class="cmtt-12"> optional</span></span></span><span
|
||||
class="cmr-12">.</span> </td>
|
||||
</tr><tr
|
||||
style="vertical-align:baseline;" id="TBL-14-12-"><td style="white-space:normal; text-align:left;" id="TBL-14-12-1"
|
||||
class="td11"><!--l. 730--><p class="noindent" > </td><td style="white-space:normal; text-align:left;" id="TBL-14-12-2"
|
||||
class="td11"><!--l. 730--><p class="noindent" ><span
|
||||
class="cmr-12">Workspace. Its size should be at least </span><span class="obeylines-h"><span class="verb"><span
|
||||
class="cmtt-12">4</span><span
|
||||
class="cmtt-12"> *</span><span
|
||||
class="cmtt-12"> psb_cd_get_local_</span></span></span>
|
||||
<span class="obeylines-h"><span class="verb"><span
|
||||
class="cmtt-12">cols(desc_a)</span></span></span> <span
|
||||
class="cmr-12">(see the PSBLAS User’s Guide). Note that </span><span
|
||||
class="cmti-12">type</span>
|
||||
style="vertical-align:baseline;" id="TBL-17-4-"><td style="white-space:normal; text-align:left;" id="TBL-17-4-1"
|
||||
class="td11"><!--l. 799--><p class="noindent" > </td><td style="white-space:normal; text-align:left;" id="TBL-17-4-2"
|
||||
class="td11"><!--l. 799--><p class="noindent" ><span
|
||||
class="cmr-12">The desired dynamic type for internal matrix components; this</span>
|
||||
<span
|
||||
class="cmr-12">and </span><span
|
||||
class="cmti-12">kind</span><span
|
||||
class="cmti-12">_parameter </span><span
|
||||
class="cmr-12">must be chosen according to the real/complex,</span>
|
||||
class="cmr-12">allows e.g. running on GPUs; it needs not be the same on all</span>
|
||||
<span
|
||||
class="cmr-12">single/double precision version of AMG4PSBLAS under use.</span> </td>
|
||||
class="cmr-12">processes. See the PSBLAS User’s Guide for details </span><span class="cite"><span
|
||||
class="cmr-12">[</span><a
|
||||
href="userhtmlli4.html#XPSBLASGUIDE"><span
|
||||
class="cmr-12">16</span></a><span
|
||||
class="cmr-12">]</span></span><span
|
||||
class="cmr-12">.</span> </td>
|
||||
</tr><tr
|
||||
style="vertical-align:baseline;" id="TBL-14-13-"><td style="white-space:normal; text-align:left;" id="TBL-14-13-1"
|
||||
style="vertical-align:baseline;" id="TBL-17-5-"><td style="white-space:normal; text-align:left;" id="TBL-17-5-1"
|
||||
class="td11"> </td> </tr></table></div>
|
||||
<!--l. 806--><p class="noindent" >
|
||||
<h5 class="subsubsectionHead"><span class="titlemark"><span
|
||||
class="cmr-12">5.9.2 </span></span> <a
|
||||
id="x24-250005.9.2"></a><span
|
||||
class="cmr-12">Method: clone</span></h5>
|
||||
<div class="center"
|
||||
>
|
||||
<!--l. 808--><p class="noindent" >
|
||||
<!--l. 809--><p class="noindent" ><span class="obeylines-h"><span class="verb"><span
|
||||
class="cmtt-12">call</span><span
|
||||
class="cmtt-12"> p%clone(pout,info)</span></span></span><br />
|
||||
</div>
|
||||
|
||||
|
||||
|
||||
<!--l. 812--><p class="noindent" ><span
|
||||
class="cmr-12">Create a (deep) copy of the preconditioner object.</span>
|
||||
<!--l. 815--><p class="noindent" ><span
|
||||
class="cmbx-12">Arguments</span>
|
||||
<div class="tabular"> <table id="TBL-18" class="tabular"
|
||||
cellspacing="0" cellpadding="0"
|
||||
><colgroup id="TBL-18-1g"><col
|
||||
id="TBL-18-1"><col
|
||||
id="TBL-18-2"></colgroup><tr
|
||||
style="vertical-align:baseline;" id="TBL-18-1-"><td style="white-space:normal; text-align:left;" id="TBL-18-1-1"
|
||||
class="td11"><!--l. 818--><p class="noindent" ><span class="obeylines-h"><span class="verb"><span
|
||||
class="cmtt-12">pout</span></span></span> </td><td style="white-space:normal; text-align:left;" id="TBL-18-1-2"
|
||||
class="td11"><!--l. 818--><p class="noindent" ><span class="obeylines-h"><span class="verb"><span
|
||||
class="cmtt-12">type(amg_</span></span></span><span
|
||||
class="cmti-12">x</span><span class="obeylines-h"><span class="verb"><span
|
||||
class="cmtt-12">prec_type),</span><span
|
||||
class="cmtt-12"> intent(out)</span></span></span><span
|
||||
class="cmr-12">.</span> </td>
|
||||
</tr><tr
|
||||
style="vertical-align:baseline;" id="TBL-18-2-"><td style="white-space:normal; text-align:left;" id="TBL-18-2-1"
|
||||
class="td11"><!--l. 819--><p class="noindent" > </td><td style="white-space:normal; text-align:left;" id="TBL-18-2-2"
|
||||
class="td11"><!--l. 819--><p class="noindent" ><span
|
||||
class="cmr-12">The copy of the preconditioner data structure. Note that </span><span
|
||||
class="cmti-12">x </span><span
|
||||
class="cmr-12">must</span>
|
||||
<span
|
||||
class="cmr-12">be chosen according to the real/complex, single/double precision</span>
|
||||
<span
|
||||
class="cmr-12">version of AMG4PSBLAS under use.</span> </td>
|
||||
</tr><tr
|
||||
style="vertical-align:baseline;" id="TBL-18-3-"><td style="white-space:normal; text-align:left;" id="TBL-18-3-1"
|
||||
class="td11"><!--l. 822--><p class="noindent" ><span class="obeylines-h"><span class="verb"><span
|
||||
class="cmtt-12">info</span></span></span> </td><td style="white-space:normal; text-align:left;" id="TBL-18-3-2"
|
||||
class="td11"><!--l. 822--><p class="noindent" ><span class="obeylines-h"><span class="verb"><span
|
||||
class="cmtt-12">integer,</span><span
|
||||
class="cmtt-12"> intent(out)</span></span></span><span
|
||||
class="cmr-12">.</span> </td>
|
||||
</tr><tr
|
||||
style="vertical-align:baseline;" id="TBL-18-4-"><td style="white-space:normal; text-align:left;" id="TBL-18-4-1"
|
||||
class="td11"><!--l. 823--><p class="noindent" > </td><td style="white-space:normal; text-align:left;" id="TBL-18-4-2"
|
||||
class="td11"><!--l. 823--><p class="noindent" ><span
|
||||
class="cmr-12">Error code. If no error, 0 is returned. See Section</span><span
|
||||
class="cmr-12"> </span><a
|
||||
href="userhtmlse7.html#x26-300007"><span
|
||||
class="cmr-12">7</span><!--tex4ht:ref: sec:errors --></a> <span
|
||||
class="cmr-12">for details.</span> </td>
|
||||
</tr><tr
|
||||
style="vertical-align:baseline;" id="TBL-18-5-"><td style="white-space:normal; text-align:left;" id="TBL-18-5-1"
|
||||
class="td11"> </td> </tr></table></div>
|
||||
<!--l. 828--><p class="noindent" >
|
||||
<h5 class="subsubsectionHead"><span class="titlemark"><span
|
||||
class="cmr-12">5.9.3 </span></span> <a
|
||||
id="x24-260005.9.3"></a><span
|
||||
class="cmr-12">Method: sizeof</span></h5>
|
||||
<div class="center"
|
||||
>
|
||||
<!--l. 830--><p class="noindent" >
|
||||
<!--l. 831--><p class="noindent" ><span class="obeylines-h"><span class="verb"><span
|
||||
class="cmtt-12">sz</span><span
|
||||
class="cmtt-12"> =</span><span
|
||||
class="cmtt-12"> </span><span
|
||||
class="cmtt-12"> p%sizeof()</span></span></span><br />
|
||||
</div>
|
||||
<!--l. 834--><p class="noindent" ><span
|
||||
class="cmr-12">Return memory footprint in bytes.</span>
|
||||
<!--l. 837--><p class="noindent" >
|
||||
<h5 class="subsubsectionHead"><span class="titlemark"><span
|
||||
class="cmr-12">5.9.4 </span></span> <a
|
||||
id="x24-270005.9.4"></a><span
|
||||
class="cmr-12">Method: allocate</span><span
|
||||
class="cmr-12">_wrk</span></h5>
|
||||
<div class="center"
|
||||
>
|
||||
<!--l. 839--><p class="noindent" >
|
||||
<!--l. 840--><p class="noindent" ><span class="obeylines-h"><span class="verb"><span
|
||||
class="cmtt-12">call</span><span
|
||||
class="cmtt-12"> p%allocate_wrk(info[,</span><span
|
||||
class="cmtt-12"> vmold])</span></span></span><br />
|
||||
</div>
|
||||
<!--l. 843--><p class="noindent" ><span
|
||||
class="cmr-12">Allocate internal work vectors. Each application of the preconditioner uses a number of</span>
|
||||
<span
|
||||
class="cmr-12">work vectors which are allocated internally as necessary; therefore allocation and</span>
|
||||
<span
|
||||
class="cmr-12">deallocation of memory occurs multiple times during the execution of a Krylov method.</span>
|
||||
<span
|
||||
class="cmr-12">In most cases this strategy is perfectly acceptable, but on some platforms, most</span>
|
||||
<span
|
||||
class="cmr-12">notably GPUs, memory allocation is a slow operation, and the default behaviour would</span>
|
||||
<span
|
||||
class="cmr-12">lead to a slowdown. This method allows to trade space for time by preallocating</span>
|
||||
<span
|
||||
class="cmr-12">the internal workspace outside of the invocation of a Krylov method. When</span>
|
||||
<span
|
||||
class="cmr-12">using GPUs or other specialized devices, the </span><span class="obeylines-h"><span class="verb"><span
|
||||
class="cmtt-12">vmold</span></span></span> <span
|
||||
class="cmr-12">argument is also necessary</span>
|
||||
<span
|
||||
class="cmr-12">to ensure the internal work vectors are of the appropriate dynamic type to</span>
|
||||
|
||||
|
||||
|
||||
<span
|
||||
class="cmr-12">exploit the accelerator hardware; when allocation occurs internally this is</span>
|
||||
<span
|
||||
class="cmr-12">taken care of based on the dynamic type of the </span><span class="obeylines-h"><span class="verb"><span
|
||||
class="cmtt-12">x</span></span></span> <span
|
||||
class="cmr-12">argument to the </span><span class="obeylines-h"><span class="verb"><span
|
||||
class="cmtt-12">apply</span></span></span>
|
||||
<span
|
||||
class="cmr-12">method.</span>
|
||||
<!--l. 859--><p class="noindent" ><span
|
||||
class="cmbx-12">Arguments</span>
|
||||
<div class="tabular"> <table id="TBL-19" class="tabular"
|
||||
cellspacing="0" cellpadding="0"
|
||||
><colgroup id="TBL-19-1g"><col
|
||||
id="TBL-19-1"><col
|
||||
id="TBL-19-2"></colgroup><tr
|
||||
style="vertical-align:baseline;" id="TBL-19-1-"><td style="white-space:normal; text-align:left;" id="TBL-19-1-1"
|
||||
class="td11"><!--l. 862--><p class="noindent" ><span class="obeylines-h"><span class="verb"><span
|
||||
class="cmtt-12">info</span></span></span> </td><td style="white-space:normal; text-align:left;" id="TBL-19-1-2"
|
||||
class="td11"><!--l. 862--><p class="noindent" ><span class="obeylines-h"><span class="verb"><span
|
||||
class="cmtt-12">integer,</span><span
|
||||
class="cmtt-12"> intent(out)</span></span></span><span
|
||||
class="cmr-12">.</span> </td>
|
||||
</tr><tr
|
||||
style="vertical-align:baseline;" id="TBL-19-2-"><td style="white-space:normal; text-align:left;" id="TBL-19-2-1"
|
||||
class="td11"><!--l. 863--><p class="noindent" > </td><td style="white-space:normal; text-align:left;" id="TBL-19-2-2"
|
||||
class="td11"><!--l. 863--><p class="noindent" ><span
|
||||
class="cmr-12">Error code. If no error, 0 is returned. See Section</span><span
|
||||
class="cmr-12"> </span><a
|
||||
href="userhtmlse7.html#x26-300007"><span
|
||||
class="cmr-12">7</span><!--tex4ht:ref: sec:errors --></a> <span
|
||||
class="cmr-12">for details.</span> </td>
|
||||
</tr><tr
|
||||
style="vertical-align:baseline;" id="TBL-19-3-"><td style="white-space:normal; text-align:left;" id="TBL-19-3-1"
|
||||
class="td11"><!--l. 864--><p class="noindent" ><span class="obeylines-h"><span class="verb"><span
|
||||
class="cmtt-12">vmold</span></span></span> </td><td style="white-space:normal; text-align:left;" id="TBL-19-3-2"
|
||||
class="td11"><!--l. 864--><p class="noindent" ><span class="obeylines-h"><span class="verb"><span
|
||||
class="cmtt-12">class(psb_</span></span></span><span
|
||||
class="cmti-12">x</span><span class="obeylines-h"><span class="verb"><span
|
||||
class="cmtt-12">_base_vect_type),</span><span
|
||||
class="cmtt-12"> intent(in),</span><span
|
||||
class="cmtt-12"> optional</span></span></span><span
|
||||
class="cmr-12">.</span> </td>
|
||||
</tr><tr
|
||||
style="vertical-align:baseline;" id="TBL-19-4-"><td style="white-space:normal; text-align:left;" id="TBL-19-4-1"
|
||||
class="td11"><!--l. 865--><p class="noindent" > </td><td style="white-space:normal; text-align:left;" id="TBL-19-4-2"
|
||||
class="td11"><!--l. 865--><p class="noindent" ><span
|
||||
class="cmr-12">The desired dynamic type for internal vector components; this</span>
|
||||
<span
|
||||
class="cmr-12">allows e.g. running on GPUs.</span> </td>
|
||||
</tr><tr
|
||||
style="vertical-align:baseline;" id="TBL-19-5-"><td style="white-space:normal; text-align:left;" id="TBL-19-5-1"
|
||||
class="td11"> </td> </tr></table></div>
|
||||
<!--l. 871--><p class="noindent" >
|
||||
<h5 class="subsubsectionHead"><span class="titlemark"><span
|
||||
class="cmr-12">5.9.5 </span></span> <a
|
||||
id="x24-280005.9.5"></a><span
|
||||
class="cmr-12">Method: free</span><span
|
||||
class="cmr-12">_wrk</span></h5>
|
||||
<div class="center"
|
||||
>
|
||||
<!--l. 873--><p class="noindent" >
|
||||
<!--l. 874--><p class="noindent" ><span class="obeylines-h"><span class="verb"><span
|
||||
class="cmtt-12">call</span><span
|
||||
class="cmtt-12"> p%free_wrk(info)</span></span></span><br />
|
||||
</div>
|
||||
<!--l. 877--><p class="noindent" ><span
|
||||
class="cmr-12">Deallocate internal work vectors.</span>
|
||||
<!--l. 880--><p class="noindent" ><span
|
||||
class="cmbx-12">Arguments</span>
|
||||
<div class="tabular"> <table id="TBL-20" class="tabular"
|
||||
cellspacing="0" cellpadding="0"
|
||||
><colgroup id="TBL-20-1g"><col
|
||||
id="TBL-20-1"><col
|
||||
id="TBL-20-2"></colgroup><tr
|
||||
style="vertical-align:baseline;" id="TBL-20-1-"><td style="white-space:normal; text-align:left;" id="TBL-20-1-1"
|
||||
class="td11"><!--l. 883--><p class="noindent" ><span class="obeylines-h"><span class="verb"><span
|
||||
class="cmtt-12">info</span></span></span> </td><td style="white-space:normal; text-align:left;" id="TBL-20-1-2"
|
||||
class="td11"><!--l. 883--><p class="noindent" ><span class="obeylines-h"><span class="verb"><span
|
||||
class="cmtt-12">integer,</span><span
|
||||
class="cmtt-12"> intent(out)</span></span></span><span
|
||||
class="cmr-12">.</span> </td>
|
||||
</tr><tr
|
||||
style="vertical-align:baseline;" id="TBL-20-2-"><td style="white-space:normal; text-align:left;" id="TBL-20-2-1"
|
||||
class="td11"><!--l. 884--><p class="noindent" > </td><td style="white-space:normal; text-align:left;" id="TBL-20-2-2"
|
||||
class="td11"><!--l. 884--><p class="noindent" ><span
|
||||
class="cmr-12">Error code. If no error, 0 is returned. See Section</span><span
|
||||
class="cmr-12"> </span><a
|
||||
href="userhtmlse7.html#x26-300007"><span
|
||||
class="cmr-12">7</span><!--tex4ht:ref: sec:errors --></a> <span
|
||||
class="cmr-12">for details.</span> </td>
|
||||
</tr><tr
|
||||
style="vertical-align:baseline;" id="TBL-20-3-"><td style="white-space:normal; text-align:left;" id="TBL-20-3-1"
|
||||
class="td11"> </td> </tr></table></div>
|
||||
|
||||
|
||||
@@ -272,11 +314,11 @@ class="td11"> </td> </tr></table></div>
|
||||
|
||||
|
||||
|
||||
<!--l. 739--><div class="crosslinks"><p class="noindent"><span
|
||||
|
||||
|
||||
|
||||
<!--l. 4--><div class="crosslinks"><p class="noindent"><span
|
||||
class="cmr-12">[</span><a
|
||||
href="userhtmlsu16.html" ><span
|
||||
class="cmr-12">next</span></a><span
|
||||
class="cmr-12">] [</span><a
|
||||
href="userhtmlsu14.html" ><span
|
||||
class="cmr-12">prev</span></a><span
|
||||
class="cmr-12">] [</span><a
|
||||
@@ -286,9 +328,9 @@ class="cmr-12">] [</span><a
|
||||
href="userhtmlsu15.html" ><span
|
||||
class="cmr-12">front</span></a><span
|
||||
class="cmr-12">] [</span><a
|
||||
href="userhtmlse6.html#userhtmlsu15.html" ><span
|
||||
href="userhtmlse5.html#userhtmlsu15.html" ><span
|
||||
class="cmr-12">up</span></a><span
|
||||
class="cmr-12">] </span></p></div>
|
||||
<!--l. 739--><p class="indent" > <a
|
||||
id="tailuserhtmlsu15.html"></a>
|
||||
<!--l. 4--><p class="indent" > <a
|
||||
id="tailuserhtmlsu15.html"></a>
|
||||
</body></html>
|
||||
|
||||
@@ -81,6 +81,12 @@ class="cmr-12">partial differential equation.</span>
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
<!--l. 1--><div class="crosslinks"><p class="noindent"><span
|
||||
class="cmr-12">[</span><a
|
||||
href="userhtmlsu4.html" ><span
|
||||
|
||||
+324
-333
@@ -1,7 +1,7 @@
|
||||
<!DOCTYPE html PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN"
|
||||
"http://www.w3.org/TR/html4/loose.dtd">
|
||||
<html >
|
||||
<head><title>AMG preconditioners</title>
|
||||
<head><title>Examples</title>
|
||||
<meta http-equiv="Content-Type" content="text/html; charset=iso-8859-1">
|
||||
<meta name="generator" content="TeX4ht (https://tug.org/tex4ht/)">
|
||||
<meta name="originator" content="TeX4ht (https://tug.org/tex4ht/)">
|
||||
@@ -10,11 +10,8 @@
|
||||
<link rel="stylesheet" type="text/css" href="userhtml.css">
|
||||
</head><body
|
||||
>
|
||||
<!--l. 56--><div class="crosslinks"><p class="noindent"><span
|
||||
<!--l. 107--><div class="crosslinks"><p class="noindent"><span
|
||||
class="cmr-12">[</span><a
|
||||
href="userhtmlsu7.html" ><span
|
||||
class="cmr-12">next</span></a><span
|
||||
class="cmr-12">] [</span><a
|
||||
href="#tailuserhtmlsu6.html"><span
|
||||
class="cmr-12">tail</span></a><span
|
||||
class="cmr-12">] [</span><a
|
||||
@@ -24,376 +21,370 @@ class="cmr-12">] </span></p></div>
|
||||
<h4 class="subsectionHead"><span class="titlemark"><span
|
||||
class="cmr-12">4.1 </span></span> <a
|
||||
id="x14-130004.1"></a><span
|
||||
class="cmr-12">AMG preconditioners</span></h4>
|
||||
<!--l. 58--><p class="noindent" ><span
|
||||
class="cmr-12">In order to describe the AMG preconditioners available in MLD2P4, we consider a</span>
|
||||
class="cmr-12">Examples</span></h4>
|
||||
<!--l. 109--><p class="noindent" ><span
|
||||
class="cmr-12">The code reported in Figure</span><span
|
||||
class="cmr-12"> </span><a
|
||||
href="#x14-130011"><span
|
||||
class="cmr-12">1</span><!--tex4ht:ref: fig:ex1 --></a> <span
|
||||
class="cmr-12">shows how to set and apply the default multilevel</span>
|
||||
<span
|
||||
class="cmr-12">linear system</span>
|
||||
<table
|
||||
class="equation"><tr><td>
|
||||
<center class="math-display" >
|
||||
<img
|
||||
src="userhtml2x.png" alt="Ax = b,
|
||||
" class="math-display" ><a
|
||||
id="x14-13001r2"></a></center></td><td class="equation-label"><span
|
||||
class="cmr-12">(2)</span></td></tr></table>
|
||||
<!--l. 62--><p class="nopar" >
|
||||
class="cmr-12">preconditioner available in the real double precision version of AMG4PSBLAS</span>
|
||||
<span
|
||||
class="cmr-12">where </span><span
|
||||
class="cmmi-12">A </span><span
|
||||
class="cmr-12">= (</span><span
|
||||
class="cmmi-12">a</span><sub><span
|
||||
class="cmmi-8">ij</span></sub><span
|
||||
class="cmr-12">) </span><span
|
||||
class="cmsy-10x-x-120">∈ </span><span
|
||||
class="msbm-10x-x-120">ℝ</span><sup><span
|
||||
class="cmmi-8">n</span><span
|
||||
class="cmsy-8">×</span><span
|
||||
class="cmmi-8">n</span></sup> <span
|
||||
class="cmr-12">is a nonsingular sparse matrix; for ease of presentation we</span>
|
||||
class="cmr-12">(see Table</span><span
|
||||
class="cmr-12"> </span><a
|
||||
href="userhtmlse4.html#x13-120151"><span
|
||||
class="cmr-12">1</span><!--tex4ht:ref: tab:precinit --></a><span
|
||||
class="cmr-12">). This preconditioner is chosen by simply specifying </span><span class="obeylines-h"><span class="verb"><span
|
||||
class="cmtt-12">’ML’</span></span></span> <span
|
||||
class="cmr-12">as the</span>
|
||||
<span
|
||||
class="cmr-12">assume </span><span
|
||||
class="cmmi-12">A </span><span
|
||||
class="cmr-12">has a symmetric sparsity pattern.</span>
|
||||
class="cmr-12">second argument of </span><span class="obeylines-h"><span class="verb"><span
|
||||
class="cmtt-12">P%init</span></span></span> <span
|
||||
class="cmr-12">(a call to </span><span class="obeylines-h"><span class="verb"><span
|
||||
class="cmtt-12">P%set</span></span></span> <span
|
||||
class="cmr-12">is not needed) and is applied</span>
|
||||
<span
|
||||
class="cmr-12">with the CG solver provided by PSBLAS (the matrix of the system to be</span>
|
||||
<span
|
||||
class="cmr-12">solved is assumed to be positive definite). As previously observed, the modules</span>
|
||||
<span class="obeylines-h"><span class="verb"><span
|
||||
class="cmtt-12">psb_base_mod</span></span></span><span
|
||||
class="cmr-12">, </span><span class="obeylines-h"><span class="verb"><span
|
||||
class="cmtt-12">amg_prec_mod</span></span></span> <span
|
||||
class="cmr-12">and </span><span class="obeylines-h"><span class="verb"><span
|
||||
class="cmtt-12">psb_krylov_mod</span></span></span> <span
|
||||
class="cmr-12">must be used by the example</span>
|
||||
<span
|
||||
class="cmr-12">program.</span>
|
||||
<!--l. 119--><p class="indent" > <span
|
||||
class="cmr-12">The part of the code concerning the reading and assembling of the sparse matrix</span>
|
||||
<span
|
||||
class="cmr-12">and the right-hand side vector, performed through the PSBLAS routines for sparse</span>
|
||||
<span
|
||||
class="cmr-12">matrix and vector management, is not reported here for brevity; the statements</span>
|
||||
<span
|
||||
class="cmr-12">concerning the deallocation of the PSBLAS data structure are neglected too. The</span>
|
||||
<span
|
||||
class="cmr-12">complete code can be found in the example program file </span><span class="obeylines-h"><span class="verb"><span
|
||||
class="cmtt-12">amg_dexample_ml.f90</span></span></span><span
|
||||
class="cmr-12">, in the</span>
|
||||
<span
|
||||
class="cmr-12">directory </span><span class="obeylines-h"><span class="verb"><span
|
||||
class="cmtt-12">examples/fileread</span></span></span> <span
|
||||
class="cmr-12">of the AMG4PSBLAS implementation (see</span>
|
||||
<span
|
||||
class="cmr-12">Section</span><span
|
||||
class="cmr-12"> </span><a
|
||||
href="userhtmlsu5.html#x12-110003.5"><span
|
||||
class="cmr-12">3.5</span><!--tex4ht:ref: sec:ex_and_test --></a><span
|
||||
class="cmr-12">). A sample test problem along with the relevant input data is available in</span>
|
||||
<span class="obeylines-h"><span class="verb"><span
|
||||
class="cmtt-12">examples/fileread/runs</span></span></span><span
|
||||
class="cmr-12">. For details on the use of the PSBLAS routines, see the</span>
|
||||
<span
|
||||
class="cmr-12">PSBLAS User’s Guide</span><span
|
||||
class="cmr-12"> </span><span class="cite"><span
|
||||
class="cmr-12">[</span><a
|
||||
href="userhtmlli4.html#XPSBLASGUIDE"><span
|
||||
class="cmr-12">16</span></a><span
|
||||
class="cmr-12">]</span></span><span
|
||||
class="cmr-12">.</span>
|
||||
<!--l. 131--><p class="indent" > <span
|
||||
class="cmr-12">The setup and application of the default multilevel preconditioner for the real single</span>
|
||||
|
||||
|
||||
|
||||
<!--l. 67--><p class="indent" > <span
|
||||
class="cmr-12">Let us consider as finest index space the set of row (column) indices of </span><span
|
||||
class="cmmi-12">A</span><span
|
||||
class="cmr-12">,</span>
|
||||
<span
|
||||
class="cmr-12">i.e., Ω = </span><span
|
||||
class="cmsy-10x-x-120">{</span><span
|
||||
class="cmr-12">1</span><span
|
||||
class="cmmi-12">, </span><span
|
||||
class="cmr-12">2</span><span
|
||||
class="cmmi-12">,</span><span
|
||||
class="cmmi-12">…</span><span
|
||||
class="cmmi-12">,n</span><span
|
||||
class="cmsy-10x-x-120">}</span><span
|
||||
class="cmr-12">. Any algebraic multilevel preconditioners implemented in</span>
|
||||
class="cmr-12">precision and the complex, single and double precision, versions are obtained</span>
|
||||
<span
|
||||
class="cmr-12">MLD2P4 generates a hierarchy of index spaces and a corresponding hierarchy of</span>
|
||||
class="cmr-12">with straightforward modifications of the previous example (see Section</span><span
|
||||
class="cmr-12"> </span><a
|
||||
href="userhtmlse5.html#x15-140005"><span
|
||||
class="cmr-12">5</span><!--tex4ht:ref: sec:userinterface --></a> <span
|
||||
class="cmr-12">for</span>
|
||||
<span
|
||||
class="cmr-12">matrices,</span>
|
||||
<center class="math-display" >
|
||||
<img
|
||||
src="userhtml3x.png" alt=" 1 2 nlev 1 2 nlev
|
||||
Ω ≡ Ω ⊃ Ω ⊃ ...⊃ Ω , A ≡ A, A ,...,A ,
|
||||
" class="math-display" ></center>
|
||||
<!--l. 72--><p class="nopar" > <span
|
||||
class="cmr-12">by using the information contained in </span><span
|
||||
class="cmmi-12">A</span><span
|
||||
class="cmr-12">, without assuming any knowledge of</span>
|
||||
<span
|
||||
class="cmr-12">the geometry of the problem from which </span><span
|
||||
class="cmmi-12">A </span><span
|
||||
class="cmr-12">originates. A vector space </span><span
|
||||
class="msbm-10x-x-120">ℝ</span><sup><span
|
||||
class="cmmi-8">n</span><sub><span
|
||||
class="cmmi-6">k</span></sub></sup> <span
|
||||
class="cmr-12">is</span>
|
||||
<span
|
||||
class="cmr-12">associated with Ω</span><sup><span
|
||||
class="cmmi-8">k</span></sup><span
|
||||
class="cmr-12">, where </span><span
|
||||
class="cmmi-12">n</span><sub>
|
||||
<span
|
||||
class="cmmi-8">k</span></sub> <span
|
||||
class="cmr-12">is the size of Ω</span><sup><span
|
||||
class="cmmi-8">k</span></sup><span
|
||||
class="cmr-12">. For all </span><span
|
||||
class="cmmi-12">k < nlev</span><span
|
||||
class="cmr-12">, a restriction</span>
|
||||
<span
|
||||
class="cmr-12">operator and a prolongation one are built, which connect two levels </span><span
|
||||
class="cmmi-12">k </span><span
|
||||
class="cmr-12">and</span>
|
||||
<span
|
||||
class="cmmi-12">k </span><span
|
||||
class="cmr-12">+ 1:</span>
|
||||
<center class="math-display" >
|
||||
<img
|
||||
src="userhtml4x.png" alt="P k ∈ ℝnk×nk+1, Rk ∈ ℝnk+1×nk ;
|
||||
" class="math-display" ></center>
|
||||
<!--l. 82--><p class="nopar" > <span
|
||||
class="cmr-12">the matrix </span><span
|
||||
class="cmmi-12">A</span><sup><span
|
||||
class="cmmi-8">k</span><span
|
||||
class="cmr-8">+1</span></sup> <span
|
||||
class="cmr-12">is computed by using the previous operators according to the</span>
|
||||
<span
|
||||
class="cmr-12">Galerkin approach, i.e.,</span>
|
||||
<center class="math-display" >
|
||||
<img
|
||||
src="userhtml5x.png" alt=" k+1 k k k
|
||||
A = R A P .
|
||||
" class="math-display" ></center>
|
||||
<!--l. 87--><p class="nopar" > <span
|
||||
class="cmr-12">In the current implementation of MLD2P4 we have </span><span
|
||||
class="cmmi-12">R</span><sup><span
|
||||
class="cmmi-8">k</span></sup> <span
|
||||
class="cmr-12">= (</span><span
|
||||
class="cmmi-12">P</span><sup><span
|
||||
class="cmmi-8">k</span></sup><span
|
||||
class="cmr-12">)</span><sup><span
|
||||
class="cmmi-8">T</span> </sup> <span
|
||||
class="cmr-12">A smoother with</span>
|
||||
<span
|
||||
class="cmr-12">iteration matrix </span><span
|
||||
class="cmmi-12">M</span><sup><span
|
||||
class="cmmi-8">k</span></sup> <span
|
||||
class="cmr-12">is set up at each level </span><span
|
||||
class="cmmi-12">k < nlev</span><span
|
||||
class="cmr-12">, and a solver is set up at the</span>
|
||||
<span
|
||||
class="cmr-12">coarsest level, so that they are ready for application (for example, setting up a solver</span>
|
||||
<span
|
||||
class="cmr-12">based on the </span><span
|
||||
class="cmmi-12">LU </span><span
|
||||
class="cmr-12">factorization means computing and storing the </span><span
|
||||
class="cmmi-12">L </span><span
|
||||
class="cmr-12">and </span><span
|
||||
class="cmmi-12">U </span><span
|
||||
class="cmr-12">factors). The</span>
|
||||
<span
|
||||
class="cmr-12">construction of the hierarchy of AMG components described so far corresponds to the</span>
|
||||
<span
|
||||
class="cmr-12">so-called build phase of the preconditioner.</span>
|
||||
<!--l. 95--><p class="indent" > <hr class="figure"><div class="figure"
|
||||
class="cmr-12">details). If these versions are installed, the corresponding codes are available in</span>
|
||||
<span class="obeylines-h"><span class="verb"><span
|
||||
class="cmtt-12">examples/fileread/</span></span></span><span
|
||||
class="cmr-12">.</span>
|
||||
<!--l. 137--><p class="indent" > <hr class="figure"><div class="figure"
|
||||
>
|
||||
|
||||
|
||||
|
||||
<a
|
||||
id="x14-130021"></a>
|
||||
id="x14-130011"></a>
|
||||
|
||||
|
||||
|
||||
<div class="center"
|
||||
>
|
||||
<!--l. 96--><p class="noindent" >
|
||||
<div class="fbox"> <div class="minipage"><table
|
||||
cellpadding="0" border="0" cellspacing="0"
|
||||
class="tabbing"><tr
|
||||
style="vertical-align:baseline;" class="tabbing"><td style="width:16;"
|
||||
class="tabbing"> </td><td style="width:16;"
|
||||
class="tabbing"> </td><td style="width:16;"
|
||||
class="tabbing"> </td><td
|
||||
class="tabbing"></td></tr></table>
|
||||
<!--l. 115--><p class="noindent" ><table
|
||||
cellpadding="0" border="0" cellspacing="0"
|
||||
class="tabbing"><tr
|
||||
style="vertical-align:baseline;" class="tabbing"><td
|
||||
class="tabbing">procedure V-cycle<img
|
||||
src="userhtml6x.png" alt="( k k k)
|
||||
k,A ,b ,u" class="left" align="middle">
|
||||
</td></tr></table>
|
||||
<!--l. 115--><p class="noindent" >
|
||||
<table
|
||||
cellpadding="0" border="0" cellspacing="0"
|
||||
class="tabbing"><tr
|
||||
style="vertical-align:baseline;" class="tabbing"><td style="width:16;"
|
||||
class="tabbing"> </td><td
|
||||
class="tabbing">if <img
|
||||
src="userhtml7x.png" alt="(k ⁄= nlev)" class="left" align="middle"> then</td></tr></table>
|
||||
<!--l. 115--><p class="noindent" >
|
||||
<table
|
||||
cellpadding="0" border="0" cellspacing="0"
|
||||
class="tabbing"><tr
|
||||
style="vertical-align:baseline;" class="tabbing"><td style="width:16;"
|
||||
class="tabbing"> </td><td style="width:16;"
|
||||
class="tabbing"> </td><td
|
||||
class="tabbing"><span
|
||||
class="cmmi-10x-x-109">u</span><sup><span
|
||||
class="cmmi-8">k</span></sup> = <span
|
||||
class="cmmi-10x-x-109">u</span><sup><span
|
||||
class="cmmi-8">k</span></sup> + <span
|
||||
class="cmmi-10x-x-109">M</span><sup><span
|
||||
class="cmmi-8">k</span></sup><img
|
||||
src="userhtml8x.png" alt="( )
|
||||
bk - Akuk" class="left" align="middle"></td></tr></table>
|
||||
<!--l. 115--><p class="noindent" >
|
||||
<table
|
||||
cellpadding="0" border="0" cellspacing="0"
|
||||
class="tabbing"><tr
|
||||
style="vertical-align:baseline;" class="tabbing"><td style="width:16;"
|
||||
class="tabbing"> </td><td style="width:16;"
|
||||
class="tabbing"> </td><td
|
||||
class="tabbing"><span
|
||||
class="cmmi-10x-x-109">b</span><sup><span
|
||||
class="cmmi-8">k</span><span
|
||||
class="cmr-8">+1</span></sup> = <span
|
||||
class="cmmi-10x-x-109">R</span><sup><span
|
||||
class="cmmi-8">k</span><span
|
||||
class="cmr-8">+1</span></sup><img
|
||||
src="userhtml9x.png" alt="(bk - Akuk )" class="left" align="middle"></td></tr></table>
|
||||
<!--l. 115--><p class="noindent" >
|
||||
<table
|
||||
cellpadding="0" border="0" cellspacing="0"
|
||||
class="tabbing"><tr
|
||||
style="vertical-align:baseline;" class="tabbing"><td style="width:16;"
|
||||
class="tabbing"> </td><td style="width:16;"
|
||||
class="tabbing"> </td><td
|
||||
class="tabbing"><span
|
||||
class="cmmi-10x-x-109">u</span><sup><span
|
||||
class="cmmi-8">k</span><span
|
||||
class="cmr-8">+1</span></sup> = V-cycle<img
|
||||
src="userhtml10x.png" alt="( )
|
||||
k + 1,Ak+1,bk+1,0" class="left" align="middle"></td></tr></table>
|
||||
<!--l. 115--><p class="noindent" >
|
||||
<table
|
||||
cellpadding="0" border="0" cellspacing="0"
|
||||
class="tabbing"><tr
|
||||
style="vertical-align:baseline;" class="tabbing"><td style="width:16;"
|
||||
class="tabbing"> </td><td style="width:16;"
|
||||
class="tabbing"> </td><td
|
||||
class="tabbing"><span
|
||||
class="cmmi-10x-x-109">u</span><sup><span
|
||||
class="cmmi-8">k</span></sup> = <span
|
||||
class="cmmi-10x-x-109">u</span><sup><span
|
||||
class="cmmi-8">k</span></sup> + <span
|
||||
class="cmmi-10x-x-109">P</span><sup><span
|
||||
class="cmmi-8">k</span><span
|
||||
class="cmr-8">+1</span></sup><span
|
||||
class="cmmi-10x-x-109">u</span><sup><span
|
||||
class="cmmi-8">k</span><span
|
||||
class="cmr-8">+1</span></sup></td></tr></table>
|
||||
<!--l. 115--><p class="noindent" >
|
||||
<table
|
||||
cellpadding="0" border="0" cellspacing="0"
|
||||
class="tabbing"><tr
|
||||
style="vertical-align:baseline;" class="tabbing"><td style="width:16;"
|
||||
class="tabbing"> </td><td style="width:16;"
|
||||
class="tabbing"> </td><td
|
||||
class="tabbing"><span
|
||||
class="cmmi-10x-x-109">u</span><sup><span
|
||||
class="cmmi-8">k</span></sup> = <span
|
||||
class="cmmi-10x-x-109">u</span><sup><span
|
||||
class="cmmi-8">k</span></sup> + <span
|
||||
class="cmmi-10x-x-109">M</span><sup><span
|
||||
class="cmmi-8">k</span></sup><img
|
||||
src="userhtml11x.png" alt="( )
|
||||
bk - Akuk" class="left" align="middle"></td></tr></table>
|
||||
<!--l. 115--><p class="noindent" >
|
||||
<table
|
||||
cellpadding="0" border="0" cellspacing="0"
|
||||
class="tabbing"><tr
|
||||
style="vertical-align:baseline;" class="tabbing"><td style="width:16;"
|
||||
class="tabbing"> </td><td
|
||||
class="tabbing">else</td></tr></table>
|
||||
<!--l. 115--><p class="noindent" >
|
||||
<table
|
||||
cellpadding="0" border="0" cellspacing="0"
|
||||
class="tabbing"><tr
|
||||
style="vertical-align:baseline;" class="tabbing"><td style="width:16;"
|
||||
class="tabbing"> </td><td style="width:16;"
|
||||
class="tabbing"> </td><td
|
||||
class="tabbing"><span
|
||||
class="cmmi-10x-x-109">u</span><sup><span
|
||||
class="cmmi-8">k</span></sup> = <img
|
||||
src="userhtml12x.png" alt="( )
|
||||
Ak" class="left" align="middle"><sup><span
|
||||
class="cmsy-8">-</span><span
|
||||
class="cmr-8">1</span></sup><span
|
||||
class="cmmi-10x-x-109">b</span><sup><span
|
||||
class="cmmi-8">k</span></sup></td></tr></table>
|
||||
<!--l. 115--><p class="noindent" >
|
||||
<table
|
||||
cellpadding="0" border="0" cellspacing="0"
|
||||
class="tabbing"><tr
|
||||
style="vertical-align:baseline;" class="tabbing"><td style="width:16;"
|
||||
class="tabbing"> </td><td
|
||||
class="tabbing">endif</td></tr></table>
|
||||
<!--l. 115--><p class="noindent" >
|
||||
<table
|
||||
cellpadding="0" border="0" cellspacing="0"
|
||||
class="tabbing"><tr
|
||||
style="vertical-align:baseline;" class="tabbing"><td style="width:16;"
|
||||
class="tabbing"> </td><td
|
||||
class="tabbing">return <span
|
||||
class="cmmi-10x-x-109">u</span><sup><span
|
||||
class="cmmi-8">k</span></sup></td></tr></table>
|
||||
<!--l. 115--><p class="noindent" >
|
||||
<table
|
||||
cellpadding="0" border="0" cellspacing="0"
|
||||
class="tabbing"><tr
|
||||
style="vertical-align:baseline;" class="tabbing"><td
|
||||
class="tabbing">end</td></tr></table>
|
||||
<!--l. 115--><p class="noindent" > </div> </div>
|
||||
<!--l. 138--><p class="noindent" >
|
||||
|
||||
|
||||
|
||||
<div class="minipage"><pre class="verbatim" id="verbatim-6">
|
||||
  use psb_base_mod
|
||||
  use amg_prec_mod
|
||||
  use psb_krylov_mod
|
||||
... ...
|
||||
!
|
||||
! sparse matrix
|
||||
  type(psb_dspmat_type) :: A
|
||||
! sparse matrix descriptor
|
||||
  type(psb_desc_type)   :: desc_A
|
||||
! preconditioner
|
||||
  type(amg_dprec_type)  :: P
|
||||
! right-hand side and solution vectors
|
||||
  type(psb_d_vect_type) :: b, x
|
||||
... ...
|
||||
!
|
||||
! initialize the parallel environment
|
||||
  call psb_init(ictxt)
|
||||
  call psb_info(ictxt,iam,np)
|
||||
... ...
|
||||
!
|
||||
! read and assemble the spd matrix A and the right-hand side b
|
||||
! using PSBLAS routines for sparse matrix / vector management
|
||||
... ...
|
||||
!
|
||||
! initialize the default multilevel preconditioner, i.e. V-cycle
|
||||
! with basic smoothed aggregation, 1 hybrid forward/backward
|
||||
! GS sweep as pre/post-smoother and UMFPACK as coarsest-level
|
||||
! solver
|
||||
  call P%init(’ML’,info)
|
||||
!
|
||||
! build the preconditioner
|
||||
  call P%hierarchy_build(A,desc_A,info)
|
||||
  call P%smoothers_build(A,desc_A,info)
|
||||
!
|
||||
! set the solver parameters and the initial guess
|
||||
  ... ...
|
||||
!
|
||||
! solve Ax=b with preconditioned CG
|
||||
  call psb_krylov(’CG’,A,P,b,x,tol,desc_A,info)
|
||||
  ... ...
|
||||
!
|
||||
! deallocate the preconditioner
|
||||
  call P%free(info)
|
||||
!
|
||||
! deallocate other data structures
|
||||
  ... ...
|
||||
!
|
||||
! exit the parallel environment
|
||||
  call psb_exit(ictxt)
|
||||
  stop
|
||||
</pre>
|
||||
<!--l. 193--><p class="nopar" >
|
||||
|
||||
|
||||
</div>
|
||||
<br /> <div class="caption"
|
||||
><span class="id">Figure 1: </span><span
|
||||
class="content">Application phase of a V-cycle preconditioner.</span></div><!--tex4ht:label?: x14-130021 -->
|
||||
class="content">setup and application of the default multilevel preconditioner (example 1). </span></div><!--tex4ht:label?: x14-130011 -->
|
||||
</div>
|
||||
|
||||
|
||||
|
||||
<!--l. 118--><p class="indent" > </div><hr class="endfigure">
|
||||
<!--l. 120--><p class="indent" > <span
|
||||
class="cmr-12">The components produced in the build phase may be combined in several ways to</span>
|
||||
<!--l. 199--><p class="indent" > </div><hr class="endfigure">
|
||||
<!--l. 201--><p class="indent" > <span
|
||||
class="cmr-12">Different versions of the multilevel preconditioner can be obtained by changing the</span>
|
||||
<span
|
||||
class="cmr-12">obtain different multilevel preconditioners; this is done in the application phase, i.e., in</span>
|
||||
<span
|
||||
class="cmr-12">the computation of a vector of type </span><span
|
||||
class="cmmi-12">w </span><span
|
||||
class="cmr-12">= </span><span
|
||||
class="cmmi-12">B</span><sup><span
|
||||
class="cmsy-8">-</span><span
|
||||
class="cmr-8">1</span></sup><span
|
||||
class="cmmi-12">v</span><span
|
||||
class="cmr-12">, where </span><span
|
||||
class="cmmi-12">B </span><span
|
||||
class="cmr-12">denotes the preconditioner,</span>
|
||||
<span
|
||||
class="cmr-12">usually within an iteration of a Krylov solver </span><span class="cite"><span
|
||||
class="cmr-12">[</span><a
|
||||
href="userhtmlli4.html#XSaad_book"><span
|
||||
class="cmr-12">24</span></a><span
|
||||
class="cmr-12">]</span></span><span
|
||||
class="cmr-12">. An example of such a combination,</span>
|
||||
<span
|
||||
class="cmr-12">known as V-cycle, is given in Figure</span><span
|
||||
class="cmr-12">default values of the preconditioner parameters. The code reported in Figure</span><span
|
||||
class="cmr-12"> </span><a
|
||||
href="#x14-130021"><span
|
||||
class="cmr-12">1</span><!--tex4ht:ref: fig:application_alg --></a><span
|
||||
class="cmr-12">. In this case, a single iteration of the same</span>
|
||||
href="#x14-130022"><span
|
||||
class="cmr-12">2</span><!--tex4ht:ref: fig:ex2 --></a> <span
|
||||
class="cmr-12">shows</span>
|
||||
<span
|
||||
class="cmr-12">smoother is used before and after the the recursive call to the V-cycle (i.e., in the</span>
|
||||
class="cmr-12">how to set a V-cycle preconditioner which applies 1 block-Jacobi sweep as pre- and</span>
|
||||
<span
|
||||
class="cmr-12">pre-smoothing and post-smoothing phases); however, different choices can be</span>
|
||||
class="cmr-12">post-smoother, and solves the coarsest-level system with 8 block-Jacobi sweeps. Note</span>
|
||||
<span
|
||||
class="cmr-12">performed. Other cycles can be defined; in MLD2P4, we implemented the</span>
|
||||
class="cmr-12">that the ILU(0) factorization (plus triangular solve) is used as local solver for the</span>
|
||||
<span
|
||||
class="cmr-12">standard V-cycle and W-cycle</span><span
|
||||
class="cmr-12"> </span><span class="cite"><span
|
||||
class="cmr-12">[</span><a
|
||||
href="userhtmlli4.html#XBriggs2000"><span
|
||||
class="cmr-12">3</span></a><span
|
||||
class="cmr-12">]</span></span><span
|
||||
class="cmr-12">, and a version of the K-cycle described</span>
|
||||
class="cmr-12">block-Jacobi sweeps, since this is the default associated with block-Jacobi</span>
|
||||
<span
|
||||
class="cmr-12">in</span><span
|
||||
class="cmr-12"> </span><span class="cite"><span
|
||||
class="cmr-12">[</span><a
|
||||
href="userhtmlli4.html#XNotay2008"><span
|
||||
class="cmr-12">23</span></a><span
|
||||
class="cmr-12">]</span></span><span
|
||||
class="cmr-12">and set by</span><span
|
||||
class="cmr-12"> </span><span class="obeylines-h"><span class="verb"><span
|
||||
class="cmtt-12">P%init</span></span></span><span
|
||||
class="cmr-12">. Furthermore, specifying block-Jacobi as coarsest-level</span>
|
||||
<span
|
||||
class="cmr-12">solver implies that the coarsest-level matrix is distributed among the processes.</span>
|
||||
<span
|
||||
class="cmr-12">Figure</span><span
|
||||
class="cmr-12"> </span><a
|
||||
href="#x14-130033"><span
|
||||
class="cmr-12">3</span><!--tex4ht:ref: fig:ex3 --></a> <span
|
||||
class="cmr-12">shows how to set a W-cycle preconditioner using the Coarsening</span>
|
||||
<span
|
||||
class="cmr-12">based on Compatible Weighted Matching. It applies 2 hybrid Gauss-Seidel</span>
|
||||
<span
|
||||
class="cmr-12">sweeps as pre- and post-smoother, and solves the coarsest-level system with the</span>
|
||||
<span
|
||||
class="cmr-12">multifrontal LU factorization implemented in MUMPS. It is specified that the</span>
|
||||
<span
|
||||
class="cmr-12">coarsest-level matrix is distributed, since MUMPS can be used on both replicated and</span>
|
||||
<span
|
||||
class="cmr-12">distributed matrices, and by default it is used on replicated ones. The code</span>
|
||||
<span
|
||||
class="cmr-12">fragments shown in Figures</span><span
|
||||
class="cmr-12"> </span><a
|
||||
href="#x14-130022"><span
|
||||
class="cmr-12">2</span><!--tex4ht:ref: fig:ex2 --></a> <span
|
||||
class="cmr-12">and </span><a
|
||||
href="#x14-130033"><span
|
||||
class="cmr-12">3</span><!--tex4ht:ref: fig:ex3 --></a> <span
|
||||
class="cmr-12">are included in the example program file</span>
|
||||
<span class="obeylines-h"><span class="verb"><span
|
||||
class="cmtt-12">amg_dexample_ml.f90</span></span></span> <span
|
||||
class="cmr-12">too. </span><span
|
||||
class="cmbx-12">DA CORREGGERE NEL CODICE ESEMPIO</span>
|
||||
<span
|
||||
class="cmbx-12">3</span>
|
||||
<!--l. 225--><p class="indent" > <span
|
||||
class="cmr-12">Finally, Figure</span><span
|
||||
class="cmr-12"> </span><a
|
||||
href="#x14-130044"><span
|
||||
class="cmr-12">4</span><!--tex4ht:ref: fig:ex4 --></a> <span
|
||||
class="cmr-12">shows the setup of a one-level additive Schwarz preconditioner,</span>
|
||||
<span
|
||||
class="cmr-12">i.e., RAS with overlap 2. Note also that a Krylov method different from CG</span>
|
||||
<span
|
||||
class="cmr-12">must be used to solve the preconditioned system, since the preconditione in</span>
|
||||
<span
|
||||
class="cmr-12">nonsymmetric. The corresponding example program is available in the file</span>
|
||||
<span class="obeylines-h"><span class="verb"><span
|
||||
class="cmtt-12">amg_dexample_1lev.f90</span></span></span><span
|
||||
class="cmr-12">.</span>
|
||||
<!--l. 232--><p class="indent" > <span
|
||||
class="cmr-12">For all the previous preconditioners, example programs where the sparse matrix and</span>
|
||||
<span
|
||||
class="cmr-12">the right-hand side are generated by discretizing a PDE with Dirichlet boundary</span>
|
||||
<span
|
||||
class="cmr-12">conditions are also available in the directory </span><span class="obeylines-h"><span class="verb"><span
|
||||
class="cmtt-12">examples/pdegen</span></span></span><span
|
||||
class="cmr-12">.</span>
|
||||
<!--l. 236--><p class="indent" > <hr class="figure"><div class="figure"
|
||||
>
|
||||
|
||||
|
||||
|
||||
<!--l. 133--><div class="crosslinks"><p class="noindent"><span
|
||||
<a
|
||||
id="x14-130022"></a>
|
||||
|
||||
|
||||
|
||||
<div class="center"
|
||||
>
|
||||
<!--l. 237--><p class="noindent" >
|
||||
<div class="minipage"><pre class="verbatim" id="verbatim-7">
|
||||
... ...
|
||||
! build a V-cycle preconditioner with 1 block-Jacobi sweep (with
|
||||
! ILU(0) on the blocks) as pre- and post-smoother, and 8  block-Jacobi
|
||||
! sweeps (with ILU(0) on the blocks) as coarsest-level solver
|
||||
  call P%init(’ML’,info)
|
||||
  call_P%set(’SMOOTHER_TYPE’,’BJAC’,info)
|
||||
  call P%set(’COARSE_SOLVE’,’BJAC’,info)
|
||||
  call P%set(’COARSE_SWEEPS’,8,info)
|
||||
  call P%hierarchy_build(A,desc_A,info)
|
||||
  call P%smoothers_build(A,desc_A,info)
|
||||
... ...
|
||||
</pre>
|
||||
<!--l. 252--><p class="nopar" ></div>
|
||||
<br /><div class="caption"
|
||||
><span class="id">Figure 2: </span><span
|
||||
class="content">setup of a multilevel preconditioner based on the default decoupled coarsening</span></div><!--tex4ht:label?: x14-130022 -->
|
||||
</div>
|
||||
|
||||
|
||||
|
||||
<!--l. 258--><p class="indent" > </div><hr class="endfigure">
|
||||
<!--l. 260--><p class="indent" > <hr class="figure"><div class="figure"
|
||||
>
|
||||
|
||||
|
||||
|
||||
<a
|
||||
id="x14-130033"></a>
|
||||
|
||||
|
||||
|
||||
<div class="center"
|
||||
>
|
||||
<!--l. 261--><p class="noindent" >
|
||||
<div class="minipage"><pre class="verbatim" id="verbatim-8">
|
||||
... ...
|
||||
! build a W-cycle preconditioner with 2 hybrid Gauss-Seidel sweeps
|
||||
! as pre- and post-smoother, a distributed coarsest
|
||||
! matrix, and MUMPS as coarsest-level solver
|
||||
  call P%init(’ML’,info)
|
||||
  call P%set(’PAR_AGGR_ALG’,’COUPLED’,info)
|
||||
  call P%set(’ML_CYCLE’,’WCYCLE’,info)
|
||||
  call P%set(’SMOOTHER_TYPE’,’FBGS’,info)
|
||||
  call P%set(’SMOOTHER_SWEEPS’,2,info)
|
||||
  call P%set(’COARSE_SOLVE’,’MUMPS’,info)
|
||||
  call P%set(’COARSE_MAT’,’DIST’,info)
|
||||
  call P%hierarchy_build(A,desc_A,info)
|
||||
  call P%smoothers_build(A,desc_A,info)
|
||||
... ...
|
||||
</pre>
|
||||
<!--l. 279--><p class="nopar" ></div>
|
||||
<br /> <div class="caption"
|
||||
><span class="id">Figure 3: </span><span
|
||||
class="content">setup of a multilevel preconditioner based on the coupled coarsening based
|
||||
on weighted matching</span></div><!--tex4ht:label?: x14-130033 -->
|
||||
</div>
|
||||
|
||||
|
||||
|
||||
<!--l. 284--><p class="indent" > </div><hr class="endfigure">
|
||||
<!--l. 286--><p class="indent" > <hr class="figure"><div class="figure"
|
||||
>
|
||||
|
||||
|
||||
|
||||
<a
|
||||
id="x14-130044"></a>
|
||||
|
||||
|
||||
|
||||
<div class="center"
|
||||
>
|
||||
<!--l. 287--><p class="noindent" >
|
||||
<div class="minipage"><pre class="verbatim" id="verbatim-9">
|
||||
... ...
|
||||
! set RAS with overlap 2 and ILU(0) on the local blocks
|
||||
  call P%init(’AS’,info)
|
||||
  call P%set(’SUB_OVR’,2,info)
|
||||
  call P%bld(A,desc_A,info)
|
||||
... ...
|
||||
! solve Ax=b with preconditioned BiCGSTAB
|
||||
  call psb_krylov(’BICGSTAB’,A,P,b,x,tol,desc_A,info)
|
||||
</pre>
|
||||
<!--l. 299--><p class="nopar" ></div>
|
||||
<br /> <div class="caption"
|
||||
><span class="id">Figure 4: </span><span
|
||||
class="content">setup of a one-level Schwarz preconditioner.</span></div><!--tex4ht:label?: x14-130044 -->
|
||||
</div>
|
||||
|
||||
|
||||
|
||||
<!--l. 304--><p class="indent" > </div><hr class="endfigure">
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
<!--l. 1--><div class="crosslinks"><p class="noindent"><span
|
||||
class="cmr-12">[</span><a
|
||||
href="userhtmlsu7.html" ><span
|
||||
class="cmr-12">next</span></a><span
|
||||
class="cmr-12">] [</span><a
|
||||
href="userhtmlsu6.html" ><span
|
||||
class="cmr-12">front</span></a><span
|
||||
class="cmr-12">] [</span><a
|
||||
href="userhtmlse4.html#userhtmlsu6.html" ><span
|
||||
class="cmr-12">up</span></a><span
|
||||
class="cmr-12">] </span></p></div>
|
||||
<!--l. 133--><p class="indent" > <a
|
||||
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|
||||
id="tailuserhtmlsu6.html"></a>
|
||||
</body></html>
|
||||
|
||||
+79
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|
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"http://www.w3.org/TR/html4/loose.dtd">
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||||
<html >
|
||||
<head><title>Smoothed Aggregation</title>
|
||||
<head><title>Method init</title>
|
||||
<meta http-equiv="Content-Type" content="text/html; charset=iso-8859-1">
|
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<meta name="generator" content="TeX4ht (https://tug.org/tex4ht/)">
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|
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<link rel="stylesheet" type="text/css" href="userhtml.css">
|
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</head><body
|
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>
|
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<!--l. 133--><div class="crosslinks"><p class="noindent"><span
|
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<!--l. 43--><div class="crosslinks"><p class="noindent"><span
|
||||
class="cmr-12">[</span><a
|
||||
href="userhtmlsu8.html" ><span
|
||||
class="cmr-12">next</span></a><span
|
||||
class="cmr-12">] [</span><a
|
||||
href="userhtmlsu6.html" ><span
|
||||
class="cmr-12">prev</span></a><span
|
||||
class="cmr-12">] [</span><a
|
||||
href="userhtmlsu6.html#tailuserhtmlsu6.html" ><span
|
||||
class="cmr-12">prev-tail</span></a><span
|
||||
class="cmr-12">] [</span><a
|
||||
href="#tailuserhtmlsu7.html"><span
|
||||
class="cmr-12">tail</span></a><span
|
||||
class="cmr-12">] [</span><a
|
||||
href="userhtmlse4.html#userhtmlsu7.html" ><span
|
||||
href="userhtmlse5.html#userhtmlsu7.html" ><span
|
||||
class="cmr-12">up</span></a><span
|
||||
class="cmr-12">] </span></p></div>
|
||||
<h4 class="subsectionHead"><span class="titlemark"><span
|
||||
class="cmr-12">4.2 </span></span> <a
|
||||
id="x15-140004.2"></a><span
|
||||
class="cmr-12">Smoothed Aggregation</span></h4>
|
||||
<!--l. 135--><p class="noindent" ><span
|
||||
class="cmr-12">In order to define the prolongator </span><span
|
||||
class="cmmi-12">P</span><sup><span
|
||||
class="cmmi-8">k</span></sup><span
|
||||
class="cmr-12">, used to compute the coarse-level matrix </span><span
|
||||
class="cmmi-12">A</span><sup><span
|
||||
class="cmmi-8">k</span><span
|
||||
class="cmr-8">+1</span></sup><span
|
||||
class="cmr-12">,</span>
|
||||
class="cmr-12">5.1 </span></span> <a
|
||||
id="x16-150005.1"></a><span
|
||||
class="cmr-12">Method init</span></h4>
|
||||
<div class="center"
|
||||
>
|
||||
<!--l. 45--><p class="noindent" >
|
||||
<!--l. 46--><p class="noindent" ><span class="obeylines-h"><span class="verb"><span
|
||||
class="cmtt-12">call</span><span
|
||||
class="cmtt-12"> p%init(icontx,ptype,info)</span></span></span></div>
|
||||
<!--l. 49--><p class="noindent" ><span
|
||||
class="cmr-12">This method allocates and initializes the preconditioner </span><span class="obeylines-h"><span class="verb"><span
|
||||
class="cmtt-12">p</span></span></span><span
|
||||
class="cmr-12">, according to the</span>
|
||||
<span
|
||||
class="cmr-12">MLD2P4 uses the smoothed aggregation algorithm described in </span><span class="cite"><span
|
||||
class="cmr-12">[</span><a
|
||||
href="userhtmlli4.html#XBREZINA_VANEK"><span
|
||||
class="cmr-12">2</span></a><span
|
||||
class="cmr-12">,</span><span
|
||||
class="cmr-12">preconditioner type chosen by the user.</span>
|
||||
<!--l. 53--><p class="noindent" ><span
|
||||
class="cmbx-12">Arguments</span>
|
||||
<div class="tabular"> <table id="TBL-2" class="tabular"
|
||||
cellspacing="0" cellpadding="0"
|
||||
><colgroup id="TBL-2-1g"><col
|
||||
id="TBL-2-1"><col
|
||||
id="TBL-2-2"></colgroup><tr
|
||||
style="vertical-align:baseline;" id="TBL-2-1-"><td style="white-space:normal; text-align:left;" id="TBL-2-1-1"
|
||||
class="td11"><!--l. 57--><p class="noindent" ><span class="obeylines-h"><span class="verb"><span
|
||||
class="cmtt-12">icontxt</span></span></span> </td> <td style="white-space:normal; text-align:left;" id="TBL-2-1-2"
|
||||
class="td11"><!--l. 57--><p class="noindent" ><span class="obeylines-h"><span class="verb"><span
|
||||
class="cmtt-12">integer,</span><span
|
||||
class="cmtt-12"> intent(in)</span></span></span><span
|
||||
class="cmr-12">.</span> </td>
|
||||
</tr><tr
|
||||
style="vertical-align:baseline;" id="TBL-2-2-"><td style="white-space:normal; text-align:left;" id="TBL-2-2-1"
|
||||
class="td11"><!--l. 58--><p class="noindent" > </td><td style="white-space:normal; text-align:left;" id="TBL-2-2-2"
|
||||
class="td11"><!--l. 58--><p class="noindent" ><span
|
||||
class="cmr-12">The communication context.</span> </td></tr><tr
|
||||
style="vertical-align:baseline;" id="TBL-2-3-"><td style="white-space:normal; text-align:left;" id="TBL-2-3-1"
|
||||
class="td11"><!--l. 59--><p class="noindent" ><span class="obeylines-h"><span class="verb"><span
|
||||
class="cmtt-12">ptype</span></span></span> </td> <td style="white-space:normal; text-align:left;" id="TBL-2-3-2"
|
||||
class="td11"><!--l. 59--><p class="noindent" ><span class="obeylines-h"><span class="verb"><span
|
||||
class="cmtt-12">character(len=*),</span><span
|
||||
class="cmtt-12"> intent(in)</span></span></span><span
|
||||
class="cmr-12">.</span></td>
|
||||
</tr><tr
|
||||
style="vertical-align:baseline;" id="TBL-2-4-"><td style="white-space:normal; text-align:left;" id="TBL-2-4-1"
|
||||
class="td11"><!--l. 60--><p class="noindent" > </td><td style="white-space:normal; text-align:left;" id="TBL-2-4-2"
|
||||
class="td11"><!--l. 60--><p class="noindent" ><span
|
||||
class="cmr-12">The type of preconditioner. Its values are specified in Table</span><span
|
||||
class="cmr-12"> </span><a
|
||||
href="userhtmlli4.html#XVANEK_MANDEL_BREZINA"><span
|
||||
class="cmr-12">29</span></a><span
|
||||
class="cmr-12">]</span></span><span
|
||||
class="cmr-12">. The basic idea</span>
|
||||
<span
|
||||
class="cmr-12">of this algorithm is to build a coarse set of indices Ω</span><sup><span
|
||||
class="cmmi-8">k</span><span
|
||||
class="cmr-8">+1</span></sup> <span
|
||||
class="cmr-12">by suitably grouping the</span>
|
||||
<span
|
||||
class="cmr-12">indices of Ω</span><sup><span
|
||||
class="cmmi-8">k</span></sup> <span
|
||||
class="cmr-12">into disjoint subsets (aggregates), and to define the coarse-to-fine space</span>
|
||||
<span
|
||||
class="cmr-12">transfer operator </span><span
|
||||
class="cmmi-12">P</span><sup><span
|
||||
class="cmmi-8">k</span></sup> <span
|
||||
class="cmr-12">by applying a suitable smoother to a simple piecewise constant</span>
|
||||
<span
|
||||
class="cmr-12">prolongation operator, with the aim of improving the quality of the coarse-space</span>
|
||||
<span
|
||||
class="cmr-12">correction.</span>
|
||||
<!--l. 144--><p class="indent" > <span
|
||||
class="cmr-12">Three main steps can be identified in the smoothed aggregation procedure:</span>
|
||||
<ol class="enumerate1" >
|
||||
<li
|
||||
class="enumerate" id="x15-14002x1"><span
|
||||
class="cmr-12">aggregation of the indices of Ω</span><sup><span
|
||||
class="cmmi-8">k</span></sup> <span
|
||||
class="cmr-12">to obtain Ω</span><sup><span
|
||||
class="cmmi-8">k</span><span
|
||||
class="cmr-8">+1</span></sup><span
|
||||
class="cmr-12">;</span>
|
||||
</li>
|
||||
<li
|
||||
class="enumerate" id="x15-14004x2"><span
|
||||
class="cmr-12">construction of the prolongator </span><span
|
||||
class="cmmi-12">P</span><sup><span
|
||||
class="cmmi-8">k</span></sup><span
|
||||
class="cmr-12">;</span>
|
||||
</li>
|
||||
<li
|
||||
class="enumerate" id="x15-14006x3"><span
|
||||
class="cmr-12">application of </span><span
|
||||
class="cmmi-12">P</span><sup><span
|
||||
class="cmmi-8">k</span></sup> <span
|
||||
class="cmr-12">and </span><span
|
||||
class="cmmi-12">R</span><sup><span
|
||||
class="cmmi-8">k</span></sup> <span
|
||||
class="cmr-12">= (</span><span
|
||||
class="cmmi-12">P</span><sup><span
|
||||
class="cmmi-8">k</span></sup><span
|
||||
class="cmr-12">)</span><sup><span
|
||||
class="cmmi-8">T</span> </sup> <span
|
||||
class="cmr-12">to build </span><span
|
||||
class="cmmi-12">A</span><sup><span
|
||||
class="cmmi-8">k</span><span
|
||||
class="cmr-8">+1</span></sup><span
|
||||
class="cmr-12">.</span></li></ol>
|
||||
<!--l. 151--><p class="indent" > <span
|
||||
class="cmr-12">In order to perform the coarsening step, the smoothed aggregation algorithm</span>
|
||||
<span
|
||||
class="cmr-12">described in</span><span
|
||||
class="cmr-12"> </span><span class="cite"><span
|
||||
class="cmr-12">[</span><a
|
||||
href="userhtmlli4.html#XVANEK_MANDEL_BREZINA"><span
|
||||
class="cmr-12">29</span></a><span
|
||||
class="cmr-12">]</span></span> <span
|
||||
class="cmr-12">is used. In this algorithm, each index </span><span
|
||||
class="cmmi-12">j </span><span
|
||||
class="cmsy-10x-x-120">∈ </span><span
|
||||
class="cmr-12">Ω</span><sup><span
|
||||
class="cmmi-8">k</span><span
|
||||
class="cmr-8">+1</span></sup> <span
|
||||
class="cmr-12">corresponds</span>
|
||||
<span
|
||||
class="cmr-12">to an aggregate Ω</span><sub><span
|
||||
class="cmmi-8">j</span></sub><sup><span
|
||||
class="cmmi-8">k</span></sup> <span
|
||||
class="cmr-12">of Ω</span><sup><span
|
||||
class="cmmi-8">k</span></sup><span
|
||||
class="cmr-12">, consisting of a suitably chosen index </span><span
|
||||
class="cmmi-12">i </span><span
|
||||
class="cmsy-10x-x-120">∈ </span><span
|
||||
class="cmr-12">Ω</span><sup><span
|
||||
class="cmmi-8">k</span></sup> <span
|
||||
class="cmr-12">and</span>
|
||||
<span
|
||||
class="cmr-12">indices that are (usually) contained in a strongly-coupled neighborood of </span><span
|
||||
class="cmmi-12">i</span><span
|
||||
class="cmr-12">,</span>
|
||||
<span
|
||||
class="cmr-12">i.e.,</span>
|
||||
<table
|
||||
class="equation"><tr><td>
|
||||
<center class="math-display" >
|
||||
<img
|
||||
src="userhtml13x.png" alt=" { ∘ -------}
|
||||
Ωkj ⊂ N ki (θ) = r ∈ Ωk : |akir| > θ |akiiakrr| ∪ {i} ,
|
||||
" class="math-display" ><a
|
||||
id="x15-14007r3"></a></center></td><td class="equation-label"><span
|
||||
class="cmr-12">(3)</span></td></tr></table>
|
||||
href="userhtmlse4.html#x13-120151"><span
|
||||
class="cmr-12">1</span><!--tex4ht:ref: tab:precinit --></a><span
|
||||
class="cmr-12">.</span> </td>
|
||||
</tr><tr
|
||||
style="vertical-align:baseline;" id="TBL-2-5-"><td style="white-space:normal; text-align:left;" id="TBL-2-5-1"
|
||||
class="td11"><!--l. 62--><p class="noindent" > </td><td style="white-space:normal; text-align:left;" id="TBL-2-5-2"
|
||||
class="td11"><!--l. 62--><p class="noindent" ><span
|
||||
class="cmr-12">Note that the strings are case insensitive.</span> </td>
|
||||
</tr><tr
|
||||
style="vertical-align:baseline;" id="TBL-2-6-"><td style="white-space:normal; text-align:left;" id="TBL-2-6-1"
|
||||
class="td11"><!--l. 63--><p class="noindent" ><span class="obeylines-h"><span class="verb"><span
|
||||
class="cmtt-12">info</span></span></span> </td><td style="white-space:normal; text-align:left;" id="TBL-2-6-2"
|
||||
class="td11"><!--l. 63--><p class="noindent" ><span class="obeylines-h"><span class="verb"><span
|
||||
class="cmtt-12">integer,</span><span
|
||||
class="cmtt-12"> intent(out)</span></span></span><span
|
||||
class="cmr-12">.</span> </td>
|
||||
</tr><tr
|
||||
style="vertical-align:baseline;" id="TBL-2-7-"><td style="white-space:normal; text-align:left;" id="TBL-2-7-1"
|
||||
class="td11"><!--l. 64--><p class="noindent" > </td><td style="white-space:normal; text-align:left;" id="TBL-2-7-2"
|
||||
class="td11"><!--l. 64--><p class="noindent" ><span
|
||||
class="cmr-12">Error code. If no error, 0 is returned. See Section</span><span
|
||||
class="cmr-12"> </span><a
|
||||
href="userhtmlse7.html#x26-300007"><span
|
||||
class="cmr-12">7</span><!--tex4ht:ref: sec:errors --></a> <span
|
||||
class="cmr-12">for details.</span> </td>
|
||||
</tr><tr
|
||||
style="vertical-align:baseline;" id="TBL-2-8-"><td style="white-space:normal; text-align:left;" id="TBL-2-8-1"
|
||||
class="td11"> </td> </tr></table></div>
|
||||
|
||||
|
||||
|
||||
<!--l. 160--><p class="nopar" >
|
||||
<span
|
||||
class="cmr-12">for a given threshold </span><span
|
||||
class="cmmi-12">θ </span><span
|
||||
class="cmsy-10x-x-120">∈ </span><span
|
||||
class="cmr-12">[0</span><span
|
||||
class="cmmi-12">, </span><span
|
||||
class="cmr-12">1] (see</span><span
|
||||
class="cmr-12"> </span><span class="cite"><span
|
||||
class="cmr-12">[</span><a
|
||||
href="userhtmlli4.html#XVANEK_MANDEL_BREZINA"><span
|
||||
class="cmr-12">29</span></a><span
|
||||
class="cmr-12">]</span></span> <span
|
||||
class="cmr-12">for the details). Since this algorithm has a</span>
|
||||
<span
|
||||
class="cmr-12">sequential nature, a decoupled version of it is applied, where each processor</span>
|
||||
<span
|
||||
class="cmr-12">independently executes the algorithm on the set of indices assigned to it in the initial</span>
|
||||
<span
|
||||
class="cmr-12">data distribution. This version is embarrassingly parallel, since it does not require any</span>
|
||||
<span
|
||||
class="cmr-12">data communication. On the other hand, it may produce some nonuniform aggregates</span>
|
||||
<span
|
||||
class="cmr-12">and is strongly dependent on the number of processors and on the initial</span>
|
||||
<span
|
||||
class="cmr-12">partitioning of the matrix </span><span
|
||||
class="cmmi-12">A</span><span
|
||||
class="cmr-12">. Nevertheless, this parallel algorithm has been chosen</span>
|
||||
<span
|
||||
class="cmr-12">for MLD2P4, since it has been shown to produce good results in practice</span>
|
||||
<span class="cite"><span
|
||||
class="cmr-12">[</span><a
|
||||
href="userhtmlli4.html#Xaaecc_07"><span
|
||||
class="cmr-12">5</span></a><span
|
||||
class="cmr-12">,</span><span
|
||||
class="cmr-12"> </span><a
|
||||
href="userhtmlli4.html#Xapnum_07"><span
|
||||
class="cmr-12">8</span></a><span
|
||||
class="cmr-12">,</span><span
|
||||
class="cmr-12"> </span><a
|
||||
href="userhtmlli4.html#XTUMINARO_TONG"><span
|
||||
class="cmr-12">28</span></a><span
|
||||
class="cmr-12">]</span></span><span
|
||||
class="cmr-12">.</span>
|
||||
<!--l. 172--><p class="indent" > <span
|
||||
class="cmr-12">The prolongator </span><span
|
||||
class="cmmi-12">P</span><sup><span
|
||||
class="cmmi-8">k</span></sup> <span
|
||||
class="cmr-12">is built starting from a tentative prolongator</span> <span class="bar-css"><span
|
||||
class="cmmi-12">P</span></span><sup><span
|
||||
class="cmmi-8">k</span></sup> <span
|
||||
class="cmsy-10x-x-120">∈ </span><span
|
||||
class="msbm-10x-x-120">ℝ</span><sup><span
|
||||
class="cmmi-8">n</span><sub><span
|
||||
class="cmmi-6">k</span></sub><span
|
||||
class="cmsy-8">×</span><span
|
||||
class="cmmi-8">n</span><sub><span
|
||||
class="cmmi-6">k</span><span
|
||||
class="cmr-6">+1</span></sub></sup><span
|
||||
class="cmr-12">,</span>
|
||||
<span
|
||||
class="cmr-12">defined as</span>
|
||||
<table
|
||||
class="equation"><tr><td>
|
||||
<center class="math-display" >
|
||||
<img
|
||||
src="userhtml14x.png" alt=" { k
|
||||
P¯k = (¯pkij), p¯kij = 1 if i ∈ Ω j,
|
||||
0 otherwise,
|
||||
" class="math-display" ><a
|
||||
id="x15-14008r4"></a></center></td><td class="equation-label"><span
|
||||
class="cmr-12">(4)</span></td></tr></table>
|
||||
<!--l. 181--><p class="nopar" >
|
||||
<span
|
||||
class="cmr-12">where Ω</span><sub><span
|
||||
class="cmmi-8">j</span></sub><sup><span
|
||||
class="cmmi-8">k</span></sup> <span
|
||||
class="cmr-12">is the aggregate of Ω</span><sup><span
|
||||
class="cmmi-8">k</span></sup> <span
|
||||
class="cmr-12">corresponding to the index </span><span
|
||||
class="cmmi-12">j </span><span
|
||||
class="cmsy-10x-x-120">∈ </span><span
|
||||
class="cmr-12">Ω</span><sup><span
|
||||
class="cmmi-8">k</span><span
|
||||
class="cmr-8">+1</span></sup><span
|
||||
class="cmr-12">. </span><span
|
||||
class="cmmi-12">P</span><sup><span
|
||||
class="cmmi-8">k</span></sup> <span
|
||||
class="cmr-12">is obtained</span>
|
||||
<span
|
||||
class="cmr-12">by applying to</span> <span class="bar-css"><span
|
||||
class="cmmi-12">P</span></span><sup><span
|
||||
class="cmmi-8">k</span></sup> <span
|
||||
class="cmr-12">a smoother </span><span
|
||||
class="cmmi-12">S</span><sup><span
|
||||
class="cmmi-8">k</span></sup> <span
|
||||
class="cmsy-10x-x-120">∈ </span><span
|
||||
class="msbm-10x-x-120">ℝ</span><sup><span
|
||||
class="cmmi-8">n</span><sub><span
|
||||
class="cmmi-6">k</span></sub><span
|
||||
class="cmsy-8">×</span><span
|
||||
class="cmmi-8">n</span><sub><span
|
||||
class="cmmi-6">k</span></sub></sup><span
|
||||
class="cmr-12">:</span>
|
||||
<center class="math-display" >
|
||||
<img
|
||||
src="userhtml15x.png" alt="Pk = Sk ¯Pk, " class="math-display" ></center> <span
|
||||
class="cmr-12">in</span>
|
||||
<span
|
||||
class="cmr-12">order to remove nonsmooth components from the range of the prolongator, and hence</span>
|
||||
<span
|
||||
class="cmr-12">to improve the convergence properties of the multilevel method</span><span
|
||||
class="cmr-12"> </span><span class="cite"><span
|
||||
class="cmr-12">[</span><a
|
||||
href="userhtmlli4.html#XBREZINA_VANEK"><span
|
||||
class="cmr-12">2</span></a><span
|
||||
class="cmr-12">,</span><span
|
||||
class="cmr-12"> </span><a
|
||||
href="userhtmlli4.html#XStuben_01"><span
|
||||
class="cmr-12">27</span></a><span
|
||||
class="cmr-12">]</span></span><span
|
||||
class="cmr-12">. A simple</span>
|
||||
<span
|
||||
class="cmr-12">choice for </span><span
|
||||
class="cmmi-12">S</span><sup><span
|
||||
class="cmmi-8">k</span></sup> <span
|
||||
class="cmr-12">is the damped Jacobi smoother:</span>
|
||||
<center class="math-display" >
|
||||
<img
|
||||
src="userhtml16x.png" alt=" k k k -1 k
|
||||
S = I - ω (D ) A F,
|
||||
" class="math-display" ></center>
|
||||
<!--l. 195--><p class="nopar" > <span
|
||||
class="cmr-12">where </span><span
|
||||
class="cmmi-12">D</span><sup><span
|
||||
class="cmmi-8">k</span></sup> <span
|
||||
class="cmr-12">is the diagonal matrix with the same diagonal entries as </span><span
|
||||
class="cmmi-12">A</span><sup><span
|
||||
class="cmmi-8">k</span></sup><span
|
||||
class="cmr-12">, </span><span
|
||||
class="cmmi-12">A</span><sub>
|
||||
<span
|
||||
class="cmmi-8">F</span> </sub><sup><span
|
||||
class="cmmi-8">k</span></sup> <span
|
||||
class="cmr-12">= (</span><span class="bar-css"><span
|
||||
class="cmmi-12">a</span></span><sub>
|
||||
<span
|
||||
class="cmmi-8">ij</span></sub><sup><span
|
||||
class="cmmi-8">k</span></sup><span
|
||||
class="cmr-12">) is</span>
|
||||
<span
|
||||
class="cmr-12">the filtered matrix defined as</span>
|
||||
<table
|
||||
class="equation"><tr><td>
|
||||
<center class="math-display" >
|
||||
<img
|
||||
src="userhtml17x.png" alt=" { k k ∑
|
||||
a¯kij = aij if j ∈ N i (θ), (j ⁄= i), ¯akii = akii - (akij - ¯akij),
|
||||
0 otherwise, j⁄=i
|
||||
" class="math-display" ><a
|
||||
id="x15-14009r5"></a></center></td><td class="equation-label"><span
|
||||
class="cmr-12">(5)</span></td></tr></table>
|
||||
<!--l. 208--><p class="nopar" >
|
||||
<span
|
||||
class="cmr-12">and </span><span
|
||||
class="cmmi-12">ω</span><sup><span
|
||||
class="cmmi-8">k</span></sup> <span
|
||||
class="cmr-12">is an approximation of 4</span><span
|
||||
class="cmmi-12">∕</span><span
|
||||
class="cmr-12">(3</span><span
|
||||
class="cmmi-12">ρ</span><sup><span
|
||||
class="cmmi-8">k</span></sup><span
|
||||
class="cmr-12">), where </span><span
|
||||
class="cmmi-12">ρ</span><sup><span
|
||||
class="cmmi-8">k</span></sup> <span
|
||||
class="cmr-12">is the spectral radius of (</span><span
|
||||
class="cmmi-12">D</span><sup><span
|
||||
class="cmmi-8">k</span></sup><span
|
||||
class="cmr-12">)</span><sup><span
|
||||
class="cmsy-8">-</span><span
|
||||
class="cmr-8">1</span></sup><span
|
||||
class="cmmi-12">A</span><sub>
|
||||
<span
|
||||
class="cmmi-8">F</span> </sub><sup><span
|
||||
class="cmmi-8">k</span></sup>
|
||||
<span class="cite"><span
|
||||
class="cmr-12">[</span><a
|
||||
href="userhtmlli4.html#XBREZINA_VANEK"><span
|
||||
class="cmr-12">2</span></a><span
|
||||
class="cmr-12">]</span></span><span
|
||||
class="cmr-12">. In MLD2P4 this approximation is obtained by using </span><span
|
||||
class="cmsy-10x-x-120">∥</span><span
|
||||
class="cmmi-12">A</span><sub><span
|
||||
class="cmmi-8">F</span> </sub><sup><span
|
||||
class="cmmi-8">k</span></sup><span
|
||||
class="cmsy-10x-x-120">∥</span><sub>
|
||||
<span
|
||||
class="cmsy-8">∞</span></sub> <span
|
||||
class="cmr-12">as an estimate of </span><span
|
||||
class="cmmi-12">ρ</span><sup><span
|
||||
class="cmmi-8">k</span></sup><span
|
||||
class="cmr-12">.</span>
|
||||
<span
|
||||
class="cmr-12">Note that for systems coming from uniformly elliptic problems, filtering the matrix </span><span
|
||||
class="cmmi-12">A</span><sup><span
|
||||
class="cmmi-8">k</span></sup>
|
||||
<span
|
||||
class="cmr-12">has little or no effect, and </span><span
|
||||
class="cmmi-12">A</span><sup><span
|
||||
class="cmmi-8">k</span></sup> <span
|
||||
class="cmr-12">can be used instead of </span><span
|
||||
class="cmmi-12">A</span><sub>
|
||||
<span
|
||||
class="cmmi-8">F</span> </sub><sup><span
|
||||
class="cmmi-8">k</span></sup><span
|
||||
class="cmr-12">. The latter choice is the</span>
|
||||
<span
|
||||
class="cmr-12">default in MLD2P4.</span>
|
||||
|
||||
|
||||
|
||||
<!--l. 216--><div class="crosslinks"><p class="noindent"><span
|
||||
<!--l. 73--><div class="crosslinks"><p class="noindent"><span
|
||||
class="cmr-12">[</span><a
|
||||
href="userhtmlsu8.html" ><span
|
||||
class="cmr-12">next</span></a><span
|
||||
class="cmr-12">] [</span><a
|
||||
href="userhtmlsu6.html" ><span
|
||||
class="cmr-12">prev</span></a><span
|
||||
class="cmr-12">] [</span><a
|
||||
href="userhtmlsu6.html#tailuserhtmlsu6.html" ><span
|
||||
class="cmr-12">prev-tail</span></a><span
|
||||
class="cmr-12">] [</span><a
|
||||
href="userhtmlsu7.html" ><span
|
||||
class="cmr-12">front</span></a><span
|
||||
class="cmr-12">] [</span><a
|
||||
href="userhtmlse4.html#userhtmlsu7.html" ><span
|
||||
href="userhtmlse5.html#userhtmlsu7.html" ><span
|
||||
class="cmr-12">up</span></a><span
|
||||
class="cmr-12">] </span></p></div>
|
||||
<!--l. 216--><p class="indent" > <a
|
||||
<!--l. 73--><p class="indent" > <a
|
||||
id="tailuserhtmlsu7.html"></a>
|
||||
</body></html>
|
||||
|
||||
+1679
-302
File diff suppressed because it is too large
Load Diff
+116
-351
@@ -1,7 +1,7 @@
|
||||
<!DOCTYPE html PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN"
|
||||
"http://www.w3.org/TR/html4/loose.dtd">
|
||||
<html >
|
||||
<head><title>Examples</title>
|
||||
<head><title>Method hierarchy_build</title>
|
||||
<meta http-equiv="Content-Type" content="text/html; charset=iso-8859-1">
|
||||
<meta name="generator" content="TeX4ht (https://tug.org/tex4ht/)">
|
||||
<meta name="originator" content="TeX4ht (https://tug.org/tex4ht/)">
|
||||
@@ -10,8 +10,17 @@
|
||||
<link rel="stylesheet" type="text/css" href="userhtml.css">
|
||||
</head><body
|
||||
>
|
||||
<!--l. 109--><div class="crosslinks"><p class="noindent"><span
|
||||
<!--l. 572--><div class="crosslinks"><p class="noindent"><span
|
||||
class="cmr-12">[</span><a
|
||||
href="userhtmlsu10.html" ><span
|
||||
class="cmr-12">next</span></a><span
|
||||
class="cmr-12">] [</span><a
|
||||
href="userhtmlsu8.html" ><span
|
||||
class="cmr-12">prev</span></a><span
|
||||
class="cmr-12">] [</span><a
|
||||
href="userhtmlsu8.html#tailuserhtmlsu8.html" ><span
|
||||
class="cmr-12">prev-tail</span></a><span
|
||||
class="cmr-12">] [</span><a
|
||||
href="#tailuserhtmlsu9.html"><span
|
||||
class="cmr-12">tail</span></a><span
|
||||
class="cmr-12">] [</span><a
|
||||
@@ -19,372 +28,128 @@ href="userhtmlse5.html#userhtmlsu9.html" ><span
|
||||
class="cmr-12">up</span></a><span
|
||||
class="cmr-12">] </span></p></div>
|
||||
<h4 class="subsectionHead"><span class="titlemark"><span
|
||||
class="cmr-12">5.1 </span></span> <a
|
||||
id="x18-170005.1"></a><span
|
||||
class="cmr-12">Examples</span></h4>
|
||||
<!--l. 111--><p class="noindent" ><span
|
||||
class="cmr-12">The code reported in Figure</span><span
|
||||
class="cmr-12"> </span><a
|
||||
href="#x18-170012"><span
|
||||
class="cmr-12">2</span><!--tex4ht:ref: fig:ex1 --></a> <span
|
||||
class="cmr-12">shows how to set and apply the default multilevel</span>
|
||||
class="cmr-12">5.3 </span></span> <a
|
||||
id="x18-170005.3"></a><span
|
||||
class="cmr-12">Method hierarchy</span><span
|
||||
class="cmr-12">_build</span></h4>
|
||||
<div class="center"
|
||||
>
|
||||
<!--l. 574--><p class="noindent" >
|
||||
<!--l. 575--><p class="noindent" ><span class="obeylines-h"><span class="verb"><span
|
||||
class="cmtt-12">call</span><span
|
||||
class="cmtt-12"> p%hierarchy_build(a,desc_a,info)</span></span></span><br />
|
||||
</div>
|
||||
<!--l. 578--><p class="noindent" ><span
|
||||
class="cmr-12">This method builds the hierarchy of matrices and restriction/prolongation operators for</span>
|
||||
<span
|
||||
class="cmr-12">preconditioner available in the real double precision version of AMG4PSBLAS</span>
|
||||
class="cmr-12">the multilevel preconditioner </span><span class="obeylines-h"><span class="verb"><span
|
||||
class="cmtt-12">p</span></span></span><span
|
||||
class="cmr-12">, according to the requirements made by the user</span>
|
||||
<span
|
||||
class="cmr-12">(see Table</span><span
|
||||
class="cmr-12"> </span><a
|
||||
href="userhtmlse5.html#x17-160151"><span
|
||||
class="cmr-12">1</span><!--tex4ht:ref: tab:precinit --></a><span
|
||||
class="cmr-12">). This preconditioner is chosen by simply specifying </span><span class="obeylines-h"><span class="verb"><span
|
||||
class="cmtt-12">’ML’</span></span></span> <span
|
||||
class="cmr-12">as the</span>
|
||||
<span
|
||||
class="cmr-12">second argument of </span><span class="obeylines-h"><span class="verb"><span
|
||||
class="cmtt-12">P%init</span></span></span> <span
|
||||
class="cmr-12">(a call to </span><span class="obeylines-h"><span class="verb"><span
|
||||
class="cmtt-12">P%set</span></span></span> <span
|
||||
class="cmr-12">is not needed) and is applied</span>
|
||||
<span
|
||||
class="cmr-12">with the CG solver provided by PSBLAS (the matrix of the system to be</span>
|
||||
<span
|
||||
class="cmr-12">solved is assumed to be positive definite). As previously observed, the modules</span>
|
||||
<span class="obeylines-h"><span class="verb"><span
|
||||
class="cmtt-12">psb_base_mod</span></span></span><span
|
||||
class="cmr-12">, </span><span class="obeylines-h"><span class="verb"><span
|
||||
class="cmtt-12">amg_prec_mod</span></span></span> <span
|
||||
class="cmr-12">through the methods </span><span class="obeylines-h"><span class="verb"><span
|
||||
class="cmtt-12">init</span></span></span> <span
|
||||
class="cmr-12">and </span><span class="obeylines-h"><span class="verb"><span
|
||||
class="cmtt-12">psb_krylov_mod</span></span></span> <span
|
||||
class="cmr-12">must be used by the example</span>
|
||||
class="cmtt-12">set</span></span></span><span
|
||||
class="cmr-12">.</span>
|
||||
<!--l. 583--><p class="noindent" ><span
|
||||
class="cmbx-12">Arguments</span>
|
||||
<div class="tabular"> <table id="TBL-11" class="tabular"
|
||||
cellspacing="0" cellpadding="0"
|
||||
><colgroup id="TBL-11-1g"><col
|
||||
id="TBL-11-1"><col
|
||||
id="TBL-11-2"></colgroup><tr
|
||||
style="vertical-align:baseline;" id="TBL-11-1-"><td style="white-space:normal; text-align:left;" id="TBL-11-1-1"
|
||||
class="td11"><!--l. 586--><p class="noindent" ><span class="obeylines-h"><span class="verb"><span
|
||||
class="cmtt-12">a</span></span></span> </td><td style="white-space:normal; text-align:left;" id="TBL-11-1-2"
|
||||
class="td11"><!--l. 586--><p class="noindent" ><span class="obeylines-h"><span class="verb"><span
|
||||
class="cmtt-12">type(psb_</span></span></span><span
|
||||
class="cmti-12">x</span><span class="obeylines-h"><span class="verb"><span
|
||||
class="cmtt-12">spmat_type),</span><span
|
||||
class="cmtt-12"> intent(in)</span></span></span><span
|
||||
class="cmr-12">.</span> </td>
|
||||
</tr><tr
|
||||
style="vertical-align:baseline;" id="TBL-11-2-"><td style="white-space:normal; text-align:left;" id="TBL-11-2-1"
|
||||
class="td11"><!--l. 587--><p class="noindent" > </td><td style="white-space:normal; text-align:left;" id="TBL-11-2-2"
|
||||
class="td11"><!--l. 587--><p class="noindent" ><span
|
||||
class="cmr-12">The sparse matrix structure containing the local part of the matrix</span>
|
||||
<span
|
||||
class="cmr-12">program.</span>
|
||||
<!--l. 121--><p class="indent" > <span
|
||||
class="cmr-12">The part of the code concerning the reading and assembling of the sparse matrix</span>
|
||||
class="cmr-12">to be preconditioned. Note that </span><span
|
||||
class="cmti-12">x </span><span
|
||||
class="cmr-12">must be chosen according to the</span>
|
||||
<span
|
||||
class="cmr-12">and the right-hand side vector, performed through the PSBLAS routines for sparse</span>
|
||||
class="cmr-12">real/complex, single/double precision version of AMG4PSBLAS</span>
|
||||
<span
|
||||
class="cmr-12">matrix and vector management, is not reported here for brevity; the statements</span>
|
||||
<span
|
||||
class="cmr-12">concerning the deallocation of the PSBLAS data structure are neglected too. The</span>
|
||||
<span
|
||||
class="cmr-12">complete code can be found in the example program file </span><span class="obeylines-h"><span class="verb"><span
|
||||
class="cmtt-12">amg_dexample_ml.f90</span></span></span><span
|
||||
class="cmr-12">, in the</span>
|
||||
<span
|
||||
class="cmr-12">directory </span><span class="obeylines-h"><span class="verb"><span
|
||||
class="cmtt-12">examples/fileread</span></span></span> <span
|
||||
class="cmr-12">of the AMG4PSBLAS implementation (see</span>
|
||||
<span
|
||||
class="cmr-12">Section</span><span
|
||||
class="cmr-12"> </span><a
|
||||
href="userhtmlsu5.html#x12-110003.5"><span
|
||||
class="cmr-12">3.5</span><!--tex4ht:ref: sec:ex_and_test --></a><span
|
||||
class="cmr-12">). A sample test problem along with the relevant input data is available in</span>
|
||||
<span class="obeylines-h"><span class="verb"><span
|
||||
class="cmtt-12">examples/fileread/runs</span></span></span><span
|
||||
class="cmr-12">. For details on the use of the PSBLAS routines, see the</span>
|
||||
<span
|
||||
class="cmr-12">PSBLAS User’s Guide</span><span
|
||||
class="cmr-12"> </span><span class="cite"><span
|
||||
class="cmr-12">under use. See the PSBLAS User’s Guide for details </span><span class="cite"><span
|
||||
class="cmr-12">[</span><a
|
||||
href="userhtmlli4.html#XPSBLASGUIDE"><span
|
||||
class="cmr-12">16</span></a><span
|
||||
class="cmr-12">]</span></span><span
|
||||
class="cmr-12">.</span>
|
||||
|
||||
|
||||
|
||||
<!--l. 133--><p class="indent" > <span
|
||||
class="cmr-12">The setup and application of the default multilevel preconditioner for the real single</span>
|
||||
class="cmr-12">.</span> </td>
|
||||
</tr><tr
|
||||
style="vertical-align:baseline;" id="TBL-11-3-"><td style="white-space:normal; text-align:left;" id="TBL-11-3-1"
|
||||
class="td11"><!--l. 592--><p class="noindent" ><span class="obeylines-h"><span class="verb"><span
|
||||
class="cmtt-12">desc_a</span></span></span></td><td style="white-space:normal; text-align:left;" id="TBL-11-3-2"
|
||||
class="td11"><!--l. 592--><p class="noindent" ><span class="obeylines-h"><span class="verb"><span
|
||||
class="cmtt-12">type(psb_desc_type),</span><span
|
||||
class="cmtt-12"> intent(in)</span></span></span><span
|
||||
class="cmr-12">.</span> </td>
|
||||
</tr><tr
|
||||
style="vertical-align:baseline;" id="TBL-11-4-"><td style="white-space:normal; text-align:left;" id="TBL-11-4-1"
|
||||
class="td11"><!--l. 593--><p class="noindent" > </td><td style="white-space:normal; text-align:left;" id="TBL-11-4-2"
|
||||
class="td11"><!--l. 593--><p class="noindent" ><span
|
||||
class="cmr-12">The communication descriptor of </span><span class="obeylines-h"><span class="verb"><span
|
||||
class="cmtt-12">a</span></span></span><span
|
||||
class="cmr-12">. See the PSBLAS User’s Guide</span>
|
||||
<span
|
||||
class="cmr-12">precision and the complex, single and double precision, versions are obtained</span>
|
||||
<span
|
||||
class="cmr-12">with straightforward modifications of the previous example (see Section</span><span
|
||||
class="cmr-12"> </span><a
|
||||
href="userhtmlse6.html#x19-180006"><span
|
||||
class="cmr-12">6</span><!--tex4ht:ref: sec:userinterface --></a> <span
|
||||
class="cmr-12">for</span>
|
||||
<span
|
||||
class="cmr-12">details). If these versions are installed, the corresponding codes are available in</span>
|
||||
<span class="obeylines-h"><span class="verb"><span
|
||||
class="cmtt-12">examples/fileread/</span></span></span><span
|
||||
class="cmr-12">.</span>
|
||||
<!--l. 139--><p class="indent" > <hr class="figure"><div class="figure"
|
||||
>
|
||||
|
||||
|
||||
|
||||
<a
|
||||
id="x18-170012"></a>
|
||||
|
||||
|
||||
|
||||
<div class="center"
|
||||
>
|
||||
<!--l. 140--><p class="noindent" >
|
||||
|
||||
|
||||
|
||||
<div class="minipage"><pre class="verbatim" id="verbatim-6">
|
||||
  use psb_base_mod
|
||||
  use amg_prec_mod
|
||||
  use psb_krylov_mod
|
||||
... ...
|
||||
!
|
||||
! sparse matrix
|
||||
  type(psb_dspmat_type) :: A
|
||||
! sparse matrix descriptor
|
||||
  type(psb_desc_type)   :: desc_A
|
||||
! preconditioner
|
||||
  type(amg_dprec_type)  :: P
|
||||
! right-hand side and solution vectors
|
||||
  type(psb_d_vect_type) :: b, x
|
||||
... ...
|
||||
!
|
||||
! initialize the parallel environment
|
||||
  call psb_init(ictxt)
|
||||
  call psb_info(ictxt,iam,np)
|
||||
... ...
|
||||
!
|
||||
! read and assemble the spd matrix A and the right-hand side b
|
||||
! using PSBLAS routines for sparse matrix / vector management
|
||||
... ...
|
||||
!
|
||||
! initialize the default multilevel preconditioner, i.e. V-cycle
|
||||
! with basic smoothed aggregation, 1 hybrid forward/backward
|
||||
! GS sweep as pre/post-smoother and UMFPACK as coarsest-level
|
||||
! solver
|
||||
  call P%init(’ML’,info)
|
||||
!
|
||||
! build the preconditioner
|
||||
  call P%hierarchy_build(A,desc_A,info)
|
||||
  call P%smoothers_build(A,desc_A,info)
|
||||
!
|
||||
! set the solver parameters and the initial guess
|
||||
  ... ...
|
||||
!
|
||||
! solve Ax=b with preconditioned CG
|
||||
  call psb_krylov(’CG’,A,P,b,x,tol,desc_A,info)
|
||||
  ... ...
|
||||
!
|
||||
! deallocate the preconditioner
|
||||
  call P%free(info)
|
||||
!
|
||||
! deallocate other data structures
|
||||
  ... ...
|
||||
!
|
||||
! exit the parallel environment
|
||||
  call psb_exit(ictxt)
|
||||
  stop
|
||||
</pre>
|
||||
<!--l. 195--><p class="nopar" >
|
||||
|
||||
|
||||
</div>
|
||||
<br /> <div class="caption"
|
||||
><span class="id">Figure 2: </span><span
|
||||
class="content">setup and application of the default multilevel preconditioner (example 1). </span></div><!--tex4ht:label?: x18-170012 -->
|
||||
</div>
|
||||
|
||||
|
||||
|
||||
<!--l. 201--><p class="indent" > </div><hr class="endfigure">
|
||||
<!--l. 203--><p class="indent" > <span
|
||||
class="cmr-12">Different versions of the multilevel preconditioner can be obtained by changing the</span>
|
||||
<span
|
||||
class="cmr-12">default values of the preconditioner parameters. The code reported in Figure</span><span
|
||||
class="cmr-12"> </span><a
|
||||
href="#x18-170023"><span
|
||||
class="cmr-12">3</span><!--tex4ht:ref: fig:ex2 --></a> <span
|
||||
class="cmr-12">shows</span>
|
||||
<span
|
||||
class="cmr-12">how to set a V-cycle preconditioner which applies 1 block-Jacobi sweep as pre- and</span>
|
||||
<span
|
||||
class="cmr-12">post-smoother, and solves the coarsest-level system with 8 block-Jacobi sweeps. Note</span>
|
||||
<span
|
||||
class="cmr-12">that the ILU(0) factorization (plus triangular solve) is used as local solver for the</span>
|
||||
<span
|
||||
class="cmr-12">block-Jacobi sweeps, since this is the default associated with block-Jacobi</span>
|
||||
<span
|
||||
class="cmr-12">and set by</span><span
|
||||
class="cmr-12"> </span><span class="obeylines-h"><span class="verb"><span
|
||||
class="cmtt-12">P%init</span></span></span><span
|
||||
class="cmr-12">. Furthermore, specifying block-Jacobi as coarsest-level</span>
|
||||
<span
|
||||
class="cmr-12">solver implies that the coarsest-level matrix is distributed among the processes.</span>
|
||||
<span
|
||||
class="cmr-12">Figure</span><span
|
||||
class="cmr-12"> </span><a
|
||||
href="#x18-170034"><span
|
||||
class="cmr-12">4</span><!--tex4ht:ref: fig:ex3 --></a> <span
|
||||
class="cmr-12">shows how to set a W-cycle preconditioner using the Coarsening</span>
|
||||
<span
|
||||
class="cmr-12">based on Compatible Weighted Matching. It applies 2 hybrid Gauss-Seidel</span>
|
||||
<span
|
||||
class="cmr-12">sweeps as pre- and post-smoother, and solves the coarsest-level system with the</span>
|
||||
<span
|
||||
class="cmr-12">multifrontal LU factorization implemented in MUMPS. It is specified that the</span>
|
||||
<span
|
||||
class="cmr-12">coarsest-level matrix is distributed, since MUMPS can be used on both replicated and</span>
|
||||
<span
|
||||
class="cmr-12">distributed matrices, and by default it is used on replicated ones. The code</span>
|
||||
<span
|
||||
class="cmr-12">fragments shown in Figures</span><span
|
||||
class="cmr-12"> </span><a
|
||||
href="#x18-170023"><span
|
||||
class="cmr-12">3</span><!--tex4ht:ref: fig:ex2 --></a> <span
|
||||
class="cmr-12">and </span><a
|
||||
href="#x18-170034"><span
|
||||
class="cmr-12">4</span><!--tex4ht:ref: fig:ex3 --></a> <span
|
||||
class="cmr-12">are included in the example program file</span>
|
||||
<span class="obeylines-h"><span class="verb"><span
|
||||
class="cmtt-12">amg_dexample_ml.f90</span></span></span> <span
|
||||
class="cmr-12">too. </span><span
|
||||
class="cmbx-12">DA CORREGGERE NEL CODICE ESEMPIO</span>
|
||||
<span
|
||||
class="cmbx-12">3</span>
|
||||
<!--l. 228--><p class="indent" > <span
|
||||
class="cmr-12">Finally, Figure</span><span
|
||||
class="cmr-12"> </span><a
|
||||
href="#x18-170045"><span
|
||||
class="cmr-12">5</span><!--tex4ht:ref: fig:ex4 --></a> <span
|
||||
class="cmr-12">shows the setup of a one-level additive Schwarz preconditioner,</span>
|
||||
<span
|
||||
class="cmr-12">i.e., RAS with overlap 2. Note also that a Krylov method different from CG</span>
|
||||
<span
|
||||
class="cmr-12">must be used to solve the preconditioned system, since the preconditione in</span>
|
||||
<span
|
||||
class="cmr-12">nonsymmetric. The corresponding example program is available in the file</span>
|
||||
<span class="obeylines-h"><span class="verb"><span
|
||||
class="cmtt-12">amg_dexample_1lev.f90</span></span></span><span
|
||||
class="cmr-12">.</span>
|
||||
<!--l. 235--><p class="indent" > <span
|
||||
class="cmr-12">For all the previous preconditioners, example programs where the sparse matrix and</span>
|
||||
<span
|
||||
class="cmr-12">the right-hand side are generated by discretizing a PDE with Dirichlet boundary</span>
|
||||
<span
|
||||
class="cmr-12">conditions are also available in the directory </span><span class="obeylines-h"><span class="verb"><span
|
||||
class="cmtt-12">examples/pdegen</span></span></span><span
|
||||
class="cmr-12">.</span>
|
||||
<!--l. 239--><p class="indent" > <hr class="figure"><div class="figure"
|
||||
>
|
||||
|
||||
|
||||
|
||||
<a
|
||||
id="x18-170023"></a>
|
||||
|
||||
|
||||
|
||||
<div class="center"
|
||||
>
|
||||
<!--l. 240--><p class="noindent" >
|
||||
<div class="minipage"><pre class="verbatim" id="verbatim-7">
|
||||
... ...
|
||||
! build a V-cycle preconditioner with 1 block-Jacobi sweep (with
|
||||
! ILU(0) on the blocks) as pre- and post-smoother, and 8  block-Jacobi
|
||||
! sweeps (with ILU(0) on the blocks) as coarsest-level solver
|
||||
  call P%init(’ML’,info)
|
||||
  call_P%set(’SMOOTHER_TYPE’,’BJAC’,info)
|
||||
  call P%set(’COARSE_SOLVE’,’BJAC’,info)
|
||||
  call P%set(’COARSE_SWEEPS’,8,info)
|
||||
  call P%hierarchy_build(A,desc_A,info)
|
||||
  call P%smoothers_build(A,desc_A,info)
|
||||
... ...
|
||||
</pre>
|
||||
<!--l. 255--><p class="nopar" ></div>
|
||||
<br /><div class="caption"
|
||||
><span class="id">Figure 3: </span><span
|
||||
class="content">setup of a multilevel preconditioner based on the default decoupled coarsening</span></div><!--tex4ht:label?: x18-170023 -->
|
||||
</div>
|
||||
|
||||
|
||||
|
||||
<!--l. 261--><p class="indent" > </div><hr class="endfigure">
|
||||
<!--l. 263--><p class="indent" > <hr class="figure"><div class="figure"
|
||||
>
|
||||
|
||||
|
||||
|
||||
<a
|
||||
id="x18-170034"></a>
|
||||
|
||||
|
||||
|
||||
<div class="center"
|
||||
>
|
||||
<!--l. 264--><p class="noindent" >
|
||||
<div class="minipage"><pre class="verbatim" id="verbatim-8">
|
||||
... ...
|
||||
! build a W-cycle preconditioner with 2 hybrid Gauss-Seidel sweeps
|
||||
! as pre- and post-smoother, a distributed coarsest
|
||||
! matrix, and MUMPS as coarsest-level solver
|
||||
  call P%init(’ML’,info)
|
||||
  call P%set(’PAR_AGGR_ALG’,’COUPLED’,info)
|
||||
  call P%set(’ML_CYCLE’,’WCYCLE’,info)
|
||||
  call P%set(’SMOOTHER_TYPE’,’FBGS’,info)
|
||||
  call P%set(’SMOOTHER_SWEEPS’,2,info)
|
||||
  call P%set(’COARSE_SOLVE’,’MUMPS’,info)
|
||||
  call P%set(’COARSE_MAT’,’DIST’,info)
|
||||
  call P%hierarchy_build(A,desc_A,info)
|
||||
  call P%smoothers_build(A,desc_A,info)
|
||||
... ...
|
||||
</pre>
|
||||
<!--l. 282--><p class="nopar" ></div>
|
||||
<br /> <div class="caption"
|
||||
><span class="id">Figure 4: </span><span
|
||||
class="content">setup of a multilevel preconditioner based on the coupled coarsening based
|
||||
on weighted matching</span></div><!--tex4ht:label?: x18-170034 -->
|
||||
</div>
|
||||
|
||||
|
||||
|
||||
<!--l. 287--><p class="indent" > </div><hr class="endfigure">
|
||||
<!--l. 289--><p class="indent" > <hr class="figure"><div class="figure"
|
||||
>
|
||||
|
||||
|
||||
|
||||
<a
|
||||
id="x18-170045"></a>
|
||||
|
||||
|
||||
|
||||
<div class="center"
|
||||
>
|
||||
<!--l. 290--><p class="noindent" >
|
||||
<div class="minipage"><pre class="verbatim" id="verbatim-9">
|
||||
... ...
|
||||
! set RAS with overlap 2 and ILU(0) on the local blocks
|
||||
  call P%init(’AS’,info)
|
||||
  call P%set(’SUB_OVR’,2,info)
|
||||
  call P%bld(A,desc_A,info)
|
||||
... ...
|
||||
! solve Ax=b with preconditioned BiCGSTAB
|
||||
  call psb_krylov(’BICGSTAB’,A,P,b,x,tol,desc_A,info)
|
||||
</pre>
|
||||
<!--l. 302--><p class="nopar" ></div>
|
||||
<br /> <div class="caption"
|
||||
><span class="id">Figure 5: </span><span
|
||||
class="content">setup of a one-level Schwarz preconditioner.</span></div><!--tex4ht:label?: x18-170045 -->
|
||||
</div>
|
||||
|
||||
|
||||
|
||||
<!--l. 307--><p class="indent" > </div><hr class="endfigure">
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
<!--l. 1--><div class="crosslinks"><p class="noindent"><span
|
||||
class="cmr-12">for details </span><span class="cite"><span
|
||||
class="cmr-12">[</span><a
|
||||
href="userhtmlli4.html#XPSBLASGUIDE"><span
|
||||
class="cmr-12">16</span></a><span
|
||||
class="cmr-12">]</span></span><span
|
||||
class="cmr-12">.</span> </td>
|
||||
</tr><tr
|
||||
style="vertical-align:baseline;" id="TBL-11-5-"><td style="white-space:normal; text-align:left;" id="TBL-11-5-1"
|
||||
class="td11"><!--l. 596--><p class="noindent" ><span class="obeylines-h"><span class="verb"><span
|
||||
class="cmtt-12">info</span></span></span> </td><td style="white-space:normal; text-align:left;" id="TBL-11-5-2"
|
||||
class="td11"><!--l. 596--><p class="noindent" ><span class="obeylines-h"><span class="verb"><span
|
||||
class="cmtt-12">integer,</span><span
|
||||
class="cmtt-12"> intent(out)</span></span></span><span
|
||||
class="cmr-12">.</span> </td>
|
||||
</tr><tr
|
||||
style="vertical-align:baseline;" id="TBL-11-6-"><td style="white-space:normal; text-align:left;" id="TBL-11-6-1"
|
||||
class="td11"><!--l. 597--><p class="noindent" > </td><td style="white-space:normal; text-align:left;" id="TBL-11-6-2"
|
||||
class="td11"><!--l. 597--><p class="noindent" ><span
|
||||
class="cmr-12">Error code. If no error, 0 is returned. See Section</span><span
|
||||
class="cmr-12"> </span><a
|
||||
href="userhtmlse7.html#x26-300007"><span
|
||||
class="cmr-12">7</span><!--tex4ht:ref: sec:errors --></a> <span
|
||||
class="cmr-12">for details.</span> </td>
|
||||
</tr><tr
|
||||
style="vertical-align:baseline;" id="TBL-11-7-"><td style="white-space:normal; text-align:left;" id="TBL-11-7-1"
|
||||
class="td11"> </td> </tr></table></div>
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
<!--l. 603--><div class="crosslinks"><p class="noindent"><span
|
||||
class="cmr-12">[</span><a
|
||||
href="userhtmlsu10.html" ><span
|
||||
class="cmr-12">next</span></a><span
|
||||
class="cmr-12">] [</span><a
|
||||
href="userhtmlsu8.html" ><span
|
||||
class="cmr-12">prev</span></a><span
|
||||
class="cmr-12">] [</span><a
|
||||
href="userhtmlsu8.html#tailuserhtmlsu8.html" ><span
|
||||
class="cmr-12">prev-tail</span></a><span
|
||||
class="cmr-12">] [</span><a
|
||||
href="userhtmlsu9.html" ><span
|
||||
class="cmr-12">front</span></a><span
|
||||
class="cmr-12">] [</span><a
|
||||
href="userhtmlse5.html#userhtmlsu9.html" ><span
|
||||
class="cmr-12">up</span></a><span
|
||||
class="cmr-12">] </span></p></div>
|
||||
<!--l. 1--><p class="indent" > <a
|
||||
<!--l. 603--><p class="indent" > <a
|
||||
id="tailuserhtmlsu9.html"></a>
|
||||
</body></html>
|
||||
|
||||
+44
-2
@@ -2,9 +2,8 @@
|
||||
\markboth{\textsc{AMG4PSBLAS User's and Reference Guide}}
|
||||
{\textsc{\ref{sec:license} License}}
|
||||
|
||||
{\bf DA CONTROLLARE E MODIFICARE INCLUDENDO I CREDITS A MLD2P4}
|
||||
|
||||
The AMG4PSBLAS is freely distributable under the following copyright
|
||||
AMG4PSBLAS is freely distributable under the following copyright
|
||||
terms: {\small
|
||||
\begin{verbatim}
|
||||
|
||||
@@ -44,3 +43,46 @@ terms: {\small
|
||||
|
||||
\end{verbatim}
|
||||
}
|
||||
\newpage
|
||||
AMG4PSBLAS is an evolution of MLD2P4, whose license we reproduce here
|
||||
to abide by its terms: {\small
|
||||
\begin{verbatim}
|
||||
|
||||
|
||||
MLD2P4 version 2.2
|
||||
MultiLevel Domain Decomposition Parallel Preconditioners Package
|
||||
based on PSBLAS (Parallel Sparse BLAS version 3.5)
|
||||
|
||||
(C) Copyright 2008-2018
|
||||
|
||||
Salvatore Filippone
|
||||
Pasqua D'Ambra
|
||||
Daniela di Serafino
|
||||
|
||||
|
||||
Redistribution and use in source and binary forms, with or without
|
||||
modification, are permitted provided that the following conditions
|
||||
are met:
|
||||
1. Redistributions of source code must retain the above copyright
|
||||
notice, this list of conditions and the following disclaimer.
|
||||
2. Redistributions in binary form must reproduce the above copyright
|
||||
notice, this list of conditions, and the following disclaimer in the
|
||||
documentation and/or other materials provided with the distribution.
|
||||
3. The name of the MLD2P4 group or the names of its contributors may
|
||||
not be used to endorse or promote products derived from this
|
||||
software without specific written permission.
|
||||
|
||||
THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
|
||||
``AS IS'' AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED
|
||||
TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR
|
||||
PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE MLD2P4 GROUP OR ITS CONTRIBUTORS
|
||||
BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR
|
||||
CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF
|
||||
SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS
|
||||
INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN
|
||||
CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
|
||||
ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
|
||||
POSSIBILITY OF SUCH DAMAGE.
|
||||
|
||||
\end{verbatim}
|
||||
}
|
||||
@@ -89,7 +89,7 @@
|
||||
\newcommand{\precdata}{\hyperlink{precdata}{{\tt mld\_prec\_type}}}
|
||||
\newcommand{\descdata}{\hyperlink{descdata}{{\tt psb\_desc\_type}}}
|
||||
\newcommand{\spdata}{\hyperlink{spdata}{{\tt psb\_spmat\_type}}}
|
||||
\newcommand{\Ref}[1]{\mbox{(\ref{#1})}}
|
||||
%\newcommand{\Ref}[1]{\mbox{(\ref{#1})}}
|
||||
|
||||
\begin{document}
|
||||
\pdfbookmark{AMG4PSBLAS User's and Reference Guide}{title}
|
||||
|
||||
@@ -87,7 +87,7 @@
|
||||
\newcommand{\precdata}{\hyperlink{precdata}{{\tt mld\_prec\_type}}}
|
||||
\newcommand{\descdata}{\hyperlink{descdata}{{\tt psb\_desc\_type}}}
|
||||
\newcommand{\spdata}{\hyperlink{spdata}{{\tt psb\_spmat\_type}}}
|
||||
\newcommand{\Ref}[1]{\mbox{(\ref{#1})}}
|
||||
%\newcommand{\Ref}[1]{\mbox{(\ref{#1})}}
|
||||
|
||||
\begin{document}
|
||||
{\LARGE\bfseries MLD2P4\\[.8ex] User's and Reference Guide}\\[\baselineskip]
|
||||
|
||||
+17
-15
@@ -240,28 +240,30 @@ be applied.
|
||||
\bsideways
|
||||
\begin{center}
|
||||
%\begin{tabular}{|p{5cm}|l|p{2.4cm}|p{2.5cm}|p{5cm}|}
|
||||
\begin{tabular}{|p{3.9cm}|l|p{2.3cm}|p{2.9cm}|p{6.9cm}|}
|
||||
\begin{tabular}{|p{5.7cm}|l|p{2.3cm}|p{2.5cm}|p{6.9cm}|}
|
||||
\hline
|
||||
\verb|what| & \textsc{data type} & \verb|val| & \textsc{default} &
|
||||
\textsc{comments} \\ \hline
|
||||
\verb|'MIN_COARSE_SIZE'| & \verb|integer|
|
||||
& Any number \par $> 0$
|
||||
& $\lfloor 40 \sqrt[3]{n} \rfloor$, where $n$ is the dimension
|
||||
of the matrix at the finest level
|
||||
& Coarse size threshold. The aggregation stops
|
||||
if the global number of variables of the
|
||||
computed coarsest matrix
|
||||
is lower than or equal to this threshold
|
||||
(see Note).
|
||||
\\ \hline
|
||||
\verb|'MIN_COARSE_SIZE_PROCESS'| & \verb|integer|
|
||||
\verb|'MIN_COARSE_SIZE_PER_PROCESS'| & \verb|integer|
|
||||
& Any number \par $> 0$
|
||||
& $200$
|
||||
& Coarse size threshold per process. The aggregation stops
|
||||
if the number of variables of the
|
||||
computed coarsest matrix on the local process
|
||||
if the global number of variables of the
|
||||
computed coarsest matrix
|
||||
is lower than or equal to this threshold
|
||||
(see Note).
|
||||
multiplied by the number of processes.
|
||||
|
||||
\\ \hline
|
||||
\verb|'MIN_COARSE_SIZE'| & \verb|integer|
|
||||
& Any number \par $> 0$
|
||||
& -1
|
||||
& Coarse size threshold. The aggregation stops
|
||||
if the global number of variables of the
|
||||
computed coarsest matrix
|
||||
is lower than or equal to this threshold
|
||||
(see Note). If negative, it is ignored in
|
||||
favour of the default for
|
||||
\verb|'MIN_COARSE_SIZE_PER_PROCESS'|.
|
||||
\\ \hline
|
||||
|
||||
\verb|'MIN_CR_RATIO'| & \verb|real|
|
||||
|
||||
Reference in New Issue
Block a user