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@ -11,222 +11,208 @@
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</head><body
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>
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<!--l. 1--><div class="crosslinks"><p class="noindent"><span
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class="cmbx-12">[</span><a
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class="cmbx-12">] [</span><a
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class="cmr-12">] [</span><a
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class="cmbx-12">] </span></p></div>
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class="cmr-12">up</span></a><span
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class="cmr-12">] </span></p></div>
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<h3 class="sectionHead"><span class="titlemark"><span
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class="cmbx-12">5 </span></span> <a
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class="cmr-12">5 </span></span> <a
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id="x17-160005"></a><span
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class="cmbx-12">Getting Started</span></h3>
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class="cmr-12">Getting Started</span></h3>
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<!--l. 5--><p class="noindent" ><span
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class="cmbx-12">We describe the basics for building and applying AMG4PSBLAS one-level</span>
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class="cmr-12">We describe the basics for building and applying AMG4PSBLAS one-level and</span>
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<span
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class="cmbx-12">and multilevel (i.e., AMG) preconditioners with the Krylov solvers included</span>
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<span
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class="cmbx-12">in PSBLAS </span><span class="cite"><span
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class="cmbx-12">[</span><a
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class="cmr-12">multilevel (i.e., AMG) preconditioners with the Krylov solvers included in PSBLAS</span>
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<span class="cite"><span
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class="cmr-12">[</span><a
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href="userhtmlli4.html#XPSBLASGUIDE"><span
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class="cmbx-12">15</span></a><span
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class="cmbx-12">]</span></span><span
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class="cmbx-12">. The following steps are required:</span>
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class="cmr-12">15</span></a><span
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class="cmr-12">]</span></span><span
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class="cmr-12">. The following steps are required:</span>
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<ol class="enumerate1" >
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<li
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class="enumerate" id="x17-16002x1"><span
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class="cmbxti-10x-x-120">Declare the preconditioner data structure</span><span
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class="cmbx-12">. It is a derived data</span>
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<span
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class="cmbx-12">type, </span><span class="obeylines-h"><span class="verb"><span
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class="cmti-12">Declare the preconditioner data structure</span><span
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class="cmr-12">. It is a derived data type,</span>
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<span class="obeylines-h"><span class="verb"><span
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class="cmtt-12">amg_</span></span></span><span
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class="cmbxti-10x-x-120">x</span><span class="obeylines-h"><span class="verb"><span
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class="cmti-12">x</span><span class="obeylines-h"><span class="verb"><span
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class="cmtt-12">prec_</span></span></span> <span class="obeylines-h"><span class="verb"><span
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class="cmtt-12">type</span></span></span><span
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class="cmbx-12">, where </span><span
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class="cmbxti-10x-x-120">x </span><span
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class="cmbx-12">may be </span><span class="obeylines-h"><span class="verb"><span
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class="cmr-12">, where </span><span
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class="cmti-12">x </span><span
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class="cmr-12">may be </span><span class="obeylines-h"><span class="verb"><span
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class="cmtt-12">s</span></span></span><span
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class="cmbx-12">, </span><span class="obeylines-h"><span class="verb"><span
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class="cmr-12">, </span><span class="obeylines-h"><span class="verb"><span
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class="cmtt-12">d</span></span></span><span
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class="cmbx-12">, </span><span class="obeylines-h"><span class="verb"><span
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class="cmr-12">, </span><span class="obeylines-h"><span class="verb"><span
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class="cmtt-12">c</span></span></span> <span
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class="cmbx-12">or </span><span class="obeylines-h"><span class="verb"><span
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class="cmr-12">or </span><span class="obeylines-h"><span class="verb"><span
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class="cmtt-12">z</span></span></span><span
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class="cmbx-12">, according to the</span>
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class="cmr-12">, according to the basic data</span>
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<span
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class="cmbx-12">basic data type of the sparse matrix (</span><span class="obeylines-h"><span class="verb"><span
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class="cmr-12">type of the sparse matrix (</span><span class="obeylines-h"><span class="verb"><span
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class="cmtt-12">s</span></span></span> <span
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class="cmbx-12">= real single precision; </span><span class="obeylines-h"><span class="verb"><span
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class="cmr-12">= real single precision; </span><span class="obeylines-h"><span class="verb"><span
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class="cmtt-12">d</span></span></span> <span
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class="cmbx-12">=</span>
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<span
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class="cmbx-12">real double precision; </span><span class="obeylines-h"><span class="verb"><span
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class="cmr-12">= real double precision;</span>
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<span class="obeylines-h"><span class="verb"><span
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class="cmtt-12">c</span></span></span> <span
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class="cmbx-12">= complex single precision; </span><span class="obeylines-h"><span class="verb"><span
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class="cmr-12">= complex single precision; </span><span class="obeylines-h"><span class="verb"><span
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class="cmtt-12">z</span></span></span> <span
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class="cmbx-12">= complex</span>
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class="cmr-12">= complex double precision). This data</span>
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<span
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class="cmbx-12">double precision). This data structure is accessed by the user only</span>
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class="cmr-12">structure is accessed by the user only through the AMG4PSBLAS routines,</span>
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<span
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class="cmbx-12">through the AMG4PSBLAS routines, following an object-oriented</span>
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<span
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class="cmbx-12">approach.</span>
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class="cmr-12">following an object-oriented approach.</span>
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</li>
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<li
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class="enumerate" id="x17-16004x2"><span
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class="cmbxti-10x-x-120">Allocate and initialize the preconditioner data structure,</span>
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<span
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class="cmbxti-10x-x-120">according to a preconditioner type chosen by the user</span><span
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class="cmbx-12">. This is</span>
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class="cmti-12">Allocate and initialize the preconditioner data structure, according to a</span>
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<span
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class="cmbx-12">performed by the routine </span><span class="obeylines-h"><span class="verb"><span
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class="cmti-12">preconditioner type chosen by the user</span><span
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class="cmr-12">. This is performed by the routine</span>
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<span class="obeylines-h"><span class="verb"><span
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class="cmtt-12">init</span></span></span><span
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class="cmbx-12">, which also sets defaults for each</span>
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class="cmr-12">, which also sets defaults for each preconditioner type selected by</span>
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<span
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class="cmbx-12">preconditioner type selected by the user. The preconditioner types</span>
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class="cmr-12">the user. The preconditioner types and the defaults associated with them</span>
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<span
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class="cmbx-12">and the defaults associated with them are given in Table</span><span
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class="cmbx-12"> </span><a
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class="cmr-12">are given in Table</span><span
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class="cmr-12"> </span><a
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href="#x17-160151"><span
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class="cmbx-12">1</span><!--tex4ht:ref: tab:precinit --></a><span
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class="cmbx-12">, where</span>
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<span
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class="cmbx-12">the strings used by </span><span class="obeylines-h"><span class="verb"><span
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class="cmr-12">1</span><!--tex4ht:ref: tab:precinit --></a><span
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class="cmr-12">, where the strings used by </span><span class="obeylines-h"><span class="verb"><span
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class="cmtt-12">init</span></span></span> <span
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class="cmbx-12">to identify the preconditioner types are</span>
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class="cmr-12">to identify the</span>
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<span
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class="cmbx-12">also given. Note that these strings are valid also if uppercase letters</span>
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class="cmr-12">preconditioner types are also given. Note that these strings are valid also if</span>
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<span
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class="cmbx-12">are substituted by corresponding lowercase ones.</span>
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class="cmr-12">uppercase letters are substituted by corresponding lowercase ones.</span>
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</li>
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<li
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class="enumerate" id="x17-16006x3"><span
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class="cmbxti-10x-x-120">Modify the selected preconditioner type, by properly setting</span>
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class="cmti-12">Modify the selected preconditioner type, by properly setting preconditioner</span>
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<span
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class="cmbxti-10x-x-120">preconditioner parameters. </span><span
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class="cmbx-12">This is performed by the routine </span><span class="obeylines-h"><span class="verb"><span
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class="cmti-12">parameters. </span><span
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class="cmr-12">This is performed by the routine </span><span class="obeylines-h"><span class="verb"><span
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class="cmtt-12">set</span></span></span><span
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class="cmbx-12">.</span>
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class="cmr-12">. This routine must be</span>
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<span
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class="cmbx-12">This routine must be called only if the user wants to modify</span>
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class="cmr-12">called only if the user wants to modify the default values of the parameters</span>
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<span
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class="cmbx-12">the default values of the parameters associated with the selected</span>
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class="cmr-12">associated with the selected preconditioner type, to obtain a variant of that</span>
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<span
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class="cmbx-12">preconditioner type, to obtain a variant of that preconditioner.</span>
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<span
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class="cmbx-12">Examples of use of </span><span class="obeylines-h"><span class="verb"><span
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class="cmr-12">preconditioner. Examples of use of </span><span class="obeylines-h"><span class="verb"><span
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class="cmtt-12">set</span></span></span> <span
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class="cmbx-12">are given in Section</span><span
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class="cmbx-12"> </span><a
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class="cmr-12">are given in Section</span><span
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class="cmr-12"> </span><a
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href="userhtmlsu9.html#x18-170005.1"><span
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class="cmbx-12">5.1</span><!--tex4ht:ref: sec:examples --></a><span
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class="cmbx-12">; a complete list</span>
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class="cmr-12">5.1</span><!--tex4ht:ref: sec:examples --></a><span
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class="cmr-12">; a complete</span>
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<span
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class="cmbx-12">of all the preconditioner parameters and their allowed and default</span>
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class="cmr-12">list of all the preconditioner parameters and their allowed and default values</span>
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<span
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class="cmbx-12">values is provided in Section</span><span
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class="cmbx-12"> </span><a
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class="cmr-12">is provided in Section</span><span
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class="cmr-12"> </span><a
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href="userhtmlse6.html#x19-180006"><span
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class="cmbx-12">6</span><!--tex4ht:ref: sec:userinterface --></a><span
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class="cmbx-12">, Tables</span><span
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class="cmbx-12"> </span><a
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class="cmr-12">6</span><!--tex4ht:ref: sec:userinterface --></a><span
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class="cmr-12">, Tables</span><span
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class="cmr-12"> </span><a
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href="userhtmlsu11.html#x21-200092"><span
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class="cmbx-12">2</span><!--tex4ht:ref: tab:p_cycle --></a><span
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class="cmbx-12">-</span><a
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class="cmr-12">2</span><!--tex4ht:ref: tab:p_cycle --></a><span
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class="cmr-12">-</span><a
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href="userhtmlsu11.html#x21-200158"><span
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class="cmbx-12">8</span><!--tex4ht:ref: tab:p_smoother_1 --></a><span
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class="cmbx-12">.</span>
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class="cmr-12">8</span><!--tex4ht:ref: tab:p_smoother_1 --></a><span
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class="cmr-12">.</span>
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</li>
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<li
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class="enumerate" id="x17-16008x4"><span
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class="cmbxti-10x-x-120">Build the preconditioner for a given matrix</span><span
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class="cmbx-12">. If the selected</span>
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<span
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class="cmbx-12">preconditioner is multilevel, then two steps must be performed, as</span>
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class="cmti-12">Build the preconditioner for a given matrix</span><span
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class="cmr-12">. If the selected preconditioner is</span>
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<span
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class="cmbx-12">specified next.</span>
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class="cmr-12">multilevel, then two steps must be performed, as specified next.</span>
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<ol class="enumerate2" >
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<li
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class="enumerate" id="x17-16009x0"><span
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class="cmbxti-10x-x-120">Build the aggregation hierarchy for a given matrix. </span><span
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class="cmbx-12">This is</span>
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class="cmti-12">Build the AMG hierarchy for a given matrix. </span><span
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class="cmr-12">This is performed by the</span>
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<span
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class="cmbx-12">performed by the routine </span><span class="obeylines-h"><span class="verb"><span
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class="cmr-12">routine </span><span class="obeylines-h"><span class="verb"><span
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class="cmtt-12">hierarchy_build</span></span></span><span
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class="cmbx-12">.</span>
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class="cmr-12">.</span>
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</li>
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<li
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class="enumerate" id="x17-16010x0"><span
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|
|
class="cmbxti-10x-x-120">Build the preconditioner for a given matrix. </span><span
|
|
|
|
|
class="cmbx-12">This is</span>
|
|
|
|
|
class="cmti-12">Build the preconditioner for a given matrix. </span><span
|
|
|
|
|
class="cmr-12">This is performed by the</span>
|
|
|
|
|
<span
|
|
|
|
|
class="cmbx-12">performed by the routine </span><span class="obeylines-h"><span class="verb"><span
|
|
|
|
|
class="cmr-12">routine </span><span class="obeylines-h"><span class="verb"><span
|
|
|
|
|
class="cmtt-12">smoothers_build</span></span></span><span
|
|
|
|
|
class="cmbx-12">.</span></li></ol>
|
|
|
|
|
class="cmr-12">.</span></li></ol>
|
|
|
|
|
<!--l. 41--><p class="noindent" ><span
|
|
|
|
|
class="cmbx-12">If the selected preconditioner is one-level, it is built in a single step,</span>
|
|
|
|
|
class="cmr-12">If the selected preconditioner is one-level, it is built in a single step, performed by</span>
|
|
|
|
|
<span
|
|
|
|
|
class="cmbx-12">performed by the routine </span><span class="obeylines-h"><span class="verb"><span
|
|
|
|
|
class="cmr-12">the routine </span><span class="obeylines-h"><span class="verb"><span
|
|
|
|
|
class="cmtt-12">bld</span></span></span><span
|
|
|
|
|
class="cmbx-12">.</span>
|
|
|
|
|
class="cmr-12">.</span>
|
|
|
|
|
</li>
|
|
|
|
|
<li
|
|
|
|
|
class="enumerate" id="x17-16012x5"><span
|
|
|
|
|
class="cmbxti-10x-x-120">Apply the preconditioner at each iteration of a Krylov solver. </span><span
|
|
|
|
|
class="cmbx-12">This is</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="cmbx-12">performed by the method </span><span class="obeylines-h"><span class="verb"><span
|
|
|
|
|
class="cmr-12">the method </span><span class="obeylines-h"><span class="verb"><span
|
|
|
|
|
class="cmtt-12">apply</span></span></span><span
|
|
|
|
|
class="cmbx-12">. When using the PSBLAS Krylov</span>
|
|
|
|
|
class="cmr-12">. When using the PSBLAS Krylov solvers, this step is</span>
|
|
|
|
|
<span
|
|
|
|
|
class="cmbx-12">solvers, this step is completely transparent to the user, since </span><span class="obeylines-h"><span class="verb"><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="cmbx-12">is</span>
|
|
|
|
|
<span
|
|
|
|
|
class="cmbx-12">called by the PSBLAS routine implementing the Krylov solver</span>
|
|
|
|
|
class="cmr-12">is called by the PSBLAS routine</span>
|
|
|
|
|
<span
|
|
|
|
|
class="cmbx-12">(</span><span class="obeylines-h"><span class="verb"><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="cmbx-12">).</span>
|
|
|
|
|
class="cmr-12">).</span>
|
|
|
|
|
</li>
|
|
|
|
|
<li
|
|
|
|
|
class="enumerate" id="x17-16014x6"><span
|
|
|
|
|
class="cmbxti-10x-x-120">Free the preconditioner data structure</span><span
|
|
|
|
|
class="cmbx-12">. This is performed by the</span>
|
|
|
|
|
<span
|
|
|
|
|
class="cmbx-12">routine </span><span class="obeylines-h"><span class="verb"><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="cmbx-12">. This step is complementary to step 1 and should be</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="cmbx-12">performed when the preconditioner is no more used.</span></li></ol>
|
|
|
|
|
class="cmr-12">preconditioner is no more used.</span></li></ol>
|
|
|
|
|
<!--l. 52--><p class="indent" > <span
|
|
|
|
|
class="cmbx-12">All the previous routines are available as methods of the preconditioner</span>
|
|
|
|
|
class="cmr-12">All the previous routines are available as methods of the preconditioner object. A</span>
|
|
|
|
|
<span
|
|
|
|
|
class="cmbx-12">object. A detailed description of them is given in Section</span><span
|
|
|
|
|
class="cmbx-12"> </span><a
|
|
|
|
|
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="cmbx-12">6</span><!--tex4ht:ref: sec:userinterface --></a><span
|
|
|
|
|
class="cmbx-12">. Examples</span>
|
|
|
|
|
class="cmr-12">6</span><!--tex4ht:ref: sec:userinterface --></a><span
|
|
|
|
|
class="cmr-12">. Examples showing the basic use of</span>
|
|
|
|
|
<span
|
|
|
|
|
class="cmbx-12">showing the basic use of AMG4PSBLAS are reported in Section</span><span
|
|
|
|
|
class="cmbx-12"> </span><a
|
|
|
|
|
class="cmr-12">AMG4PSBLAS are reported in Section</span><span
|
|
|
|
|
class="cmr-12"> </span><a
|
|
|
|
|
href="userhtmlsu9.html#x18-170005.1"><span
|
|
|
|
|
class="cmbx-12">5.1</span><!--tex4ht:ref: sec:examples --></a><span
|
|
|
|
|
class="cmbx-12">.</span>
|
|
|
|
|
class="cmr-12">5.1</span><!--tex4ht:ref: sec:examples --></a><span
|
|
|
|
|
class="cmr-12">.</span>
|
|
|
|
|
<div class="table">
|
|
|
|
|
|
|
|
|
|
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|
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|
|
@ -261,7 +247,7 @@ 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:wrap; text-align:left;" id="TBL-1-1-3"
|
|
|
|
|
class="small-caps">g</span></span> </td><td style="white-space:wrap; 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
|
|
|
|
|
@ -284,73 +270,82 @@ 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="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:wrap; 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:wrap; 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>
|
|
|
|
|
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:wrap; 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> or
|
|
|
|
|
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">’JACOBI’</span></span></span> </td><td style="white-space:wrap; text-align:left;" id="TBL-1-3-3"
|
|
|
|
|
class="cmtt-10x-x-109">’L1-JACOBI’</span></span></span> </td><td style="white-space:wrap; 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
|
|
|
|
|
entry of the matrix to be preconditioned, the
|
|
|
|
|
corresponding entry of the preconditioner is set
|
|
|
|
|
to 1. </td>
|
|
|
|
|
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:wrap; 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> </td><td style="white-space:wrap; 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>
|
|
|
|
|
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:wrap; 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:wrap; 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> </td><td style="white-space:wrap; 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>
|
|
|
|
|
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:wrap; 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:wrap; 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> </td><td style="white-space:wrap; 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>
|
|
|
|
|
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:wrap; 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:wrap; 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:wrap; text-align:left;" id="TBL-1-7-3"
|
|
|
|
|
class="cmtt-10x-x-109">’AS’</span></span></span> </td><td style="white-space:wrap; 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>
|
|
|
|
|
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:wrap; 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:wrap; 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, basic
|
|
|
|
|
smoothed aggregation as coarsening algorithm,
|
|
|
|
|
and LU (plus triangular solve) as coarsest-level
|
|
|
|
|
solver. See the default values in Tables <a
|
|
|
|
|
class="cmtt-10x-x-109">’ML’</span></span></span> </td><td style="white-space:wrap; 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>
|
|
|
|
|
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"
|
|
|
|
|
@ -365,72 +360,70 @@ class="content">Preconditioner types, corresponding strings and default choices.
|
|
|
|
|
</div><hr class="endfloat" />
|
|
|
|
|
</div>
|
|
|
|
|
<!--l. 91--><p class="indent" > <span
|
|
|
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class="cmbx-12">Note that the module </span><span class="obeylines-h"><span class="verb"><span
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class="cmr-12">Note that the module </span><span class="obeylines-h"><span class="verb"><span
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class="cmtt-12">amg_prec_mod</span></span></span><span
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class="cmbx-12">, containing the definition of</span>
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class="cmr-12">, containing the definition of the preconditioner</span>
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<span
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class="cmbx-12">the preconditioner data type and the interfaces to the routines of</span>
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class="cmr-12">data type and the interfaces to the routines of AMG4PSBLAS, must be used</span>
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<span
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class="cmbx-12">AMG4PSBLAS, must be used in any program calling such routines. The</span>
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<span
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class="cmbx-12">modules </span><span class="obeylines-h"><span class="verb"><span
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class="cmr-12">in any program calling such routines. The modules </span><span class="obeylines-h"><span class="verb"><span
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class="cmtt-12">psb_base_mod</span></span></span><span
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class="cmbx-12">, for the sparse matrix and communication descriptor</span>
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class="cmr-12">, for the</span>
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<span
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class="cmbx-12">data types, and </span><span class="obeylines-h"><span class="verb"><span
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class="cmr-12">sparse matrix and communication descriptor data types, and </span><span class="obeylines-h"><span class="verb"><span
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class="cmtt-12">psb_krylov_mod</span></span></span><span
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class="cmbx-12">, for interfacing with the Krylov solvers,</span>
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class="cmr-12">,</span>
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<span
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class="cmbx-12">must be also used (see Section</span><span
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class="cmbx-12"> </span><a
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class="cmr-12">for interfacing with the Krylov solvers, must be also used (see Section</span><span
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class="cmr-12"> </span><a
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href="userhtmlsu9.html#x18-170005.1"><span
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class="cmbx-12">5.1</span><!--tex4ht:ref: sec:examples --></a><span
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class="cmbx-12">). </span><br
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class="cmr-12">5.1</span><!--tex4ht:ref: sec:examples --></a><span
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class="cmr-12">).</span>
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<br
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class="newline" />
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<!--l. 98--><p class="indent" > <span
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class="cmbx-12">Remark 1. Coarsest-level solvers based on the LU factorization, such as</span>
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<span
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class="cmbx-12">those implemented in UMFPACK, MUMPS, SuperLU, and SuperLU</span><span
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class="cmbx-12">_Dist,</span>
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class="cmbx-12">Remark 1. </span><span
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class="cmr-12">Coarsest-level solvers based on the LU factorization, such as those</span>
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<span
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class="cmbx-12">usually lead to smaller numbers of preconditioned Krylov iterations</span>
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class="cmr-12">implemented in UMFPACK, MUMPS, SuperLU, and SuperLU</span><span
|
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class="cmr-12">_Dist, usually lead to</span>
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<span
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class="cmbx-12">than inexact solvers, when the linear system comes from a standard</span>
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class="cmr-12">smaller numbers of preconditioned Krylov iterations than inexact solvers, when the</span>
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<span
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class="cmbx-12">discretization of basic scalar elliptic PDE problems. However, this does not</span>
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class="cmr-12">linear system comes from a standard discretization of basic scalar elliptic PDE</span>
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<span
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class="cmbx-12">necessarily correspond to the smallest execution time on parallel</span>
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class="cmr-12">problems. However, this does not necessarily correspond to the shortest execution time</span>
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<span
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class="cmbx-12">computers.</span>
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class="cmr-12">on parallel computers.</span>
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<!--l. 107--><p class="indent" > <span
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class="cmbxti-10x-x-120">DA MODIFICARE PER INSERIRE TIPO DI AGGREGAZIONE</span>
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class="cmti-12">DA MODIFICARE PER INSERIRE TIPO DI AGGREGAZIONE</span>
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<div class="subsectionTOCS">
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<span
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class="cmbx-12"> </span><span class="subsectionToc" ><span
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class="cmbx-12">5.1 </span><a
|
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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"><span
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class="cmbx-12">Examples</span></a></span>
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class="cmr-12">Examples</span></a></span>
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</div>
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<!--l. 1--><div class="crosslinks"><p class="noindent"><span
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class="cmbx-12">[</span><a
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class="cmr-12">[</span><a
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href="userhtmlse6.html" ><span
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class="cmbx-12">next</span></a><span
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class="cmbx-12">] [</span><a
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class="cmr-12">next</span></a><span
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class="cmr-12">] [</span><a
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href="userhtmlse4.html" ><span
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class="cmbx-12">prev</span></a><span
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class="cmbx-12">] [</span><a
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class="cmr-12">prev</span></a><span
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class="cmr-12">] [</span><a
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href="userhtmlse4.html#tailuserhtmlse4.html" ><span
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class="cmbx-12">prev-tail</span></a><span
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class="cmbx-12">] [</span><a
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class="cmr-12">prev-tail</span></a><span
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class="cmr-12">] [</span><a
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class="cmbx-12">front</span></a><span
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class="cmbx-12">] [</span><a
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class="cmr-12">front</span></a><span
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class="cmr-12">] [</span><a
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href="userhtml.html#userhtmlse5.html" ><span
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class="cmbx-12">up</span></a><span
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class="cmbx-12">] </span></p></div>
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class="cmr-12">up</span></a><span
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class="cmr-12">] </span></p></div>
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id="tailuserhtmlse5.html"></a>
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Cirdans-Home
4 years ago
