@ -29,7 +29,7 @@ class="cmr-12">up</span></a><span
class="cmr-12">] < / span > < / p > < / div >
class="cmr-12">] < / span > < / p > < / div >
< h3 class = "sectionHead" > < span class = "titlemark" > < span
< h3 class = "sectionHead" > < span class = "titlemark" > < span
class="cmr-12">4 < / span > < / span > < a
class="cmr-12">4 < / span > < / span > < a
id="x14 -130004">< / a > < span
id="x7 -130004">< / a > < span
class="cmr-12">Getting Started< / span > < / h3 >
class="cmr-12">Getting Started< / span > < / h3 >
<!-- l. 5 --> < p class = "noindent" > < span <!-- l. 5 --> < p class = "noindent" > < span
class="cmr-12">This section describes the basics for building and applying AMG4PSBLAS one-level< / span >
class="cmr-12">This section describes the basics for building and applying AMG4PSBLAS one-level< / span >
@ -39,7 +39,7 @@ class="cmr-12">and multilevel (i.e., AMG) preconditioners with the Krylov solver
class="cmr-12">PSBLAS< / span > < span
class="cmr-12">PSBLAS< / span > < span
class="cmr-12">  < / span > < span class = "cite" > < span
class="cmr-12">  < / span > < span class = "cite" > < span
class="cmr-12">[< / span > < a
class="cmr-12">[< / span > < a
href="userhtmlli5 .html#XPSBLASGUIDE">< span
href="userhtmlli3 .html#XPSBLASGUIDE">< span
class="cmr-12">21< / span > < / a > < span
class="cmr-12">21< / span > < / a > < span
class="cmr-12">]< / span > < / span > < span
class="cmr-12">]< / span > < / span > < span
class="cmr-12">.< / span >
class="cmr-12">.< / span >
@ -47,25 +47,36 @@ class="cmr-12">.</span>
class="cmr-12">The following steps are required:< / span >
class="cmr-12">The following steps are required:< / span >
< ol class = "enumerate1" >
< ol class = "enumerate1" >
< li < li
class="enumerate" id="x14 -13002x1">
class="enumerate" id="x7 -13002x1">
<!-- l. 11 --> < p class = "noindent" > < span
<!-- l. 11 --> < p class = "noindent" > < span
class="cmti-12">Declare the preconditioner data structure< / span > < span
class="cmti-12">Declare the preconditioner data structure< / span > < span
class="cmr-12">. It is a derived data type,< / span >
class="cmr-12">. It is a derived data type,< / span >
< span class = "obeylines-h" > < code class = "verb" > amg_< / code > < / span > < span
< span class = "obeylines-h" > < span class = "verb" > < span
class="cmti-12">x< / span > < span class = "obeylines-h" > < code class = "verb" > prec_< / code > < / span > < span class = "obeylines-h" > < code class = "verb" > type< / code > < / span > < 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="cmr-12">, where < / span > < span
class="cmti-12">x < / span > < span
class="cmti-12">x < / span > < span
class="cmr-12">may be < / span > < span class = "obeylines-h" > < code class = "verb" > s< / code > < / span > < span
class="cmr-12">may be < / span > < span class = "obeylines-h" > < span class = "verb" > < span
class="cmr-12">, < / span > < span class = "obeylines-h" > < code class = "verb" > d< / code > < / span > < span
class="cmtt-12">s< / span > < / span > < / span > < span
class="cmr-12">, < / span > < span class = "obeylines-h" > < code class = "verb" > c< / code > < / span > < span
class="cmr-12">, < / span > < span class = "obeylines-h" > < span class = "verb" > < span
class="cmr-12">or < / span > < span class = "obeylines-h" > < code class = "verb" > z< / code > < / span > < 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 >
class="cmr-12">, according to the basic data< / span >
< span
< span
class="cmr-12">type of the sparse matrix (< / span > < span class = "obeylines-h" > < code class = "verb" > s< / code > < / span > < span
class="cmr-12">type of the sparse matrix (< / span > < span class = "obeylines-h" > < span class = "verb" > < span
class="cmr-12">= real single precision; < / span > < span class = "obeylines-h" > < code class = "verb" > d< / code > < / span > < 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 >
class="cmr-12">= real double precision;< / span >
< span class = "obeylines-h" > < code class = "verb" > c< / code > < / span > < span
< span class = "obeylines-h" > < span class = "verb" > < span
class="cmr-12">= complex single precision; < / span > < span class = "obeylines-h" > < code class = "verb" > z< / code > < / span > < 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 >
class="cmr-12">= complex double precision). This data< / span >
< span
< span
class="cmr-12">structure is accessed by the user only through the AMG4PSBLAS routines,< / span >
class="cmr-12">structure is accessed by the user only through the AMG4PSBLAS routines,< / span >
@ -73,7 +84,7 @@ class="cmr-12">structure is accessed by the user only through the AMG4PSBLAS rou
class="cmr-12">following an object-oriented approach.< / span >
class="cmr-12">following an object-oriented approach.< / span >
< / li >
< / li >
< li < li
class="enumerate" id="x14 -13004x2">
class="enumerate" id="x7 -13004x2">
<!-- l. 19 --> < p class = "noindent" > < span
<!-- l. 19 --> < p class = "noindent" > < span
class="cmti-12">Allocate and initialize the preconditioner data structure, according to a< / span >
class="cmti-12">Allocate and initialize the preconditioner data structure, according to a< / span >
< span
< span
@ -86,7 +97,7 @@ class="cmr-12">the user. The preconditioner types and the defaults associated wi
< span
< span
class="cmr-12">are given in Table< / span > < span
class="cmr-12">are given in Table< / span > < span
class="cmr-12">  < / span > < a
class="cmr-12">  < / span > < a
href="#x14 -13015r1">< span
href="#x7 -13015r1">< span
class="cmr-12">1< / span > <!-- tex4ht:ref: tab:precinit --> < / a > < span
class="cmr-12">1< / span > <!-- tex4ht:ref: tab:precinit --> < / a > < span
class="cmr-12">, where the strings used by < / span > < code class = "lstinline" > < span style = "color:#000000" > init< / span > < / code > < span
class="cmr-12">, where the strings used by < / span > < code class = "lstinline" > < span style = "color:#000000" > init< / span > < / code > < span
class="cmr-12">to identify the< / span >
class="cmr-12">to identify the< / span >
@ -96,7 +107,7 @@ class="cmr-12">preconditioner types are also given. Note that these strings are
class="cmr-12">uppercase letters are substituted by corresponding lowercase ones.< / span >
class="cmr-12">uppercase letters are substituted by corresponding lowercase ones.< / span >
< / li >
< / li >
< li < li
class="enumerate" id="x14 -13006x3">
class="enumerate" id="x7 -13006x3">
<!-- l. 29 --> < p class = "noindent" > < span
<!-- l. 29 --> < p class = "noindent" > < span
class="cmti-12">Modify the selected preconditioner type, by properly setting preconditioner< / span >
class="cmti-12">Modify the selected preconditioner type, by properly setting preconditioner< / span >
< span
< span
@ -111,30 +122,30 @@ class="cmr-12">associated with the selected preconditioner type, to obtain a var
class="cmr-12">preconditioner. Examples of use of < / span > < code class = "lstinline" > < span style = "color:#000000" > set< / span > < / code > < span
class="cmr-12">preconditioner. Examples of use of < / span > < code class = "lstinline" > < span style = "color:#000000" > set< / span > < / code > < span
class="cmr-12">are given in Section< / span > < span
class="cmr-12">are given in Section< / span > < span
class="cmr-12">  < / span > < a
class="cmr-12">  < / span > < a
href="userhtmlsu6.html#x15 -140004.1">< span
href="#x7 -140004.1">< span
class="cmr-12">4.1< / span > <!-- tex4ht:ref: sec:examples --> < / a > < span
class="cmr-12">4.1< / span > <!-- tex4ht:ref: sec:examples --> < / a > < span
class="cmr-12">; a complete< / span >
class="cmr-12">; a complete< / span >
< span
< span
class="cmr-12">list of all the preconditioner parameters and their allowed and default values< / span >
class="cmr-12">list of all the preconditioner parameters and their allowed and default values< / span >
< span
< span
class="cmr-12">is provided in Section< / span > < span
class="cmr-12">is provided in Section< / span > < span
class="cmr-12">  < / span > < a
class="cmr-12">  < / span > < a
href="userhtmlse5.html#x17 -160005">< span
href="userhtmlse5.html#x8 -160005">< span
class="cmr-12">5< / span > <!-- tex4ht:ref: sec:userinterface --> < / a > < span
class="cmr-12">5< / span > <!-- tex4ht:ref: sec:userinterface --> < / a > < span
class="cmr-12">, Tables< / span > < span
class="cmr-12">, Tables< / span > < span
class="cmr-12">  < / span > < a
class="cmr-12">  < / span > < a
href="userhtmlsu9.html#x19 -18009r2">< span
href="userhtmlse5.html#x8 -18009r2">< span
class="cmr-12">2< / span > <!-- tex4ht:ref: tab:p_cycle --> < / a > < span
class="cmr-12">2< / span > <!-- tex4ht:ref: tab:p_cycle --> < / a > < span
class="cmr-12">-< / span > < a
class="cmr-12">-< / span > < a
href="userhtmlsu9.html#x19 -18015r8">< span
href="userhtmlse5.html#x8 -18015r8">< span
class="cmr-12">8< / span > <!-- tex4ht:ref: tab:p_smoother_1 --> < / a > < span
class="cmr-12">8< / span > <!-- tex4ht:ref: tab:p_smoother_1 --> < / a > < span
class="cmr-12">.< / span >
class="cmr-12">.< / span >
< / li >
< / li >
< li < li
class="enumerate" id="x14-13008x4">
class="enumerate" id="x7 -13008x4">
<!-- l. 40 --> < p class = "noindent" > < span
<!-- l. 40 --> < p class = "noindent" > < span
class="cmti-12">Build the preconditioner for a given matrix< / span > < span
class="cmti-12">Build the preconditioner for a given matrix< / span > < span
class="cmr-12">. If the selected preconditioner is< / span >
class="cmr-12">. If the selected preconditioner is< / span >
@ -142,7 +153,7 @@ class="cmr-12">. If the selected preconditioner is</span>
class="cmr-12">multilevel, then two steps must be performed, as specified next.< / span >
class="cmr-12">multilevel, then two steps must be performed, as specified next.< / span >
< ol class = "enumerate2" >
< ol class = "enumerate2" >
< li < li
class="enumerate" id="x14 -13009x0">
class="enumerate" id="x7 -13009x0">
<!-- l. 43 --> < p class = "noindent" > < span
<!-- l. 43 --> < p class = "noindent" > < span
class="cmti-12">Build the AMG hierarchy for a given matrix. < / span > < span
class="cmti-12">Build the AMG hierarchy for a given matrix. < / span > < span
class="cmr-12">This is performed by the< / span >
class="cmr-12">This is performed by the< / span >
@ -151,7 +162,7 @@ class="cmr-12">routine </span><code class="lstinline"><span style="color:#000000
class="cmr-12">.< / span >
class="cmr-12">.< / span >
< / li >
< / li >
< li < li
class="enumerate" id="x14 -13010x0">
class="enumerate" id="x7 -13010x0">
<!-- l. 45 --> < p class = "noindent" > < span
<!-- l. 45 --> < p class = "noindent" > < span
class="cmti-12">Build the preconditioner for a given matrix. < / span > < span
class="cmti-12">Build the preconditioner for a given matrix. < / span > < span
class="cmr-12">This is performed by the< / span >
class="cmr-12">This is performed by the< / span >
@ -165,7 +176,7 @@ class="cmr-12">the routine </span><code class="lstinline"><span style="color:#00
class="cmr-12">.< / span >
class="cmr-12">.< / span >
< / li >
< / li >
< li < li
class="enumerate" id="x14 -13012x5">
class="enumerate" id="x7 -13012x5">
<!-- l. 50 --> < p class = "noindent" > < span
<!-- l. 50 --> < p class = "noindent" > < span
class="cmti-12">Apply the preconditioner at each iteration of a Krylov solver. < / span > < span
class="cmti-12">Apply the preconditioner at each iteration of a Krylov solver. < / span > < span
class="cmr-12">This is performed by< / span >
class="cmr-12">This is performed by< / span >
@ -180,7 +191,7 @@ class="cmr-12">implementing the Krylov solver (</span><code class="lstinline"><s
class="cmr-12">).< / span >
class="cmr-12">).< / span >
< / li >
< / li >
< li < li
class="enumerate" id="x14 -13014x6">
class="enumerate" id="x7 -13014x6">
<!-- l. 54 --> < p class = "noindent" > < span
<!-- l. 54 --> < p class = "noindent" > < span
class="cmti-12">Free the preconditioner data structure< / span > < span
class="cmti-12">Free the preconditioner data structure< / span > < span
class="cmr-12">. This is performed by the routine < / span > < code class = "lstinline" > < span style = "color:#000000" > free< / span > < / code > < span
class="cmr-12">. This is performed by the routine < / span > < code class = "lstinline" > < span style = "color:#000000" > free< / span > < / code > < span
@ -194,13 +205,13 @@ class="cmr-12">All the previous routines are available as methods of the precond
< span < span
class="cmr-12">detailed description of them is given in Section< / span > < span
class="cmr-12">detailed description of them is given in Section< / span > < span
class="cmr-12">  < / span > < a
class="cmr-12">  < / span > < a
href="userhtmlse5.html#x17 -160005">< span
href="userhtmlse5.html#x8 -160005">< span
class="cmr-12">5< / span > <!-- tex4ht:ref: sec:userinterface --> < / a > < span
class="cmr-12">5< / span > <!-- tex4ht:ref: sec:userinterface --> < / a > < span
class="cmr-12">. Examples showing the basic use of< / span >
class="cmr-12">. Examples showing the basic use of< / span >
< span < span
class="cmr-12">AMG4PSBLAS are reported in Section< / span > < span
class="cmr-12">AMG4PSBLAS are reported in Section< / span > < span
class="cmr-12">  < / span > < a
class="cmr-12">  < / span > < a
href="userhtmlsu6.html#x15 -140004.1">< span
href="#x7 -140004.1">< span
class="cmr-12">4.1< / span > <!-- tex4ht:ref: sec:examples --> < / a > < span
class="cmr-12">4.1< / span > <!-- tex4ht:ref: sec:examples --> < / a > < span
class="cmr-12">.< / span >
class="cmr-12">.< / span >
< div class = "table" >
< div class = "table" >
@ -208,7 +219,7 @@ class="cmr-12">.</span>
<!-- l. 63 --> < p class = "indent" > < a <!-- l. 63 --> < p class = "indent" > < a
id="x14 -13015r1">< / a > < hr class = "float" > < div class = "float"
id="x7 -13015r1">< / a > < hr class = "float" > < div class = "float"
>
>
@ -263,79 +274,59 @@ 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
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"
style="vertical-align:baseline;" id="TBL-1-2-">< td style = "white-space:nowrap; text-align:left;" id = "TBL-1-2-1"
class="td11">
class="td11">No preconditioner < / td > < td style = "white-space:normal; text-align:left;" id = "TBL-1-2-2"
No preconditioner < / td > < td style = "white-space:normal; text-align:left;" id = "TBL-1-2-2"
class="td11"><!-- l. 69 --> < p class = "noindent" > < code class = "lstinline" > < span style = "color:#000000" > ’ < / span > < span style = "color:#000000" > NONE< / span > < span style = "color:#000000" > ’ < / span > < / code > < / td > < td style = "white-space:normal; text-align:left;" id = "TBL-1-2-3"
class="td11"> <!-- l. 69 --> < p class = "noindent" > < code class = "lstinline" > < span style = "color:#000000" > ’ < / span > < span style = "color:#000000" > NONE< / span > < span style = "color:#000000" > ’ < / span > < / code >
< / td > < td style = "white-space:normal; text-align:left;" id = "TBL-1-2-3"
class="td11"><!-- l. 69 --> < p class = "noindent" > Considered to use the PSBLAS Krylov
class="td11"><!-- l. 69 --> < p class = "noindent" > Considered to use the PSBLAS Krylov
solvers with no preconditioner.
solvers with no preconditioner. < / td >
< / td >
< / tr > < tr < / tr > < tr
class="hline">< td > < hr > < / td > < td > < hr > < / td > < td > < hr > < / 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"
style="vertical-align:baseline;" id="TBL-1-3-">< td style = "white-space:nowrap; text-align:left;" id = "TBL-1-3-1"
class="td11">
class="td11">Diagonal < / td > < td style = "white-space:normal; text-align:left;" id = "TBL-1-3-2"
Diagonal < / td > < td style = "white-space:normal; text-align:left;" id = "TBL-1-3-2"
class="td11"><!-- l. 71 --> < p class = "noindent" > < code class = "lstinline" > < span style = "color:#000000" > ’ < / span > < span style = "color:#000000" > DIAG< / span > < span style = "color:#000000" > ’ < / span > < / code > ,
class="td11"><!-- l. 71 --> < p class = "noindent" > < code class = "lstinline" > < span style = "color:#000000" > ’ < / span > < span style = "color:#000000" > DIAG< / span > < span style = "color:#000000" > ’ < / span > < / code > ,
< code class = "lstinline" > < span style = "color:#000000" > ’ < / span > < span style = "color:#000000" > JACOBI< / span > < span style = "color:#000000" > ’ < / span > < / code > ,< code class = "lstinline" > < span style = "color:#000000" > ’ < / span > < span style = "color:#000000" > JACOBI< / span > < span style = "color:#000000" > ’ < / span > < / code > ,
< code class = "lstinline" > < span style = "color:#000000" > ’ < / span > < span style = "color:#000000" > L1< / span > < span style = "color:#000000" > -< / span > < span style = "color:#000000" > JACOBI< / span > < span style = "color:#000000" > ’ < / span > < / code >
< code class = "lstinline" > < span style = "color:#000000" > ’ < / span > < span style = "color:#000000" > L1< / span > < span style = "color:#000000" > -< / span > < span style = "color:#000000" > JACOBI< / span > < span style = "color:#000000" > ’ < / span > < / code > < / td > < td style = "white-space:normal; text-align:left;" id = "TBL-1-3-3"
< / td > < td style = "white-space:normal; text-align:left;" id = "TBL-1-3-3"
class="td11"><!-- l. 71 --> < p class = "noindent" > Diagonal preconditioner. For any zero
class="td11"><!-- l. 71 --> < p class = "noindent" > Diagonal preconditioner. For any zero
diagonal entry of the matrix to be
diagonal entry of the matrix to be
preconditioned, the corresponding entry
preconditioned, the corresponding entry
of the preconditioner is set to  1.
of the preconditioner is set to  1. < / td >
< / td >
< / tr > < tr < / tr > < tr
class="hline">< td > < hr > < / td > < td > < hr > < / td > < td > < hr > < / 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"
style="vertical-align:baseline;" id="TBL-1-4-">< td style = "white-space:nowrap; text-align:left;" id = "TBL-1-4-1"
class="td11">
class="td11">Gauss-Seidel < / td > < td style = "white-space:normal; text-align:left;" id = "TBL-1-4-2"
Gauss-Seidel < / td > < td style = "white-space:normal; text-align:left;" id = "TBL-1-4-2"
class="td11"><!-- l. 74 --> < p class = "noindent" > < code class = "lstinline" > < span style = "color:#000000" > ’ < / span > < span style = "color:#000000" > GS< / span > < span style = "color:#000000" > ’ < / span > < / code > ,
class="td11"><!-- l. 74 --> < p class = "noindent" > < code class = "lstinline" > < span style = "color:#000000" > ’ < / span > < span style = "color:#000000" > GS< / span > < span style = "color:#000000" > ’ < / span > < / code > ,
< code class = "lstinline" > < span style = "color:#000000" > ’ < / span > < span style = "color:#000000" > L1< / span > < span style = "color:#000000" > -< / span > < span style = "color:#000000" > GS< / span > < span style = "color:#000000" > ’ < / span > < / code >
< code class = "lstinline" > < span style = "color:#000000" > ’ < / span > < span style = "color:#000000" > L1< / span > < span style = "color:#000000" > -< / span > < span style = "color:#000000" > GS< / span > < span style = "color:#000000" > ’ < / span > < / code > < / td > < td style = "white-space:normal; text-align:left;" id = "TBL-1-4-3"
< / td > < td style = "white-space:normal; text-align:left;" id = "TBL-1-4-3"
class="td11"><!-- l. 74 --> < p class = "noindent" > Hybrid Gauss-Seidel (forward), that is,
class="td11"><!-- l. 74 --> < p class = "noindent" > Hybrid Gauss-Seidel (forward), that is,
global block Jacobi with Gauss-Seidel as
global block Jacobi with Gauss-Seidel as
local solver.
local solver. < / td >
< / td >
< / tr > < tr < / tr > < tr
class="hline">< td > < hr > < / td > < td > < hr > < / td > < td > < hr > < / 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"
style="vertical-align:baseline;" id="TBL-1-5-">< td style = "white-space:nowrap; text-align:left;" id = "TBL-1-5-1"
class="td11">
class="td11">Symmetrized Gauss-Seidel< / td > < td style = "white-space:normal; text-align:left;" id = "TBL-1-5-2"
Symmetrized Gauss-Seidel < / td > < td style = "white-space:normal; text-align:left;" id = "TBL-1-5-2"
class="td11"><!-- l. 77 --> < p class = "noindent" > < code class = "lstinline" > < span style = "color:#000000" > ’ < / span > < span style = "color:#000000" > FBGS< / span > < span style = "color:#000000" > ’ < / span > < / code > ,
class="td11"><!-- l. 77 --> < p class = "noindent" > < code class = "lstinline" > < span style = "color:#000000" > ’ < / span > < span style = "color:#000000" > FBGS< / span > < span style = "color:#000000" > ’ < / span > < / code > ,
< code class = "lstinline" > < span style = "color:#000000" > ’ < / span > < span style = "color:#000000" > L1< / span > < span style = "color:#000000" > -< / span > < span style = "color:#000000" > FBGS< / span > < span style = "color:#000000" > ’ < / span > < / code >
< code class = "lstinline" > < span style = "color:#000000" > ’ < / span > < span style = "color:#000000" > L1< / span > < span style = "color:#000000" > -< / span > < span style = "color:#000000" > FBGS< / span > < span style = "color:#000000" > ’ < / span > < / code > < / td > < td style = "white-space:normal; text-align:left;" id = "TBL-1-5-3"
< / td > < td style = "white-space:normal; text-align:left;" id = "TBL-1-5-3"
class="td11"><!-- l. 77 --> < p class = "noindent" > Symmetrized hybrid Gauss-Seidel, that
class="td11"><!-- l. 77 --> < p class = "noindent" > Symmetrized hybrid Gauss-Seidel, that
is, forward Gauss-Seidel followed by
is, forward Gauss-Seidel followed by
backward Gauss-Seidel.
backward Gauss-Seidel. < / td >
< / td >
< / tr > < tr < / tr > < tr
class="hline">< td > < hr > < / td > < td > < hr > < / td > < td > < hr > < / 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"
style="vertical-align:baseline;" id="TBL-1-6-">< td style = "white-space:nowrap; text-align:left;" id = "TBL-1-6-1"
class="td11">
class="td11">Block Jacobi < / td > < td style = "white-space:normal; text-align:left;" id = "TBL-1-6-2"
Block Jacobi < / td > < td style = "white-space:normal; text-align:left;" id = "TBL-1-6-2"
class="td11"><!-- l. 80 --> < p class = "noindent" > < code class = "lstinline" > < span style = "color:#000000" > ’ < / span > < span style = "color:#000000" > BJAC< / span > < span style = "color:#000000" > ’ < / span > < / code > ,
class="td11"><!-- l. 80 --> < p class = "noindent" > < code class = "lstinline" > < span style = "color:#000000" > ’ < / span > < span style = "color:#000000" > BJAC< / span > < span style = "color:#000000" > ’ < / span > < / code > ,
< code class = "lstinline" > < span style = "color:#000000" > ’ < / span > < span style = "color:#000000" > L1< / span > < span style = "color:#000000" > -< / span > < span style = "color:#000000" > BJAC< / span > < span style = "color:#000000" > ’ < / span > < / code >
< code class = "lstinline" > < span style = "color:#000000" > ’ < / span > < span style = "color:#000000" > L1< / span > < span style = "color:#000000" > -< / span > < span style = "color:#000000" > BJAC< / span > < span style = "color:#000000" > ’ < / span > < / code > < / td > < td style = "white-space:normal; text-align:left;" id = "TBL-1-6-3"
< / td > < td style = "white-space:normal; text-align:left;" id = "TBL-1-6-3"
class="td11"><!-- l. 80 --> < p class = "noindent" > Block-Jacobi with ILU(0) on the local
class="td11"><!-- l. 80 --> < p class = "noindent" > Block-Jacobi with ILU(0) on the local
blocks.
blocks. < / td >
< / td >
< / tr > < tr < / tr > < tr
class="hline">< td > < hr > < / td > < td > < hr > < / td > < td > < hr > < / 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"
style="vertical-align:baseline;" id="TBL-1-7-">< td style = "white-space:nowrap; text-align:left;" id = "TBL-1-7-1"
class="td11">
class="td11">Additive Schwarz < / td > < td style = "white-space:normal; text-align:left;" id = "TBL-1-7-2"
Additive Schwarz < / td > < td style = "white-space:normal; text-align:left;" id = "TBL-1-7-2"
class="td11"><!-- l. 81 --> < p class = "noindent" > < code class = "lstinline" > < span style = "color:#000000" > ’ < / span > < span style = "color:#000000" > AS< / span > < span style = "color:#000000" > ’ < / span > < / code > < / td > < td style = "white-space:normal; text-align:left;" id = "TBL-1-7-3"
class="td11"> <!-- l. 81 --> < p class = "noindent" > < code class = "lstinline" > < span style = "color:#000000" > ’ < / span > < span style = "color:#000000" > AS< / span > < span style = "color:#000000" > ’ < / span > < / code >
< / td > < td style = "white-space:normal; text-align:left;" id = "TBL-1-7-3"
class="td11"><!-- l. 81 --> < p class = "noindent" > Additive Schwarz (AS), with overlap  1
class="td11"><!-- l. 81 --> < p class = "noindent" > Additive Schwarz (AS), with overlap  1
and ILU(0) on the local blocks.
and ILU(0) on the local blocks. < / td >
< / td >
< / tr > < tr < / tr > < tr
class="hline">< td > < hr > < / td > < td > < hr > < / td > < td > < hr > < / 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"
style="vertical-align:baseline;" id="TBL-1-8-">< td style = "white-space:nowrap; text-align:left;" id = "TBL-1-8-1"
class="td11">
class="td11">Multilevel < / td > < td style = "white-space:normal; text-align:left;" id = "TBL-1-8-2"
Multilevel < / td > < td style = "white-space:normal; text-align:left;" id = "TBL-1-8-2"
class="td11"><!-- l. 83 --> < p class = "noindent" > < code class = "lstinline" > < span style = "color:#000000" > ’ < / span > < span style = "color:#000000" > ML< / span > < span style = "color:#000000" > ’ < / span > < / code > < / td > < td style = "white-space:normal; text-align:left;" id = "TBL-1-8-3"
class="td11"> <!-- l. 83 --> < p class = "noindent" > < code class = "lstinline" > < span style = "color:#000000" > ’ < / span > < span style = "color:#000000" > ML< / span > < span style = "color:#000000" > ’ < / span > < / code >
< / td > < td style = "white-space:normal; text-align:left;" id = "TBL-1-8-3"
class="td11"><!-- l. 83 --> < p class = "noindent" > V-cycle with one hybrid
class="td11"><!-- l. 83 --> < p class = "noindent" > V-cycle with one hybrid
forward Gauss-Seidel (GS) sweep as
forward Gauss-Seidel (GS) sweep as
pre-smoother and one hybrid backward
pre-smoother and one hybrid backward
@ -344,17 +335,16 @@ class="td11"> <!--l. 83--><p class="noindent" >V-cycle with one
algorithm, and LU (plus triangular solve)
algorithm, and LU (plus triangular solve)
as coarsest-level solver. See the default
as coarsest-level solver. See the default
values in Tables  < a
values in Tables  < a
href="userhtmlsu9.html#x19-18009r2">2<!-- tex4ht:ref: tab:p_cycle --> < / a > -< a
href="userhtmlse5.html#x8-18009r2">2<!-- tex4ht:ref: tab:p_cycle --> < / a > -< a
href="userhtmlsu9.html#x19-18015r8">8<!-- tex4ht:ref: tab:p_smoother_1 --> < / a > for further details of
href="userhtmlse5.html#x8-18015r8">8<!-- tex4ht:ref: tab:p_smoother_1 --> < / a > for further details of
the preconditioner.
the preconditioner. < / td >
< / td >
< / tr > < tr < / tr > < tr
class="hline">< td > < hr > < / td > < td > < hr > < / td > < td > < hr > < / 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"
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 >
class="td11"> < / td > < / tr > < / table > < / div >
< br / > < div class = "caption" < br / > < div class = "caption"
>< span class = "id" > Table  1: < / span > < span
>< span class = "id" > Table  1: < / span > < span
class="content">Preconditioner types, corresponding strings and default choices. < / span > < / div > <!-- tex4ht:label?: x 14 - 13015r1 -->
class="content">Preconditioner types, corresponding strings and default choices. < / span > < / div > <!-- tex4ht:label?: x 7 - 13015r1 -->
< / div > < / div >
@ -375,7 +365,7 @@ class="cmr-12">,</span>
< span < span
class="cmr-12">for interfacing with the Krylov solvers, must be also used (see Section< / span > < span
class="cmr-12">for interfacing with the Krylov solvers, must be also used (see Section< / span > < span
class="cmr-12">  < / span > < a
class="cmr-12">  < / span > < a
href="userhtmlsu6.html#x15 -140004.1">< span
href="#x7 -140004.1">< span
class="cmr-12">4.1< / span > <!-- tex4ht:ref: sec:examples --> < / a > < span
class="cmr-12">4.1< / span > <!-- tex4ht:ref: sec:examples --> < / a > < span
class="cmr-12">).< / span >
class="cmr-12">).< / span >
< br < br
@ -395,19 +385,552 @@ class="cmr-12">problems. However, this does not necessarily correspond to the sh
< span < span
class="cmr-12">on parallel< / span > < span
class="cmr-12">on parallel< / span > < span
class="cmr-12">  computers.< / span >
class="cmr-12">  computers.< / span >
< div class = "subsectionTOCS" >
< h4 class = "subsectionHead" > < span class = "titlemark" > < span
< span class = "subsectionToc" > < span
class="cmr-12">4.1 < / span > < / span > < a
class="cmr-12">4.1 < / span > < a
id="x7-140004.1">< / a > < span
href="userhtmlsu6.html#x15-140004.1">< span
class="cmr-12">Examples< / span > < / h4 >
class="cmr-12">Examples< / span > < / a > < / span >
<!-- l. 116 --> < p class = "noindent" > < span
< br / > < span class = "subsectionToc" > < span class="cmr-12">The code reported in Figure< / span > < span
class="cmr-12">4.2 < / span > < a
class="cmr-12">  < / span > < a
href="userhtmlsu7.html#x16-150004.2">< span
href="#x7-14001r1">< span
class="cmr-12">GPU example< / span > < / a > < / 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">preconditioner available in the real double precision version of AMG4PSBLAS< / span >
< span
class="cmr-12">(see Table< / span > < span
class="cmr-12">  < / span > < a
href="#x7-13015r1">< span
class="cmr-12">1< / span > <!-- tex4ht:ref: tab:precinit --> < / a > < span
class="cmr-12">). This preconditioner is chosen by simply specifying < / span > < code class = "lstinline" > < span style = "color:#000000" > ’ < / span > < span style = "color:#000000" > ML< / span > < span style = "color:#000000" > ’ < / span > < / code > < span
class="cmr-12">as the< / span >
< span
class="cmr-12">second argument of < / span > < code class = "lstinline" > < span style = "color:#000000" > P< / span > < span style = "color:#000000" > %< / span > < span style = "color:#000000" > init< / span > < / code > < span
class="cmr-12">(a call to < / span > < code class = "lstinline" > < span style = "color:#000000" > P< / span > < span style = "color:#000000" > %< / span > < span style = "color:#000000" > set< / span > < / code > < 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 >
< code class = "lstinline" > < span style = "color:#000000" > psb_base_mod< / span > < / code > < span
class="cmr-12">, < / span > < code class = "lstinline" > < span style = "color:#000000" > amg_prec_mod< / span > < / code > < span
class="cmr-12">and < / span > < code class = "lstinline" > < span style = "color:#000000" > psb_krylov_mod< / span > < / code > < span
class="cmr-12">must be used by the example< / span >
< span
class="cmr-12">program.< / span >
<!-- l. 126 --> < p class = "indent" > < span
class="cmr-12">The part of the code dealing with reading and assembling the sparse matrix and the< / span >
< span
class="cmr-12">right-hand side vector and the deallocation of the relevant data structures, performed< / span >
< span
class="cmr-12">through the PSBLAS routines for sparse matrix and vector management,< / span >
< span
class="cmr-12">is not reported here for the sake of conciseness. The complete code can be< / span >
< span
class="cmr-12">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 directory< / span >
< span class = "obeylines-h" > < span class = "verb" > < span
class="cmtt-12">samples/simple/file< / span > < / span > < / span > < span class = "obeylines-h" > < span class = "verb" > < span
class="cmtt-12">read< / span > < / span > < / span > < span
class="cmr-12">of the AMG4PSBLAS implementation (see Section< / span > < span
class="cmr-12">  < / span > < a
href="userhtmlse3.html#x6-120003.5">< span
class="cmr-12">3.5< / span > <!-- tex4ht:ref: sec:ex_and_test --> < / a > < span
class="cmr-12">). A< / span >
< span
class="cmr-12">sample test problem along with the relevant input data is available in< / span >
< span class = "obeylines-h" > < span class = "verb" > < span
class="cmtt-12">samples/simple/fileread/runs< / span > < / span > < / span > < span
class="cmr-12">. For details on the use of the PSBLAS routines, see< / span >
< span
class="cmr-12">the PSBLAS User’ s Guide< / span > < span
class="cmr-12">  < / span > < span class = "cite" > < span
class="cmr-12">[< / span > < a
href="userhtmlli3.html#XPSBLASGUIDE">< span
class="cmr-12">21< / span > < / a > < span
class="cmr-12">]< / span > < / span > < span
class="cmr-12">.< / span >
<!-- l. 138 --> < p class = "indent" > < span
class="cmr-12">The setup and application of the default multilevel preconditioner for the real single< / 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="userhtmlse5.html#x8-160005">< span
class="cmr-12">5< / 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">samples/simple/file< / span > < / span > < / span > < span class = "obeylines-h" > < span class = "verb" > < span
class="cmtt-12">read< / span > < / span > < / span > < span
class="cmr-12">.< / span >
<!-- l. 144 --> < p class = "indent" > < a
id="x7-14001r1">< / a > < hr class = "float" > < div class = "float"
>
< div class = "center"
>
<!-- l. 145 --> < p class = "noindent" >
< div class = "minipage" > < pre class = "verbatim" id = "verbatim-7" >
    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(ctxt)
    call  psb_info(ctxt,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(ctxt,’ 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  FCG
    call  psb_krylov(’ FCG’ ,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(ctxt)
    stop
< / pre >
<!-- l. 255 --> < p class = "nopar" > < / div >
< br / > < div class = "caption"
>< span class = "id" > Listing 1: < / span > < span
class="content">setup and application of the default multilevel preconditioner (example 1).
< / span > < / div > <!-- tex4ht:label?: x7 - 14001r1 -->
< / div > < / div >
< / div > < hr class = "endfloat" / >
<!-- l. 264 --> < 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="#x7-14002r2">< span
class="cmr-12">2< / 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-< / span >
< span
class="cmr-12">and post-smoother, and solves the coarsest-level system with 8 block-Jacobi< / span >
< span
class="cmr-12">sweeps. Note that the ILU(0) factorization (plus triangular solve) is used as< / span >
< span
class="cmr-12">local solver for the block-Jacobi sweeps, since this is the default associated< / span >
< span
class="cmr-12">with block-Jacobi and set by< / span > < span
class="cmr-12">  < / span > < code class = "lstinline" > < span style = "color:#000000" > P< / span > < span style = "color:#000000" > %< / span > < span style = "color:#000000" > init< / span > < / code > < span
class="cmr-12">. Furthermore, specifying block-Jacobi as< / span >
< span
class="cmr-12">coarsest-level solver implies that the coarsest-level matrix is distributed among< / span >
< span
class="cmr-12">the processes. Figure< / span > < span
class="cmr-12">  < / span > < a
href="#x7-14003r3">< 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< / span >
< span
class="cmr-12">Coarsening based on Compatible Weighted Matching, aggregates of size at< / span >
< span
class="cmr-12">most 8 and smoothed prolongators. It applies 2 hybrid Gauss-Seidel sweeps as< / span >
< span
class="cmr-12">pre- and post-smoother, and solves the coarsest-level system with the parallel< / span >
< span
class="cmr-12">flexible Conjugate Gradient method (KRM) coupled with the block-Jacobi< / span >
< span
class="cmr-12">preconditioner having ILU(0) on the blocks. Default parameters are used for stopping< / span >
< span
class="cmr-12">criterion of the coarsest solver. Note that, also in this case, specifying KRM as< / span >
< span
class="cmr-12">coarsest-level solver implies that the coarsest-level matrix is distributed among the< / span >
< span
class="cmr-12">processes.< / span >
<!-- l. 291 --> < p class = "indent" > < span
class="cmr-12">The code fragments shown in Figures< / span > < span
class="cmr-12">  < / span > < a
href="#x7-14002r2">< span
class="cmr-12">2< / span > <!-- tex4ht:ref: fig:ex2 --> < / a > < span
class="cmr-12">and < / span > < a
href="#x7-14003r3">< span
class="cmr-12">3< / span > <!-- tex4ht:ref: fig:ex3 --> < / a > < span
class="cmr-12">are included in the example program< / span >
< span
class="cmr-12">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 >
<!-- l. 294 --> < p class = "indent" > < span
class="cmr-12">Finally, Figure< / span > < span
class="cmr-12">  < / span > < a
href="#x7-14004r4">< 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. 301 --> < p class = "indent" > < span
class="cmr-12">For all the previous preconditioners, example programs where the sparse matrix< / span >
< span
class="cmr-12">and the right-hand side are generated by discretizing a PDE with Dirichlet< / span >
< span
class="cmr-12">boundary conditions are also available in the directory < / span > < span class = "obeylines-h" > < span class = "verb" > < span
class="cmtt-12">samples/simple/pdegen< / span > < / span > < / span > < span
class="cmr-12">.< / span >
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id="x7-14002r2">< / a > < hr class = "float" > < div class = "float"
>
< div class = "center"
>
<!-- l. 318 --> < p class = "noindent" >
< div class = "minipage" > < pre class = "verbatim" id = "verbatim-8" >
...  ...
!  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(ctxt,’ 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. 333 --> < p class = "nopar" > < / div > < / div >
< br / > < div class = "caption"
>< span class = "id" > Listing 2: < / span > < span
class="content">setup of a multilevel preconditioner based on the default decoupled coarsening< / span > < / div > <!-- tex4ht:label?: x7 - 14002r2 -->
< / div > < hr class = "endfloat" / >
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id="x7-14003r3">< / a > < hr class = "float" > < div class = "float"
>
< div class = "center"
>
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< div class = "minipage" > < pre class = "verbatim" id = "verbatim-9" >
...  ...
!  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(ctxt,’ ML’ ,info)
    call  P%set(’ PAR_AGGR_ALG’ ,’ COUPLED’ ,info)
    call  P%set(’ AGGR_TYPE’ ,’ MATCHBOXP’ ,info)
    call  P%set(’ AGGR_SIZE’ ,8,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’ ,’ KRM’ ,info)
    call  P%set(’ COARSE_MAT’ ,’ DIST’ ,info)
    call  P%set(’ KRM_METHOD’ ,’ FCG’ ,info)
    call  P%hierarchy_build(A,desc_A,info)
    call  P%smoothers_build(A,desc_A,info)
...  ...
< / pre >
<!-- l. 383 --> < p class = "nopar" > < / div > < / div >
< br / > < div class = "caption"
>< span class = "id" > Listing 3: < / span > < span
class="content">setup of a multilevel preconditioner based on the coupled coarsening using
weighted matching< / span > < / div > <!-- tex4ht:label?: x7 - 14003r3 -->
< / div > < hr class = "endfloat" / >
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id="x7-14004r4">< / a > < hr class = "float" > < div class = "float"
>
< div class = "center"
>
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< div class = "minipage" > < pre class = "verbatim" id = "verbatim-10" >
...  ...
!  set  RAS  with  overlap  2  and  ILU(0)  on  the  local  blocks
    call  P%init(ctxt,’ 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. 414 --> < p class = "nopar" > < / div > < / div >
< br / > < div class = "caption"
>< span class = "id" > Listing 4: < / span > < span
class="content">setup of a one-level Schwarz preconditioner.< / span > < / div > <!-- tex4ht:label?: x7 - 14004r4 -->
< / div > < hr class = "endfloat" / >
< h4 class = "subsectionHead" > < span class = "titlemark" > < span
class="cmr-12">4.2 < / span > < / span > < a
id="x7-150004.2">< / a > < span
class="cmr-12">GPU example< / span > < / h4 >
<!-- l. 426 --> < p class = "noindent" > < span
class="cmr-12">The code discussed here shows how to set up a program exploiting the combined GPU< / span >
< span
class="cmr-12">capabilities of PSBLAS and AMG4PSBLAS. The code example is available in the< / span >
< span
class="cmr-12">source distribution directory < / span > < span class = "obeylines-h" > < span class = "verb" > < span
class="cmtt-12">amg4psblas/examples/gpu< / span > < / span > < / span > < span
class="cmr-12">.< / span >
<!-- l. 431 --> < p class = "indent" > < span
class="cmr-12">First of all, we need to include the appropriate modules and declare some auxiliary< / span >
< span
class="cmr-12">variables:< / span >
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id="x7-15001r5">< / a > < hr class = "float" > < div class = "float"
>
< div class = "center"
>
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< div class = "minipage" > < pre class = "verbatim" id = "verbatim-11" >
program  amg_dexample_gpu
    use  psb_base_mod
    use  amg_prec_mod
    use  psb_krylov_mod
    use  psb_util_mod
    use  psb_gpu_mod
    use  data_input
    use  amg_d_pde_mod
    implicit  none
    .......
    !  GPU  variables
    type(psb_d_hlg_sparse_mat)  ::  agmold
    type(psb_d_vect_gpu)              ::  vgmold
    type(psb_i_vect_gpu)              ::  igmold
 
< / pre >
<!-- l. 471 --> < p class = "nopar" > < / div > < / div >
< br / > < div class = "caption"
>< span class = "id" > Listing 5: < / span > < span
class="content">setup of a GPU-enabled test program part one.< / span > < / div > <!-- tex4ht:label?: x7 - 15001r5 -->
< / div > < hr class = "endfloat" / >
<!-- l. 478 --> < p class = "indent" > < span
class="cmr-12">In this particular example we are choosing to employ a < / span > < span class = "obeylines-h" > < span class = "verb" > < span
class="cmtt-12">HLG< / span > < / span > < / span > < span
class="cmr-12">data structure for< / span >
< span
class="cmr-12">sparse matrices on GPUs; for more information please refer to the PSBLAS-EXT users’ < / span >
< span
class="cmr-12">guide.< / span >
<!-- l. 482 --> < p class = "indent" > < span
class="cmr-12">We then have to initialize the GPU environment, and pass the appropriate MOLD< / span >
< span
class="cmr-12">variables to the build methods (see also the PSBLAS and PSBLAS-EXT users’ < / span >
< span
class="cmr-12">guides).< / span >
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id="x7-15002r6">< / a > < hr class = "float" > < div class = "float"
>
< div class = "center"
>
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< div class = "minipage" > < pre class = "verbatim" id = "verbatim-12" >
    call  psb_init(ctxt)
    call  psb_info(ctxt,iam,np)
    !
    !  BEWARE:  if  you  have  NGPUS    per  node,  the  default  is  to
    !  attach  to  mod(IAM,NGPUS)
    !
    call  psb_gpu_init(ictxt)
    ......
    t1  =  psb_wtime()
    call  prec%smoothers_build(a,desc_a,info,  amold=agmold,  vmold=vgmold,  imold=igmold)
 
< / pre >
<!-- l. 516 --> < p class = "nopar" > < / div > < / div >
< br / > < div class = "caption"
>< span class = "id" > Listing 6: < / span > < span
class="content">setup of a GPU-enabled test program part two.< / span > < / div > <!-- tex4ht:label?: x7 - 15002r6 -->
< / div > < hr class = "endfloat" / >
<!-- l. 523 --> < p class = "indent" > < span
class="cmr-12">Finally, we convert the input matrix, the descriptor and the vectors to use a< / span >
< span
class="cmr-12">GPU-enabled internal storage format. We then preallocate the preconditioner< / span >
< span
class="cmr-12">workspace before entering the Krylov method. At the end of the code, we close the< / span >
< span
class="cmr-12">GPU environment< / span >
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id="x7-15003r7">< / a > < hr class = "float" > < div class = "float"
>
< div class = "center"
>
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< div class = "minipage" > < pre class = "verbatim" id = "verbatim-13" >
    call  desc_a%cnv(mold=igmold)
    call  a%cscnv(info,mold=agmold)
    call  psb_geasb(x,desc_a,info,mold=vgmold)
    call  psb_geasb(b,desc_a,info,mold=vgmold)
    !
    !  iterative  method  parameters
    !
    call  psb_barrier(ctxt)
    call  prec%allocate_wrk(info)
    t1  =  psb_wtime()
    call  psb_krylov(s_choice%kmethd,a,prec,b,x,s_choice%eps,&
              &   desc_a,info,itmax=s_choice%itmax,iter=iter,err=err,itrace=s_choice%itrace,&
              &   istop=s_choice%istopc,irst=s_choice%irst)
    call  prec%deallocate_wrk(info)
    call  psb_barrier(ctxt)
    tslv  =  psb_wtime()  -  t1
    ......
    call  psb_gpu_exit()
    call  psb_exit(ctxt)
    stop
 
< / pre >
<!-- l. 584 --> < p class = "nopar" > < / div > < / div >
< br / > < div class = "caption"
>< span class = "id" > Listing 7: < / span > < span
class="content">setup of a GPU-enabled test program part three.< / span > < / div > <!-- tex4ht:label?: x7 - 15003r7 -->
< / div > < hr class = "endfloat" / >
<!-- l. 592 --> < p class = "indent" > < span
class="cmr-12">It is very important to employ smoothers and coarsest solvers that are suited to the< / span >
< span
class="cmr-12">GPU, i.e. methods that do NOT employ triangular system solve kernels. Methods that< / span >
< span
class="cmr-12">satisfy this constraint include:< / span >
< ul class = "itemize1" >
< li class = "itemize" >
<!-- l. 596 --> < p class = "noindent" > < span class = "obeylines-h" > < span class = "verb" > < span
class="cmtt-12">JACOBI< / span > < / span > < / span >
< / li >
< li class = "itemize" >
<!-- l. 597 --> < p class = "noindent" > < span class = "obeylines-h" > < span class = "verb" > < span
class="cmtt-12">BJAC< / span > < / span > < / span > < span
class="cmr-12">with the following methods on the local blocks:< / span >
< ul class = "itemize2" >
< li class = "itemize" >
<!-- l. 599 --> < p class = "noindent" > < span class = "obeylines-h" > < span class = "verb" > < span
class="cmtt-12">INVK< / span > < / span > < / span >
< / li >
< li class = "itemize" >
<!-- l. 600 --> < p class = "noindent" > < span class = "obeylines-h" > < span class = "verb" > < span
class="cmtt-12">INVT< / span > < / span > < / span >
< / li >
< li class = "itemize" >
<!-- l. 601 --> < p class = "noindent" > < span class = "obeylines-h" > < span class = "verb" > < span
class="cmtt-12">AINV< / span > < / span > < / span > < / li > < / ul >
< / li > < / ul >
<!-- l. 604 --> < p class = "noindent" > < span
class="cmr-12">and their < / span > < span
class="cmmi-12">ℓ < / span > < sub > < span
class="cmr-8">1< / span > < / sub > < span
class="cmr-12">variants.< / span >
<!-- l. 1 --> < div class = "crosslinks" > < p class = "noindent" > < span
<!-- l. 1 --> < div class = "crosslinks" > < p class = "noindent" > < span
class="cmr-12">[< / span > < a
class="cmr-12">[< / span > < a
sfilippone
1 month ago