1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
|
<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML3.2 EN">
<HTML>
<HEAD> <link rel="canonical" href="http://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/PC/PCFieldSplitSetSchurFactType.html" />
<META NAME="GENERATOR" CONTENT="DOCTEXT">
<TITLE>PCFieldSplitSetSchurFactType</TITLE>
</HEAD>
<BODY BGCOLOR="FFFFFF">
<div id="version" align=right><b>petsc-3.14.5 2021-03-03</b></div>
<div id="bugreport" align=right><a href="mailto:petsc-maint@mcs.anl.gov?subject=Typo or Error in Documentation &body=Please describe the typo or error in the documentation: petsc-3.14.5 v3.14.5 docs/manualpages/PC/PCFieldSplitSetSchurFactType.html "><small>Report Typos and Errors</small></a></div>
<A NAME="PCFieldSplitSetSchurFactType"><H1>PCFieldSplitSetSchurFactType</H1></A>
sets which blocks of the approximate block factorization to retain in the preconditioner
<H3><FONT COLOR="#CC3333">Synopsis</FONT></H3>
<PRE>
#include "petscpc.h"
<A HREF="../Sys/PetscErrorCode.html#PetscErrorCode">PetscErrorCode</A> <A HREF="../PC/PCFieldSplitSetSchurFactType.html#PCFieldSplitSetSchurFactType">PCFieldSplitSetSchurFactType</A>(<A HREF="../PC/PC.html#PC">PC</A> pc,<A HREF="../PC/PCFieldSplitSchurFactType.html#PCFieldSplitSchurFactType">PCFieldSplitSchurFactType</A> ftype)
</PRE>
Collective on <A HREF="../PC/PC.html#PC">PC</A>
<P>
<H3><FONT COLOR="#CC3333">Input Parameters</FONT></H3>
<TABLE border="0" cellpadding="0" cellspacing="0">
<TR><TD WIDTH=40></TD><TD ALIGN=LEFT VALIGN=TOP><B>pc </B></TD><TD>- the preconditioner context
</TD></TR>
<TR><TD WIDTH=40></TD><TD ALIGN=LEFT VALIGN=TOP><B>ftype </B></TD><TD>- which blocks of factorization to retain, <A HREF="../PC/PCFieldSplitSchurFactType.html#PCFieldSplitSchurFactType">PC_FIELDSPLIT_SCHUR_FACT_FULL</A> is default
</TD></TR></TABLE>
<P>
<H3><FONT COLOR="#CC3333">Options Database</FONT></H3>
<TABLE border="0" cellpadding="0" cellspacing="0">
<TR><TD WIDTH=40></TD><TD ALIGN=LEFT VALIGN=TOP><B>-pc_fieldsplit_schur_fact_type <diag,lower,upper,full> default is full</B></TD></TABLE>
<P>
<P>
<P>
<H3><FONT COLOR="#CC3333">Notes</FONT></H3>
The FULL factorization is
<P>
<pre>
(A B) = (1 0) (A 0) (1 Ainv*B) = L D U
</pre>
<pre>
(C E) (C*Ainv 1) (0 S) (0 1)
</pre>
<P>
where S = E - C*Ainv*B. In practice, the full factorization is applied via block triangular solves with the grouping L*(D*U). UPPER uses D*U, LOWER uses L*D,
and DIAG is the diagonal part with the sign of S flipped (because this makes the preconditioner positive definite for many formulations, thus allowing the use of <A HREF="../KSP/KSPMINRES.html#KSPMINRES">KSPMINRES</A>). Sign flipping of S can be turned off with <A HREF="../PC/PCFieldSplitSetSchurScale.html#PCFieldSplitSetSchurScale">PCFieldSplitSetSchurScale</A>().
<P>
<pre>
If A and S are solved exactly
</pre>
<pre>
*) FULL factorization is a direct solver.
</pre>
<pre>
*) The preconditioned operator with LOWER or UPPER has all eigenvalues equal to 1 and minimal polynomial of degree 2, so <A HREF="../KSP/KSPGMRES.html#KSPGMRES">KSPGMRES</A> converges in 2 iterations.
</pre>
<pre>
*) With DIAG, the preconditioned operator has three distinct nonzero eigenvalues and minimal polynomial of degree at most 4, so <A HREF="../KSP/KSPGMRES.html#KSPGMRES">KSPGMRES</A> converges in at most 4 iterations.
</pre>
<P>
If the iteration count is very low, consider using <A HREF="../KSP/KSPFGMRES.html#KSPFGMRES">KSPFGMRES</A> or <A HREF="../KSP/KSPGCR.html#KSPGCR">KSPGCR</A> which can use one less preconditioner
application in this case. Note that the preconditioned operator may be highly non-normal, so such fast convergence may not be observed in practice.
<P>
For symmetric problems in which A is positive definite and S is negative definite, DIAG can be used with <A HREF="../KSP/KSPMINRES.html#KSPMINRES">KSPMINRES</A>.
<P>
Note that a flexible method like <A HREF="../KSP/KSPFGMRES.html#KSPFGMRES">KSPFGMRES</A> or <A HREF="../KSP/KSPGCR.html#KSPGCR">KSPGCR</A> must be used if the fieldsplit preconditioner is nonlinear (e.g. a few iterations of a Krylov method is used to solve with A or S).
<P>
<H3><FONT COLOR="#CC3333">References</FONT></H3>
<TABLE border="0" cellpadding="0" cellspacing="0">
<TR><TD WIDTH=40></TD><TD ALIGN=LEFT VALIGN=TOP><B>1. </B></TD><TD>- Murphy, Golub, and Wathen, A note on preconditioning indefinite linear systems, SIAM J. Sci. Comput., 21 (2000).
</TD></TR>
<TR><TD WIDTH=40></TD><TD ALIGN=LEFT VALIGN=TOP><B>2. </B></TD><TD>- Ipsen, A note on preconditioning nonsymmetric matrices, SIAM J. Sci. Comput., 23 (2001).
</TD></TR></TABLE>
<P>
<H3><FONT COLOR="#CC3333">See Also</FONT></H3>
<A HREF="../PC/PCFieldSplitGetSubKSP.html#PCFieldSplitGetSubKSP">PCFieldSplitGetSubKSP</A>(), <A HREF="../PC/PCFIELDSPLIT.html#PCFIELDSPLIT">PCFIELDSPLIT</A>, <A HREF="../PC/PCFieldSplitSetFields.html#PCFieldSplitSetFields">PCFieldSplitSetFields</A>(), <A HREF="../PC/PCFieldSplitSchurPreType.html#PCFieldSplitSchurPreType">PCFieldSplitSchurPreType</A>, <A HREF="../PC/PCFieldSplitSetSchurScale.html#PCFieldSplitSetSchurScale">PCFieldSplitSetSchurScale</A>()
<BR><P><B></B><H3><FONT COLOR="#CC3333">Level</FONT></H3>intermediate<BR>
<H3><FONT COLOR="#CC3333">Location</FONT></H3>
</B><A HREF="../../../src/ksp/pc/impls/fieldsplit/fieldsplit.c.html#PCFieldSplitSetSchurFactType">src/ksp/pc/impls/fieldsplit/fieldsplit.c</A>
<P><H3><FONT COLOR="CC3333">Implementations</FONT></H3><A HREF="../../../src/ksp/pc/impls/fieldsplit/fieldsplit.c.html#PCFieldSplitSetSchurFactType_FieldSplit">PCFieldSplitSetSchurFactType_FieldSplit in src/ksp/pc/impls/fieldsplit/fieldsplit.c</A><BR>
<BR><A HREF="./index.html">Index of all PC routines</A>
<BR><A HREF="../../index.html">Table of Contents for all manual pages</A>
<BR><A HREF="../singleindex.html">Index of all manual pages</A>
</BODY></HTML>
|
