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<div id="version" align=right><b>petsc-3.4.2 2013-07-02</b></div>
<A NAME="PCFieldSplitSetSchurFactType"><H1>PCFieldSplitSetSchurFactType</H1></A>
sets which blocks of the approximate block factorization to retain
<H3><FONT COLOR="#CC3333">Synopsis</FONT></H3>
<PRE>
#include "petscpc.h"
PetscErrorCode PCFieldSplitSetSchurFactType(PC pc,PCFieldSplitSchurFactType 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, PC_FIELDSPLIT_SCHUR_FACT_FULL is default
</TD></TR></TABLE>
<P>
<H3><FONT COLOR="#CC3333">Options Database</FONT></H3>
<DT><B>-pc_fieldsplit_schur_fact_type <diag,lower,upper,full> default is full</B> -
<br>
<P>
<P>
<H3><FONT COLOR="#CC3333">Notes</FONT></H3>
The FULL factorization is
<P>
<pre>
(A B) = (1 0) (A 0) (1 Ainv*B)
</pre>
<pre>
(C D) (C*Ainv 1) (0 S) (0 1 )
</pre>
<P>
where S = D - 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>).
<P>
If applied exactly, FULL factorization is a direct solver. 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. 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. 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.
<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>. 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 inside a split).
<P>
<H3><FONT COLOR="#CC3333">References</FONT></H3>
Murphy, Golub, and Wathen, A note on preconditioning indefinite linear systems, SIAM J. Sci. Comput., 21 (2000) pp. 1969-1972.
<P>
Ipsen, A note on preconditioning nonsymmetric matrices, SIAM J. Sci. Comput., 23 (2001), pp. 1050-1051.
<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>
<BR><P><B><P><B><FONT COLOR="#CC3333">Level:</FONT></B>intermediate
<BR><FONT COLOR="#CC3333">Location:</FONT></B><A HREF="../../../src/ksp/pc/impls/fieldsplit/fieldsplit.c.html#PCFieldSplitSetSchurFactType">src/ksp/pc/impls/fieldsplit/fieldsplit.c</A>
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