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<div id="version" align=right><b>petsc-3.14.5 2021-03-03</b></div>
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<A NAME="KSPPIPEGCR"><H1>KSPPIPEGCR</H1></A>
Implements a Pipelined Generalized Conjugate Residual method.
<H3><FONT COLOR="#CC3333">Options Database Keys</FONT></H3>
<TABLE border="0" cellpadding="0" cellspacing="0">
<TR><TD WIDTH=40></TD><TD ALIGN=LEFT VALIGN=TOP><B>-ksp_pipegcr_mmax <N> </B></TD><TD>- the max number of Krylov directions to orthogonalize against
</TD></TR>
<TR><TD WIDTH=40></TD><TD ALIGN=LEFT VALIGN=TOP><B>-ksp_pipegcr_unroll_w </B></TD><TD>- unroll w at the storage cost of a maximum of (mmax+1) extra vectors with the benefit of better pipelining (default: <A HREF="../Sys/PETSC_TRUE.html#PETSC_TRUE">PETSC_TRUE</A>)
</TD></TR>
<TR><TD WIDTH=40></TD><TD ALIGN=LEFT VALIGN=TOP><B>-ksp_pipegcr_nprealloc <N> </B></TD><TD>- the number of vectors to preallocated for storing Krylov directions. Once exhausted new directions are allocated blockwise (default: 5)
</TD></TR>
<TR><TD WIDTH=40></TD><TD ALIGN=LEFT VALIGN=TOP><B>-ksp_pipegcr_truncation_type <standard,notay> </B></TD><TD>- which previous search directions to orthogonalize against
</TD></TR></TABLE>
<P>
<P>
<H3><FONT COLOR="#CC3333">Notes</FONT></H3>
The PIPEGCR Krylov method supports non-symmetric matrices and permits the use of a preconditioner
which may vary from one iteration to the next. Users can can define a method to vary the
preconditioner between iterates via <A HREF="../KSP/KSPPIPEGCRSetModifyPC.html#KSPPIPEGCRSetModifyPC">KSPPIPEGCRSetModifyPC</A>().
Restarts are solves with x0 not equal to zero. When a restart occurs, the initial starting
solution is given by the current estimate for x which was obtained by the last restart
iterations of the PIPEGCR algorithm.
The method implemented requires at most the storage of 4 x mmax + 5 vectors, roughly twice as much as GCR.
<P>
Only supports left preconditioning.
<P>
The natural "norm" for this method is (u,Au), where u is the preconditioned residual. This norm is available at no additional computational cost, as with standard CG. Choosing preconditioned or unpreconditioned norm types involves a blocking reduction which prevents any benefit from pipelining.
<P>
<H3><FONT COLOR="#CC3333">Reference</FONT></H3>
P. Sanan, S.M. Schnepp, and D.A. May,
"Pipelined, Flexible Krylov Subspace Methods,"
SIAM Journal on Scientific Computing 2016 38:5, C441-C470,
DOI: 10.1137/15M1049130
<P>
<P>
<H3><FONT COLOR="#CC3333">See Also</FONT></H3>
<A HREF="../KSP/KSPCreate.html#KSPCreate">KSPCreate</A>(), <A HREF="../KSP/KSPSetType.html#KSPSetType">KSPSetType</A>(), <A HREF="../KSP/KSPType.html#KSPType">KSPType</A> (for list of available types), <A HREF="../KSP/KSP.html#KSP">KSP</A>,
<BR><A HREF="../KSP/KSPPIPEFGMRES.html#KSPPIPEFGMRES">KSPPIPEFGMRES</A>, <A HREF="../KSP/KSPPIPECG.html#KSPPIPECG">KSPPIPECG</A>, <A HREF="../KSP/KSPPIPECR.html#KSPPIPECR">KSPPIPECR</A>, <A HREF="../KSP/KSPPIPEFCG.html#KSPPIPEFCG">KSPPIPEFCG</A>,<A HREF="../KSP/KSPPIPEGCRSetTruncationType.html#KSPPIPEGCRSetTruncationType">KSPPIPEGCRSetTruncationType</A>(),<A HREF="../KSP/KSPPIPEGCRSetNprealloc.html#KSPPIPEGCRSetNprealloc">KSPPIPEGCRSetNprealloc</A>(),<A HREF="../KSP/KSPPIPEGCRSetUnrollW.html#KSPPIPEGCRSetUnrollW">KSPPIPEGCRSetUnrollW</A>(),<A HREF="../KSP/KSPPIPEGCRSetMmax.html#KSPPIPEGCRSetMmax">KSPPIPEGCRSetMmax</A>()
<P>
<P>
<P><B></B><H3><FONT COLOR="#CC3333">Level</FONT></H3>intermediate<BR>
<H3><FONT COLOR="#CC3333">Location</FONT></H3>
</B><A HREF="../../../src/ksp/ksp/impls/gcr/pipegcr/pipegcr.c.html#KSPPIPEGCR">src/ksp/ksp/impls/gcr/pipegcr/pipegcr.c</A>
<BR><A HREF="./index.html">Index of all KSP routines</A>
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