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<div id="version" align=right><b>petsc-3.7.5 2017-01-01</b></div>
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<A NAME="KSPDGMRES"><H1>KSPDGMRES</H1></A>
Implements the deflated GMRES as defined in [1,2]. In this implementation, the adaptive strategy allows to switch to the deflated GMRES when the stagnation occurs.
<H3><FONT COLOR="#CC3333">Options Database Keys</FONT></H3>
<H3><FONT COLOR="#CC3333">GMRES Options (inherited)</FONT></H3>
<TABLE border="0" cellpadding="0" cellspacing="0">
<TR><TD WIDTH=40></TD><TD ALIGN=LEFT VALIGN=TOP><B>-ksp_gmres_restart <restart> </B></TD><TD>- the number of Krylov directions to orthogonalize against
</TD></TR>
<TR><TD WIDTH=40></TD><TD ALIGN=LEFT VALIGN=TOP><B>-ksp_gmres_haptol <tol> </B></TD><TD>- sets the tolerance for "happy ending" (exact convergence)
</TD></TR>
<TR><TD WIDTH=40></TD><TD ALIGN=LEFT VALIGN=TOP><B>-ksp_gmres_preallocate </B></TD><TD>- preallocate all the Krylov search directions initially (otherwise groups of
vectors are allocated as needed)
</TD></TR>
<TR><TD WIDTH=40></TD><TD ALIGN=LEFT VALIGN=TOP><B>-ksp_gmres_classicalgramschmidt </B></TD><TD>- use classical (unmodified) Gram-Schmidt to orthogonalize against the Krylov space (fast) (the default)
</TD></TR>
<TR><TD WIDTH=40></TD><TD ALIGN=LEFT VALIGN=TOP><B>-ksp_gmres_modifiedgramschmidt </B></TD><TD>- use modified Gram-Schmidt in the orthogonalization (more stable, but slower)
</TD></TR>
<TR><TD WIDTH=40></TD><TD ALIGN=LEFT VALIGN=TOP><B>-ksp_gmres_cgs_refinement_type <never,ifneeded,always> </B></TD><TD>- determine if iterative refinement is used to increase the
stability of the classical Gram-Schmidt orthogonalization.
</TD></TR>
<TR><TD WIDTH=40></TD><TD ALIGN=LEFT VALIGN=TOP><B>-ksp_gmres_krylov_monitor </B></TD><TD>- plot the Krylov space generated
</TD></TR></TABLE>
<P>
<H3><FONT COLOR="#CC3333">DGMRES Options Database Keys</FONT></H3>
<TABLE border="0" cellpadding="0" cellspacing="0">
<TR><TD WIDTH=40></TD><TD ALIGN=LEFT VALIGN=TOP><B>-ksp_dgmres_eigen <neig> </B></TD><TD>- number of smallest eigenvalues to extract at each restart
</TD></TR>
<TR><TD WIDTH=40></TD><TD ALIGN=LEFT VALIGN=TOP><B>-ksp_dgmres_max_eigen <max_neig> </B></TD><TD>- maximum number of eigenvalues that can be extracted during the iterative
process
</TD></TR>
<TR><TD WIDTH=40></TD><TD ALIGN=LEFT VALIGN=TOP><B>-ksp_dgmres_force </B></TD><TD>- use the deflation at each restart; switch off the adaptive strategy.
</TD></TR>
<TR><TD WIDTH=40></TD><TD ALIGN=LEFT VALIGN=TOP><B>-ksp_dgmres_view_deflation_vecs <viewerspec> </B></TD><TD>- View the deflation vectors, where viewerspec is a key that can be
parsed by <A HREF="../Viewer/PetscOptionsGetViewer.html#PetscOptionsGetViewer">PetscOptionsGetViewer</A>(). If neig > 1, viewerspec should
end with ":append". No vectors will be viewed if the adaptive
strategy chooses not to deflate, so -ksp_dgmres_force should also
be given.
The deflation vectors span a subspace that may be a good
approximation of the subspace of smallest eigenvectors of the
preconditioned operator, so this option can aid in understanding
the performance of a preconditioner.
</TD></TR></TABLE>
<P>
<P>
Notes: Left and right preconditioning are supported, but not symmetric preconditioning. Complex arithmetic is not yet supported
<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>- J. Erhel, K. Burrage and B. Pohl, Restarted GMRES preconditioned by deflation,J. Computational and Applied Mathematics, 69(1996).
</TD></TR>
<TR><TD WIDTH=40></TD><TD ALIGN=LEFT VALIGN=TOP><B>2. </B></TD><TD>- D. NUENTSA WAKAM and F. PACULL, Memory Efficient Hybrid Algebraic Solvers for Linear Systems Arising from Compressible Flows, Computers and Fluids,
In Press, http://dx.doi.org/10.1016/j.compfluid.2012.03.023
</TD></TR></TABLE>
<P>
Contributed by: Desire NUENTSA WAKAM,INRIA
<P>
.seealso: <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>, <A HREF="../KSP/KSPFGMRES.html#KSPFGMRES">KSPFGMRES</A>, <A HREF="../KSP/KSPLGMRES.html#KSPLGMRES">KSPLGMRES</A>,
<A HREF="../KSP/KSPGMRESSetRestart.html#KSPGMRESSetRestart">KSPGMRESSetRestart</A>(), <A HREF="../KSP/KSPGMRESSetHapTol.html#KSPGMRESSetHapTol">KSPGMRESSetHapTol</A>(), <A HREF="../KSP/KSPGMRESSetPreAllocateVectors.html#KSPGMRESSetPreAllocateVectors">KSPGMRESSetPreAllocateVectors</A>(), <A HREF="../KSP/KSPGMRESSetOrthogonalization.html#KSPGMRESSetOrthogonalization">KSPGMRESSetOrthogonalization</A>(), <A HREF="../KSP/KSPGMRESGetOrthogonalization.html#KSPGMRESGetOrthogonalization">KSPGMRESGetOrthogonalization</A>(),
<A HREF="../KSP/KSPGMRESClassicalGramSchmidtOrthogonalization.html#KSPGMRESClassicalGramSchmidtOrthogonalization">KSPGMRESClassicalGramSchmidtOrthogonalization</A>(), <A HREF="../KSP/KSPGMRESModifiedGramSchmidtOrthogonalization.html#KSPGMRESModifiedGramSchmidtOrthogonalization">KSPGMRESModifiedGramSchmidtOrthogonalization</A>(),
<A HREF="../KSP/KSPGMRESCGSRefinementType.html#KSPGMRESCGSRefinementType">KSPGMRESCGSRefinementType</A>, <A HREF="../KSP/KSPGMRESSetCGSRefinementType.html#KSPGMRESSetCGSRefinementType">KSPGMRESSetCGSRefinementType</A>(), <A HREF="../KSP/KSPGMRESGetCGSRefinementType.html#KSPGMRESGetCGSRefinementType">KSPGMRESGetCGSRefinementType</A>(), <A HREF="../KSP/KSPGMRESMonitorKrylov.html#KSPGMRESMonitorKrylov">KSPGMRESMonitorKrylov</A>(), <A HREF="../KSP/KSPSetPCSide.html#KSPSetPCSide">KSPSetPCSide</A>()
<P>
<P><B><P><B><FONT COLOR="#CC3333">Level:</FONT></B>beginner
<BR><FONT COLOR="#CC3333">Location:</FONT></B><A HREF="../../../src/ksp/ksp/impls/gmres/dgmres/dgmres.c.html#KSPDGMRES">src/ksp/ksp/impls/gmres/dgmres/dgmres.c</A>
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