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<div id="version" align=right><b>petsc-3.4.2 2013-07-02</b></div>
<A NAME="PCILU"><H1>PCILU</H1></A>
Incomplete factorization preconditioners.
<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>-pc_factor_levels <k> </B></TD><TD>- number of levels of fill for ILU(k)
</TD></TR>
<TR><TD WIDTH=40></TD><TD ALIGN=LEFT VALIGN=TOP><B>-pc_factor_in_place </B></TD><TD>- only for ILU(0) with natural ordering, reuses the space of the matrix for
its factorization (overwrites original matrix)
</TD></TR>
<TR><TD WIDTH=40></TD><TD ALIGN=LEFT VALIGN=TOP><B>-pc_factor_diagonal_fill </B></TD><TD>- fill in a zero diagonal even if levels of fill indicate it wouldn't be fill
</TD></TR>
<TR><TD WIDTH=40></TD><TD ALIGN=LEFT VALIGN=TOP><B>-pc_factor_reuse_ordering </B></TD><TD>- reuse ordering of factorized matrix from previous factorization
</TD></TR>
<TR><TD WIDTH=40></TD><TD ALIGN=LEFT VALIGN=TOP><B>-pc_factor_fill <nfill> </B></TD><TD>- expected amount of fill in factored matrix compared to original matrix, nfill > 1
</TD></TR>
<TR><TD WIDTH=40></TD><TD ALIGN=LEFT VALIGN=TOP><B>-pc_factor_nonzeros_along_diagonal </B></TD><TD>- reorder the matrix before factorization to remove zeros from the diagonal,
this decreases the chance of getting a zero pivot
</TD></TR>
<TR><TD WIDTH=40></TD><TD ALIGN=LEFT VALIGN=TOP><B>-pc_factor_mat_ordering_type <natural,nd,1wd,rcm,qmd> </B></TD><TD>- set the row/column ordering of the factored matrix
</TD></TR>
<TR><TD WIDTH=40></TD><TD ALIGN=LEFT VALIGN=TOP><B>-pc_factor_pivot_in_blocks </B></TD><TD>- for block ILU(k) factorization, i.e. with BAIJ matrices with block size larger
than 1 the diagonal blocks are factored with partial pivoting (this increases the
stability of the ILU factorization
</TD></TR>
<P>
<P>
<P>
Notes: Only implemented for some matrix formats. (for parallel see <A HREF="../PC/PCHYPRE.html#PCHYPRE">PCHYPRE</A> for hypre's ILU)
<P>
For BAIJ matrices this implements a point block ILU
<P>
The "symmetric" application of this preconditioner is not actually symmetric since L is not transpose(U)
even when the matrix is not symmetric since the U stores the diagonals of the factorization.
<P>
If you are using <A HREF="../Mat/MATSEQAIJCUSP.html#MATSEQAIJCUSP">MATSEQAIJCUSP</A> matrices (or MATMPIAIJCUSP matrices with block Jacobi) you must have ./configured
PETSc with also --download-txpetscgpu to have the triangular solves performed on the GPU (factorization is never
done on the GPU).
<P>
<H3><FONT COLOR="#CC3333">References</FONT></H3>
T. Dupont, R. Kendall, and H. Rachford. An approximate factorization procedure for solving
self-adjoint elliptic difference equations. SIAM J. Numer. Anal., 5:559--573, 1968.
<P>
T.A. Oliphant. An implicit numerical method for solving two-dimensional time-dependent dif-
fusion problems. Quart. Appl. Math., 19:221--229, 1961.
<P>
Review article: APPROXIMATE AND INCOMPLETE FACTORIZATIONS, TONY F. CHAN AND HENK A. VAN DER VORST
http://igitur-archive.library.uu.nl/math/2001-0621-115821/proc.pdf chapter in Parallel Numerical
Algorithms, edited by D. Keyes, A. Semah, V. Venkatakrishnan, ICASE/LaRC Interdisciplinary Series in
Science and Engineering, Kluwer, pp. 167--202.
<P>
<P>
<H3><FONT COLOR="#CC3333">See Also</FONT></H3>
<A HREF="../PC/PCCreate.html#PCCreate">PCCreate</A>(), <A HREF="../PC/PCSetType.html#PCSetType">PCSetType</A>(), <A HREF="../PC/PCType.html#PCType">PCType</A> (for list of available types), <A HREF="../PC/PC.html#PC">PC</A>, <A HREF="../PC/PCSOR.html#PCSOR">PCSOR</A>, <A HREF="../Mat/MatOrderingType.html#MatOrderingType">MatOrderingType</A>,
<BR><A HREF="../PC/PCFactorSetZeroPivot.html#PCFactorSetZeroPivot">PCFactorSetZeroPivot</A>(), PCFactorSetShiftSetType(), PCFactorSetAmount(),
PCFactorSetDropTolerance(),<A HREF="../PC/PCFactorSetFill.html#PCFactorSetFill">PCFactorSetFill</A>(), <A HREF="../PC/PCFactorSetMatOrderingType.html#PCFactorSetMatOrderingType">PCFactorSetMatOrderingType</A>(), <A HREF="../PC/PCFactorSetReuseOrdering.html#PCFactorSetReuseOrdering">PCFactorSetReuseOrdering</A>(),
<A HREF="../PC/PCFactorSetLevels.html#PCFactorSetLevels">PCFactorSetLevels</A>(), <A HREF="../PC/PCFactorSetUseInPlace.html#PCFactorSetUseInPlace">PCFactorSetUseInPlace</A>(), <A HREF="../PC/PCFactorSetAllowDiagonalFill.html#PCFactorSetAllowDiagonalFill">PCFactorSetAllowDiagonalFill</A>(), <A HREF="../PC/PCFactorSetPivotInBlocks.html#PCFactorSetPivotInBlocks">PCFactorSetPivotInBlocks</A>()
<P>
<P><B><P><B><FONT COLOR="#CC3333">Level:</FONT></B>beginner
<BR><FONT COLOR="#CC3333">Location:</FONT></B><A HREF="../../../src/ksp/pc/impls/factor/ilu/ilu.c.html#PCILU">src/ksp/pc/impls/factor/ilu/ilu.c</A>
<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>
<P><H3><FONT COLOR="#CC3333">Examples</FONT></H3>
<A HREF="../../../src/ksp/pc/examples/tutorials/ex1.c.html">src/ksp/pc/examples/tutorials/ex1.c.html</A><BR>
<A HREF="../../../src/ksp/ksp/examples/tutorials/ex7.c.html">src/ksp/ksp/examples/tutorials/ex7.c.html</A><BR>
<A HREF="../../../src/ksp/ksp/examples/tutorials/ex8.c.html">src/ksp/ksp/examples/tutorials/ex8.c.html</A><BR>
<A HREF="../../../src/ksp/ksp/examples/tutorials/ex8g.c.html">src/ksp/ksp/examples/tutorials/ex8g.c.html</A><BR>
<A HREF="../../../src/ksp/ksp/examples/tutorials/ex52.c.html">src/ksp/ksp/examples/tutorials/ex52.c.html</A><BR>
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