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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="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></TABLE>
<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/MATSEQAIJCUSPARSE.html#MATSEQAIJCUSPARSE">MATSEQAIJCUSPARSE</A> matrices (or MATMPIAIJCUSPARESE matrices with block Jacobi), factorization
is never done on the GPU).
<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>- T. Dupont, R. Kendall, and H. Rachford. An approximate factorization procedure for solving
self adjoint elliptic difference equations. SIAM J. Numer. Anal., 5, 1968.
</TD></TR>
<TR><TD WIDTH=40></TD><TD ALIGN=LEFT VALIGN=TOP><B>2. </B></TD><TD>- T.A. Oliphant. An implicit numerical method for solving two dimensional timedependent diffusion problems. Quart. Appl. Math., 19, 1961.
</TD></TR>
<TR><TD WIDTH=40></TD><TD ALIGN=LEFT VALIGN=TOP><B>3. </B></TD><TD>- TONY F. CHAN AND HENK A. VAN DER VORST, APPROXIMATE AND INCOMPLETE FACTORIZATIONS,
Chapter in Parallel Numerical
Algorithms, edited by D. Keyes, A. Semah, V. Venkatakrishnan, ICASE/LaRC Interdisciplinary Series in
Science and Engineering, Kluwer.
</TD></TR></TABLE>
<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>(),
<A HREF="../PC/PCFactorGetAllowDiagonalFill.html#PCFactorGetAllowDiagonalFill">PCFactorGetAllowDiagonalFill</A>(), <A HREF="../PC/PCFactorGetUseInPlace.html#PCFactorGetUseInPlace">PCFactorGetUseInPlace</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/ex52.c.html">src/ksp/ksp/examples/tutorials/ex52.c.html</A><BR>
<A HREF="../../../src/ksp/ksp/examples/tutorials/ex62.c.html">src/ksp/ksp/examples/tutorials/ex62.c.html</A><BR>
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