petsc-3.5.1 2014-08-06
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PCILU

Incomplete factorization preconditioners.

Options Database Keys

Notes: Only implemented for some matrix formats. (for parallel see PCHYPRE for hypre's ILU)

For BAIJ matrices this implements a point block ILU

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.

If you are using MATSEQAIJCUSPARSE matrices (or MATMPIAIJCUSPARESE matrices with block Jacobi), factorization is never done on the GPU).

References

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.

T.A. Oliphant. An implicit numerical method for solving two-dimensional time-dependent dif- fusion problems. Quart. Appl. Math., 19:221--229, 1961.

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.

See Also

PCCreate(), PCSetType(), PCType (for list of available types), PC, PCSOR, MatOrderingType,
PCFactorSetZeroPivot(), PCFactorSetShiftSetType(), PCFactorSetAmount(), PCFactorSetDropTolerance(),PCFactorSetFill(), PCFactorSetMatOrderingType(), PCFactorSetReuseOrdering(), PCFactorSetLevels(), PCFactorSetUseInPlace(), PCFactorSetAllowDiagonalFill(), PCFactorSetPivotInBlocks()

Level:beginner
Location:
src/ksp/pc/impls/factor/ilu/ilu.c
Index of all PC routines
Table of Contents for all manual pages
Index of all manual pages

Examples

src/ksp/pc/examples/tutorials/ex1.c.html
src/ksp/ksp/examples/tutorials/ex7.c.html
src/ksp/ksp/examples/tutorials/ex8.c.html
src/ksp/ksp/examples/tutorials/ex8g.c.html
src/ksp/ksp/examples/tutorials/ex52.c.html
-pc_factor_levels <k> - number of levels of fill for ILU(k)
-pc_factor_in_place - only for ILU(0) with natural ordering, reuses the space of the matrix for its factorization (overwrites original matrix)
-pc_factor_diagonal_fill - fill in a zero diagonal even if levels of fill indicate it wouldn't be fill
-pc_factor_reuse_ordering - reuse ordering of factorized matrix from previous factorization
-pc_factor_fill <nfill> - expected amount of fill in factored matrix compared to original matrix, nfill > 1
-pc_factor_nonzeros_along_diagonal - reorder the matrix before factorization to remove zeros from the diagonal, this decreases the chance of getting a zero pivot
-pc_factor_mat_ordering_type <natural,nd,1wd,rcm,qmd> - set the row/column ordering of the factored matrix
-pc_factor_pivot_in_blocks - 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