# PCILU#

Incomplete factorization preconditioners.

## Options Database Keys#

• -pc_factor_levels - 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 - 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

## Notes#

Only implemented for some matrix format and sequential. For parallel see PCHYPRE for hypre’s ILU

For MATSEQBAIJ 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 MATMPIAIJCUSPARSE 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, 1968.

• **** -*** T.A. Oliphant. An implicit numerical method for solving two dimensional timedependent diffusion problems. Quart. Appl. Math., 19, 1961.

• **** -*** 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.

PCCreate(), PCSetType(), PCType, PC, PCSOR, MatOrderingType, PCLU, PCICC, PCCHOLESKY, PCFactorSetZeroPivot(), PCFactorSetShiftSetType(), PCFactorSetAmount(), PCFactorSetDropTolerance(), PCFactorSetFill(), PCFactorSetMatOrderingType(), PCFactorSetReuseOrdering(), PCFactorSetLevels(), PCFactorSetUseInPlace(), PCFactorSetAllowDiagonalFill(), PCFactorSetPivotInBlocks(), PCFactorGetAllowDiagonalFill(), PCFactorGetUseInPlace()

beginner

## Location#

src/ksp/pc/impls/factor/ilu/ilu.c

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