PCILU#
Incomplete factorization preconditioners [DKR68], [Oli61], [CVDV97]
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
MATBAIJ
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#
Tony F Chan and Henk A Van Der Vorst. Approximate and incomplete factorizations. In Parallel numerical algorithms, pages 167–202. Springer, 1997.
Todd Dupont, Richard P Kendall, and HH Rachford, Jr. An approximate factorization procedure for solving self-adjoint elliptic difference equations. SIAM Journal on Numerical Analysis, 5(3):559–573, 1968.
Thomas A Oliphant. An implicit, numerical method for solving two-dimensional time-dependent diffusion problems. Quarterly of Applied mathematics, 19(3):221–229, 1961.
See Also#
KSP: Linear System Solvers, PCCreate()
, PCSetType()
, PCType
, PC
, PCSOR
, MatOrderingType
, PCLU
, PCICC
, PCCHOLESKY
,
PCFactorSetZeroPivot()
, PCFactorSetShiftSetType()
, PCFactorSetAmount()
,
PCFactorSetDropTolerance()
, PCFactorSetFill()
, PCFactorSetMatOrderingType()
, PCFactorSetReuseOrdering()
,
PCFactorSetLevels()
, PCFactorSetUseInPlace()
, PCFactorSetAllowDiagonalFill()
, PCFactorSetPivotInBlocks()
,
PCFactorGetAllowDiagonalFill()
, PCFactorGetUseInPlace()
Level#
beginner
Location#
Examples#
src/ksp/ksp/tutorials/ex7.c
src/ksp/ksp/tutorials/ex52.c
src/ksp/pc/tutorials/ex1.c
src/ksp/pc/tutorials/ex4.c
src/ksp/ksp/tutorials/ex62.c
src/ksp/ksp/tutorials/ex8.c
Index of all PC routines
Table of Contents for all manual pages
Index of all manual pages