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.