petsc-3.10.5 2019-03-28
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# PCILU

Incomplete factorization preconditioners.

### Options Database Keys

| -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

### 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

| 1. | - T. Dupont, R. Kendall, and H. Rachford. An approximate factorization procedure for solving self adjoint elliptic difference equations. SIAM J. Numer. Anal., 5, 1968.
| 2. | - T.A. Oliphant. An implicit numerical method for solving two dimensional timedependent diffusion problems. Quart. Appl. Math., 19, 1961.
| 3. | - 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.

### See Also

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

### Level

beginner

### Location

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

### 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/ex52.c.html
src/ksp/ksp/examples/tutorials/ex62.c.html
Index of all PC routines
Table of Contents for all manual pages
Index of all manual pages