petsc-3.10.5 2019-03-28
MatCreateSchurComplementPmat
create a preconditioning matrix for the Schur complement by assembling Sp = A11 - A10 inv(diag(A00)) A01
Synopsis
#include "petscksp.h"
PetscErrorCode MatCreateSchurComplementPmat(Mat A00,Mat A01,Mat A10,Mat A11,MatSchurComplementAinvType ainvtype,MatReuse preuse,Mat *Spmat)
Collective on Mat
Input Parameters
| A00,A01,A10,A11 | - the four parts of the original matrix A = [A00 A01; A10 A11] (A01,A10, and A11 are optional, implying zero matrices)
|
| ainvtype | - type of approximation for inv(A00) used when forming Sp = A11 - A10 inv(A00) A01
|
| preuse | - MAT_INITIAL_MATRIX for a new Sp, or MAT_REUSE_MATRIX to reuse an existing Sp, or MAT_IGNORE_MATRIX to put nothing in Sp
|
Output Parameter
Spmat -approximate Schur complement suitable for preconditioning S = A11 - A10 inv(diag(A00)) A01
Note
Since the real Schur complement is usually dense, providing a good approximation to newpmat usually requires
application-specific information. The default for assembled matrices is to use the inverse of the diagonal of
the (0,0) block A00 in place of A00^{-1}. This rarely produce a scalable algorithm. Optionally, A00 can be lumped
before forming inv(diag(A00)).
See Also
MatCreateSchurComplement(), MatGetSchurComplement(), MatSchurComplementGetPmat(), MatSchurComplementAinvType
Level
advanced
Location
src/ksp/ksp/utils/schurm/schurm.c
Index of all KSP routines
Table of Contents for all manual pages
Index of all manual pages