petsc-3.10.2 2018-10-09
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MatSchurComplementGetPmat

Obtain a preconditioning matrix for the Schur complement by assembling Sp = A11 - A10 inv(diag(A00)) A01

Synopsis

#include "petscksp.h" 
PetscErrorCode  MatSchurComplementGetPmat(Mat S,MatReuse preuse,Mat *Sp)
Collective on Mat

Input Parameters

S - matrix obtained with MatCreateSchurComplement() (or equivalent) and implementing the action of A11 - A10 ksp(A00,Ap00) 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

Sp -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)).

Sometimes users would like to provide problem-specific data in the Schur complement, usually only for special row and column index sets. In that case, the user should call PetscObjectComposeFunction() to set "MatSchurComplementGetPmat_C" to their function. If their function needs to fall back to the default implementation, it should call MatSchurComplementGetPmat_Basic().

Developer Notes

The API that includes MatGetSchurComplement(), MatCreateSchurComplement(), MatSchurComplementGetPmat() should be refactored to remove redundancy and be clearer and simplier.

See Also

MatCreateSubMatrix(), PCFIELDSPLIT, MatGetSchurComplement(), MatCreateSchurComplement(), MatSchurComplementSetAinvType()

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