MatSchurComplementGetPmat#

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

Synopsis#

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


Collective

Input Parameters#

• S - matrix obtained with MatCreateSchurComplement() (or equivalent) that implements 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 the exact Schur complement S = A11 - A10 inv(A00) A01

Notes#

The approximation of Sp depends on the the argument passed to to MatSchurComplementSetAinvType() MAT_SCHUR_COMPLEMENT_AINV_DIAG, MAT_SCHUR_COMPLEMENT_AINV_LUMP, MAT_SCHUR_COMPLEMENT_AINV_BLOCK_DIAG, or MAT_SCHUR_COMPLEMENT_AINV_FULL -mat_schur_complement_ainv_type <diag,lump,blockdiag,full>

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 Note#

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

This routine should be called MatSchurComplementCreatePmat()

KSP: Linear System Solvers, MatCreateSubMatrix(), PCFIELDSPLIT, MatGetSchurComplement(), MatCreateSchurComplement(), MatSchurComplementSetAinvType()