MatCreateSchurComplementPmat

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

Synopsis

#include "petscksp.h" 
PetscErrorCode MatCreateSchurComplementPmat(Mat A00, Mat A01, Mat A10, Mat A11, MatSchurComplementAinvType ainvtype, MatReuse preuse, Mat *Sp)

Collective

Input Parameters

• A00 - the upper-left part of the original matrix \(A = [A00 A01; A10 A11]\)

• A01 - (optional) the upper-right part of the original matrix \(A = [A00 A01; A10 A11]\)

• A10 - (optional) the lower-left part of the original matrix \(A = [A00 A01; A10 A11]\)

• A11 - (optional) the lower-right part of the original matrix \(A = [A00 A01; A10 A11]\)

• ainvtype - type of approximation for DIAGFORM(A00) used when forming \(Sp = A11 - A10 inv(DIAGFORM(A00)) A01\). See MatSchurComplementAinvType.

• 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 constructing a preconditioner for the true Schur complement \(S = A11 - A10 inv(A00) A01\)

See Also

KSP: Linear System Solvers, MatCreateSchurComplement(), MatGetSchurComplement(), MatSchurComplementGetPmat(), MatSchurComplementAinvType

Level

advanced

Location

src/ksp/ksp/utils/schurm/schurm.c

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