# MatSchurComplementSetSubMatrices#

Sets the matrices that define the Schur complement

## Synopsis#

#include "petscksp.h"
PetscErrorCode MatSchurComplementSetSubMatrices(Mat S, Mat A00, Mat Ap00, Mat A01, Mat A10, Mat A11)


Collective

## Input Parameters#

• S - matrix obtained with MatSetType(S,MATSCHURCOMPLEMENT)

• A00,A01,A10,A11 - the four parts of A = [A00 A01; A10 A11] (A11 is optional)

• Ap00 - preconditioning matrix for use in ksp(A00,Ap00) to approximate the action of A^{-1}.

## Notes#

The Schur complement is NOT explicitly formed! Rather, this object performs the matrix-vector product of the Schur complement by using formula S = A11 - A10 ksp(A00,Ap00) A01

All four matrices must have the same MPI communicator.

A00 and A11 must be square matrices.

This is to be used in the context of code such as

     MatSetType(S,MATSCHURCOMPLEMENT);
MatSchurComplementSetSubMatrices(S,...);


while MatSchurComplementUpdateSubMatrices() should only be called after MatCreateSchurComplement() or MatSchurComplementSetSubMatrices()

KSP: Linear System Solvers, Mat, MatCreateNormal(), MatMult(), MatCreate(), MatSchurComplementGetKSP(), MatSchurComplementUpdateSubMatrices(), MatCreateTranspose(), MatCreateSchurComplement(), MatGetSchurComplement()