petsc-master 2015-11-29
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Creates a new matrix object that behaves like the Schur complement of a matrix


#include "petscksp.h" 
PetscErrorCode  MatCreateSchurComplement(Mat A00,Mat Ap00,Mat A01,Mat A10,Mat A11,Mat *S)
Collective on Mat

Input Parameters

A00,A01,A10,A11 - the four parts of the original matrix A = [A00 A01; A10 A11] (A11 is optional)
Ap00 - preconditioning matrix for use in ksp(A00,Ap00) to approximate the action of A^{-1}

Output Parameter

S -the matrix that the Schur complement S = A11 - A10 ksp(A00,Ap00) A01

Notes: The Schur complement is NOT actually formed! Rather, this object performs the matrix-vector product by using formula S = A11 - A10 A^{-1} A01 for Schur complement S and a KSP solver to approximate the action of A^{-1}.

All four matrices must have the same MPI communicator.

A00 and A11 must be square matrices.

See Also

MatCreateNormal(), MatMult(), MatCreate(), MatSchurComplementGetKSP(), MatSchurComplementUpdateSubMatrices(), MatCreateTranspose(), MatGetSchurComplement()

Index of all KSP routines
Table of Contents for all manual pages
Index of all manual pages