petsc-3.11.4 2019-09-28
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create a preconditioning matrix for the Schur complement by assembling Sp = A11 - A10 inv(diag(A00)) A01


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

Input Parameters

A00,A01,A10,A11 - the four parts of the original matrix A = [A00 A01; A10 A11] (A01,A10, and A11 are optional, implying zero matrices)
ainvtype - type of approximation for inv(A00) used when forming Sp = A11 - A10 inv(A00) 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

Spmat -approximate Schur complement suitable for preconditioning S = A11 - A10 inv(diag(A00)) A01


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)).

See Also

MatCreateSchurComplement(), MatGetSchurComplement(), MatSchurComplementGetPmat(), MatSchurComplementAinvType




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