petsc-3.7.3 2016-07-24
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# MatCreateSchurComplementPmat

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

### Synopsis

    #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

### Note

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

Level:advanced
Location: src/ksp/ksp/utils/schurm.c
Index of all KSP routines
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Index of all manual pages