MatSchurComplementGetPmat — PETSc 3.22.5 documentation

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# MatSchurComplementGetPmat

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

## Synopsis

    #include "petscksp.h"
    PetscErrorCode MatSchurComplementGetPmat(Mat S, MatReuse preuse, Mat *Sp)

Collective

## Input Parameters

- S - matrix obtained with MatCreateSchurComplement() (or equivalent) that implements the action of \(A11 - A10 ksp(A00,Ap00) A01\)

- 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

- Sp - approximate Schur complement suitable for preconditioning the exact Schur complement \(S = A11 - A10 inv(A00) A01\)

## Notes

The approximation of `Sp` depends on the argument passed to `MatSchurComplementSetAinvType()` `MAT_SCHUR_COMPLEMENT_AINV_DIAG`, `MAT_SCHUR_COMPLEMENT_AINV_LUMP`, `MAT_SCHUR_COMPLEMENT_AINV_BLOCK_DIAG`, or `MAT_SCHUR_COMPLEMENT_AINV_FULL` -mat_schur_complement_ainv_type <diag,lump,blockdiag,full>

Sometimes users would like to provide problem-specific data in the Schur complement, usually only for special row and column index sets. In that case, the user should call `PetscObjectComposeFunction()` to set “MatSchurComplementGetPmat_C” to their function. If their function needs to fall back to the default implementation, it should call `MatSchurComplementGetPmat_Basic()`.

## Developer Notes

The API that includes `MatGetSchurComplement()`, `MatCreateSchurComplement()`, `MatSchurComplementGetPmat()` should be refactored to remove redundancy and be clearer and simpler.

This routine should be called `MatSchurComplementCreatePmat()`

## See Also

KSP: Linear System Solvers, `MatCreateSubMatrix()`, `PCFIELDSPLIT`, `MatGetSchurComplement()`, `MatCreateSchurComplement()`, `MatSchurComplementSetAinvType()`

## Level

advanced

## Location

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

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