petsc-3.4.4 2014-03-13

MatGetSchurComplement

Obtain the Schur complement from eliminating part of the matrix in another part.

Synopsis

#include "petscksp.h" 
PetscErrorCode  MatGetSchurComplement(Mat mat,IS isrow0,IS iscol0,IS isrow1,IS iscol1,MatReuse mreuse,Mat *newmat,MatReuse preuse,Mat *newpmat)
Collective on Mat

Input Parameters

mat - Matrix in which the complement is to be taken
isrow0 - rows to eliminate
iscol0 - columns to eliminate, (isrow0,iscol0) should be square and nonsingular
isrow1 - rows in which the Schur complement is formed
iscol1 - columns in which the Schur complement is formed
mreuse - MAT_INITIAL_MATRIX or MAT_REUSE_MATRIX, use MAT_IGNORE_MATRIX to put nothing in newmat
preuse - MAT_INITIAL_MATRIX or MAT_REUSE_MATRIX, use MAT_IGNORE_MATRIX to put nothing in newpmat

Output Parameters

newmat - exact Schur complement, often of type MATSCHURCOMPLEMENT which is difficult to use for preconditioning
newpmat - approximate Schur complement suitable for preconditioning

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 diagonal of the (0,0) block which will rarely produce a scalable algorithm.

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 "MatNestGetSubMat_C" to their function. If their function needs to fall back to the default implementation, it should call MatGetSchurComplement_Basic().

See Also

MatGetSubMatrix(), PCFIELDSPLIT, MatCreateSchurComplement()

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