petsc-3.5.4 2015-05-23
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Obtain the Schur complement from eliminating part of the matrix in another part.


#include "petscksp.h" 
PetscErrorCode  MatGetSchurComplement(Mat A,IS isrow0,IS iscol0,IS isrow1,IS iscol1,MatReuse mreuse,Mat *S,MatSchurComplementAinvType ainvtype,MatReuse preuse,Mat *Sp)
Collective on Mat

Input Parameters

A - 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
plump - the type of approximation used for the inverse of the (0,0) block used in forming Sp: MAT_SCHUR_COMPLEMENT_AINV_DIAG | MAT_SCHUR_COMPLEMENT_AINV_LUMP
preuse - MAT_INITIAL_MATRIX or MAT_REUSE_MATRIX, use MAT_IGNORE_MATRIX to put nothing in newpmat

Output Parameters

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


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)).

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(), MatSchurComplementAinvType

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