petsc-3.7.7 2017-09-25

MatGetSchurComplement

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

Synopsis

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

Output Parameters

	S	- exact Schur complement, often of type MATSCHURCOMPLEMENT which is difficult to use for preconditioning
	Sp	- 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 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() on the *S matrix and pass mreuse of MAT_REUSE_MATRIX to set "MatGetSchurComplement_C" to their function. If their function needs to fall back to the default implementation, it should call MatGetSchurComplement_Basic().

MatGetSchurComplement

Synopsis

Input Parameters

Output Parameters

Note

See Also