Obtain the Schur complement from eliminating part of the matrix in another part.
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
ainvtype - the type of approximation used for the inverse of the (0,0) block used in forming Sp:
S - exact Schur complement, often of type
MATSCHURCOMPLEMENTwhich is difficult to use for preconditioning
Sp - approximate Schur complement from which a preconditioner can be built A11 - A10 inv(DIAGFORM(A00)) A01
Since the real Schur complement is usually dense, providing a good approximation to Sp usually requires application-specific information.
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
MatCreateSchurComplement() takes as arguments the four submatrices and returns the virtual Schur complement (what this function returns in S).
MatSchurComplementGetPmat() takes the virtual Schur complement and returns an explicit approximate Schur complement (what this returns in Sp).
In other words calling
MatCreateSchurComplement() followed by
MatSchurComplementGetPmat() produces the same output as this function but with slightly different
inputs. The actually submatrices of the original block matrix instead of index sets to the submatrices.