PCFieldSplitSetSchurPre#

Indicates from what operator the preconditioner is constructed for the Schur complement. The default is the A11 matrix.

Synopsis#

#include "petscpc.h" 
PetscErrorCode PCFieldSplitSetSchurPre(PC pc, PCFieldSplitSchurPreType ptype, Mat pre)

Collective

Input Parameters#

pc - the preconditioner context
ptype - which matrix to use for preconditioning the Schur complement: PC_FIELDSPLIT_SCHUR_PRE_A11 (default), PC_FIELDSPLIT_SCHUR_PRE_SELF, PC_FIELDSPLIT_SCHUR_PRE_USER, PC_FIELDSPLIT_SCHUR_PRE_SELFP, and PC_FIELDSPLIT_SCHUR_PRE_FULL
pre - matrix to use for preconditioning, or NULL

Options Database Keys#

-pc_fieldsplit_schur_precondition <self,selfp,user,a11,full> - default is a11. See notes for meaning of various arguments
-fieldsplit_1_pc_type - the preconditioner algorithm that is used to construct the preconditioner from the operator

Notes#

If ptype is

a11 - the preconditioner for the Schur complement is generated from the block diagonal part of the preconditioner matrix associated with the Schur complement (i.e. A11), not the Schur complement matrix
self - the preconditioner for the Schur complement is generated from the symbolic representation of the Schur complement matrix: The only preconditioners that currently work with this symbolic representation matrix object are PCLSC and PCHPDDM
user - the preconditioner for the Schur complement is generated from the user provided matrix (pre argument to this function).
selfp - the preconditioning for the Schur complement is generated from an explicitly-assembled approximation \( Sp = A11 - A10 inv(diag(A00)) A01 \) This is only a good preconditioner when diag(A00) is a good preconditioner for A00. Optionally, A00 can be lumped before extracting the diagonal using the additional option -fieldsplit_1_mat_schur_complement_ainv_type lump
full - the preconditioner for the Schur complement is generated from the exact Schur complement matrix representation computed internally by PCFIELDSPLIT (this is expensive) useful mostly as a test that the Schur complement approach can work for your problem

When solving a saddle point problem, where the A11 block is identically zero, using a11 as the ptype only makes sense with the additional option -fieldsplit_1_pc_type none. Usually for saddle point problems one would use a ptype of self and -fieldsplit_1_pc_type lsc which uses the least squares commutator to compute a preconditioner for the Schur complement.