#include "petscpc.h" PetscErrorCode PCFieldSplitSetSchurPre(PC pc,PCFieldSplitSchurPreType ptype,Mat pre)Collective on PC
| 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 | |
| userpre | - matrix to use for preconditioning, or NULL |
| -pc_fieldsplit_schur_precondition <self,selfp,user,a11,full> | - default is a11. See notes for meaning of various arguments | |
| -fieldsplit_1_pc_type <pctype> | - the preconditioner algorithm that is used to construct the preconditioner from the operator |
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 preconditioner that currently works with this symbolic respresentation matrix object is the PCLSC
preconditioner
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.