#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 |
If ptype is
a11 then 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 then the preconditioner for the Schur complement is generated from the user provided matrix (pre argument
to this function).
selfp then 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 then the preconditioner for the Schur complement is generated from the exact Schur complement matrix representation computed internally by PFIELDSPLIT (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.