petsc-3.8.4 2018-03-24

PCFieldSplitSetSchurPre

Indicates what operator is used to construct the preconditioner for the Schur complement. A11 matrix. Otherwise no preconditioner is used.

Synopsis

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

Collective on PC

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
	userpre	- matrix to use for preconditioning, or NULL

Options Database

-pc_fieldsplit_schur_precondition <self,selfp,user,a11,full> -default is a11. See notes for meaning of various arguments

Notes

   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.

Examples