MatSOR#

Computes relaxation (SOR, Gauss-Seidel) sweeps.

Synopsis#

#include "petscmat.h" 
PetscErrorCode MatSOR(Mat mat, Vec b, PetscReal omega, MatSORType flag, PetscReal shift, PetscInt its, PetscInt lits, Vec x)

Neighbor-wise Collective

Input Parameters#

mat - the matrix
b - the right-hand side
omega - the relaxation factor
flag - flag indicating the type of SOR (see below)
shift - diagonal shift
its - the number of iterations
lits - the number of local iterations

Output Parameter#

x - the solution (can contain an initial guess, use option SOR_ZERO_INITIAL_GUESS to indicate no guess)

SOR Flags#

SOR_FORWARD_SWEEP - forward SOR
SOR_BACKWARD_SWEEP - backward SOR
SOR_SYMMETRIC_SWEEP - SSOR (symmetric SOR)
SOR_LOCAL_FORWARD_SWEEP - local forward SOR
SOR_LOCAL_BACKWARD_SWEEP - local forward SOR
SOR_LOCAL_SYMMETRIC_SWEEP - local SSOR
SOR_EISENSTAT - SOR with Eisenstat trick
SOR_APPLY_UPPER, SOR_APPLY_LOWER - applies upper/lower triangular part of matrix to vector (with omega)
SOR_ZERO_INITIAL_GUESS - zero initial guess

Notes#

SOR_LOCAL_FORWARD_SWEEP, SOR_LOCAL_BACKWARD_SWEEP, and SOR_LOCAL_SYMMETRIC_SWEEP perform separate independent smoothings on each processor.

Application programmers will not generally use MatSOR() directly, but instead will employ PCSOR or PCEISENSTAT

For MATBAIJ, MATSBAIJ, and MATAIJ matrices with inodes, this does a block SOR smoothing, otherwise it does a pointwise smoothing. For MATAIJ matrices with inodes, the block sizes are determined by the inode sizes, not the block size set with MatSetBlockSize()

Vectors x and b CANNOT be the same

The flags are implemented as bitwise inclusive or operations. For example, use (SOR_ZERO_INITIAL_GUESS | SOR_SYMMETRIC_SWEEP) to specify a zero initial guess for SSOR.