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 the KSP/PC interface.

For MATBAIJ, MATSBAIJ, and MATAIJ matrices with Inodes this does a block SOR smoothing, otherwise it does a pointwise smoothing

Most users should employ the KSP interface for linear solvers instead of working directly with matrix algebra routines such as this. See, e.g., KSPCreate().

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.