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.

Developer Note#

We should add block SOR support for MATAIJ matrices with block size set to great than one and no inodes

Level#

developer

Location#

src/mat/interface/matrix.c

Examples#

src/tao/pde_constrained/tutorials/parabolic.c
src/tao/pde_constrained/tutorials/hyperbolic.c

Implementations#

MatSOR_MPIAIJ() in src/mat/impls/aij/mpi/mpiaij.c
MatSOR_SeqAIJ() in src/mat/impls/aij/seq/aij.c
MatSOR_SeqAIJSELL() in src/mat/impls/aij/seq/aijsell/aijsell.c
MatSOR_MPIBAIJ() in src/mat/impls/baij/mpi/mpibaij.c
MatSOR_SeqBAIJ() in src/mat/impls/baij/seq/baij.c
MatSOR_BlockMat() in src/mat/impls/blockmat/seq/blockmat.c
MatSOR_ConstantDiagonal() in src/mat/impls/cdiagonal/cdiagonal.c
MatSOR_SeqDense() in src/mat/impls/dense/seq/dense.c
MatSOR_SeqKAIJ() in src/mat/impls/kaij/kaij.c
MatSOR_MPISBAIJ() in src/mat/impls/sbaij/mpi/mpisbaij.c
MatSOR_SeqSBAIJ() in src/mat/impls/sbaij/seq/relax.h
MatSOR_MPISELL() in src/mat/impls/sell/mpi/mpisell.c
MatSOR_SeqSELL() in src/mat/impls/sell/seq/sell.c

Index of all Mat routines
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Index of all manual pages