#include "petscmat.h" PetscErrorCode MatCreateMFFD(MPI_Comm comm,PetscInt m,PetscInt n,PetscInt M,PetscInt N,Mat *J)Collective on Vec
| comm | - MPI communicator | |
| m | - number of local rows (or PETSC_DECIDE to have calculated if M is given) This value should be the same as the local size used in creating the y vector for the matrix-vector product y = Ax. | |
| n | - This value should be the same as the local size used in creating the x vector for the matrix-vector product y = Ax. (or PETSC_DECIDE to have calculated if N is given) For square matrices n is almost always m. | |
| M | - number of global rows (or PETSC_DETERMINE to have calculated if m is given) | |
| N | - number of global columns (or PETSC_DETERMINE to have calculated if n is given) |
| J | - the matrix-free matrix |
Options Database Keys: call MatSetFromOptions() to trigger these
| -mat_mffd_type | - wp or ds (see MATMFFD_WP or MATMFFD_DS) | |
| -mat_mffd_err | - square root of estimated relative error in function evaluation | |
| -mat_mffd_period | - how often h is recomputed, defaults to 1, everytime | |
| -mat_mffd_check_positivity | - possibly decrease h until U + h*a has only positive values | |
| -mat_mffd_complex | - use the Lyness trick with complex numbers to compute the matrix-vector product instead of differencing (requires real valued functions but that PETSc be configured for complex numbers) |
The default code uses the following approach to compute h
F'(u)*a = [F(u+h*a) - F(u)]/h where
h = error_rel*u'a/||a||^2 if |u'a| > umin*||a||_{1}
= error_rel*umin*sign(u'a)*||a||_{1}/||a||^2 otherwise
where
error_rel = square root of relative error in function evaluation
umin = minimum iterate parameter
You can call SNESSetJacobian() with MatMFFDComputeJacobian() if you are using matrix and not a different preconditioner matrix
The user can set the error_rel via MatMFFDSetFunctionError() and umin via MatMFFDDSSetUmin(); see Users-Manual: ch_snes for details.
The user should call MatDestroy() when finished with the matrix-free matrix context.
| -mat_mffd_err <error_rel> | - Sets error_rel | |
| -mat_mffd_unim <umin> | - Sets umin (for default PETSc routine that computes h only) | |
| -mat_mffd_check_positivity |