petsc-3.3-p7 2013-05-11

MatCreateMFFD

Creates a matrix-free matrix. See also MatCreateSNESMF()

Synopsis

#include "petscmat.h"   
PetscErrorCode  MatCreateMFFD(MPI_Comm comm,PetscInt m,PetscInt n,PetscInt M,PetscInt N,Mat *J)

Collective on Vec

Input Parameters

	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)

Output Parameter

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

Notes

The matrix-free matrix context merely contains the function pointers and work space for performing finite difference approximations of Jacobian-vector products, F'(u)*a,

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

The user can set the error_rel via MatMFFDSetFunctionError() and umin via MatMFFDDSSetUmin(); see the <A href="../../docs/manual.pdf#nameddest=ch_snes">SNES chapter of the users manual</A> for details.

The user should call MatDestroy() when finished with the matrix-free matrix context.

Options Database Keys

	-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	-

Keywords

default, matrix-free, create, matrix

Examples

src/snes/examples/tutorials/ex22.c.html