# MatCreateMFFD#

Creates a matrix-free matrix of type MATMFFD. See also MatCreateSNESMF()

## Synopsis#

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


Collective

## 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#

• -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, every time

• -mat_mffd_check_positivity - possibly decrease h until U + h*a has only positive values

• -mat_mffd_umin - Sets umin (for default PETSc routine that computes h only)

• -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)

## 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


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.

MATMFFD, MatDestroy(), MatMFFDSetFunctionError(), MatMFFDDSSetUmin(), MatMFFDSetFunction() MatMFFDSetHHistory(), MatMFFDResetHHistory(), MatCreateSNESMF(), MatMFFDGetH(), MatMFFDRegister(), MatMFFDComputeJacobian()