PETSc version 3.17.4
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# 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, every time
| -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)

### 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.

### Options Database Keys

| -mat_mffd_err <error_rel> | - Sets error_rel
| -mat_mffd_umin <umin> | - Sets umin (for default PETSc routine that computes h only)
| -mat_mffd_check_positivity | - check positivity

### See Also

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

### Level

advanced

### Location

src/mat/impls/mffd/mffd.c

### Examples

src/snes/tutorials/ex22.c.html

### Implementations

MatCreateMFFD_DS in src/mat/impls/mffd/mffddef.c
MatCreateMFFD_WP in src/mat/impls/mffd/wp.c
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