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# MATMFFD_WP

Implements an approach for computing the differencing parameter h used with the finite difference based matrix-free Jacobian. From Walker-Pernice [PW98] $\( h = error_rel * sqrt(1 + ||u||) / ||a|| \)$

## Options Database Key

- -mat_mffd_compute_normu - Compute the norm of u every time see `MatMFFDWPSetComputeNormU()`

## Notes

\( || U || \) does not change between linear iterations so is reused

In `KSPGMRES` \( || a || == 1 \) and so does not need to ever be computed except at restart when it is recomputed. Thus requires no global collectives when used with `KSPGMRES`

## References

[PW98]

M. Pernice and H. F. Walker. NITSOL: a Newton iterative solver for nonlinear systems. SIAM J. Sci. Stat. Comput., 19:302–318, 1998.

## See Also

`MATMFFD`, `MATMFFD_DS`, `MatCreateMFFD()`, `MatCreateSNESMF()`, `MATMFFD_DS`

## Level

intermediate

## Location

src/mat/impls/mffd/wp.c

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