petsc-3.13.6 2020-09-29
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MATMFFD_WP

 Implements an alternative approach for computing the differencing parameter h used with the finite difference based matrix-free Jacobian. This code implements the strategy of M. Pernice and H. Walker: h = error_rel * sqrt(1 + ||U||) / ||a||

Notes

1) || U || does not change between linear iterations so is reused 2) In GMRES || a || == 1 and so does not need to ever be computed except at restart when it is recomputed.

Reference: M. Pernice and H. F. Walker, "NITSOL: A Newton Iterative Solver for Nonlinear Systems", SIAM J. Sci. Stat. Comput.", 1998, vol 19, pp. 302--318.

Options Database Keys

-mat_mffd_compute_normu -Compute the norm of u everytime see MatMFFDWPSetComputeNormU()

Notes

Requires no global collectives when used with GMRES

Formula used

F'(u)*a = [F(u+h*a) - F(u)]/h where

See Also

MATMFFD, MatCreateMFFD(), MatCreateSNESMF(), MATMFFD_DS

Level

intermediate

Location

src/mat/impls/mffd/wp.c
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