MATMFFD_DS

algorithm for compute the “h” used in the finite difference matrix-free matrix vector product, MatMult().

Options Database Keys

• -mat_mffd_umin - see MatMFFDDSSetUmin()

Notes

Requires 2 norms and 1 inner product, but they are computed together so only one parallel collective operation is needed. See MATMFFD_WP for a method (with KSPGMRES) that requires NO collective operations.

Formula used

F’(u)a = [F(u+ha) - F(u)]/h where h = error_relu’a/||a||^2 if |u’a| > umin||a||{1} = error_reluminsign(u’a)*||a||{1}/||a||^2 otherwise where error_rel = square root of relative error in function evaluation umin = minimum iterate parameter

References

• **** -*** Dennis and Schnabel, “Numerical Methods for Unconstrained Optimization and Nonlinear Equations”

See Also

MATMFFD, MATMFFD_WP, MatCreateMFFD(), MatCreateSNESMF(), MATMFFD_WP, MatMFFDDSSetUmin()

Level

intermediate

Location

src/mat/impls/mffd/mffddef.c

Examples

src/snes/tutorials/ex14.c

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