petsc-3.13.6 2020-09-29
MATMFFD_DS
the code for compute the "h" used in the finite difference matrix-free matrix vector product. This code implements the strategy in Dennis and Schnabel, "Numerical Methods for Unconstrained Optimization and Nonlinear Equations".
Options Database Keys
-mat_mffd_umin <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 GMRES) that requires NO collective operations.
Formula used
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
See Also
MATMFFD, MatCreateMFFD(), MatCreateSNESMF(), MATMFFD_WP, MatMFFDDSSetUmin()
Level
intermediate
Location
src/mat/impls/mffd/mffddef.c
Examples
src/snes/tutorials/ex14.c.html
Index of all Mat routines
Table of Contents for all manual pages
Index of all manual pages