MATSNESMF_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 can be reused
2) In GMRES || a || == 1 and so does not need to ever be computed if you never
have a restart. Unfortunately a RESTART computes a matrix vector product
with ||a|| != 0 which breaks this
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
Notes: Requires no global collectives when used with GMRES
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, MatCreateMF(), MatCreateSNESMF(), MATSNESMF_DEFAULT
Level:intermediate
Location:src/snes/mf/wp.c
Index of all SNESMF routines
Table of Contents for all manual pages
Index of all manual pages