Rheolef
7.2
an efficient C++ finite element environment
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This function implements a generic Newton method for the resolution of the following problem:
F(u) = 0
A simple call to the algorithm writes:
my_problem P; field uh (Xh); newton (P, uh, tol, max_iter);
The my_problem
class should contain some methods for the evaluation of F, i.e. the residue
of the problem, and its derivative. The minimal requirements are:
class my_problem { public: typedef value_type; value_type residue (const value_type& uh) const; void update_derivative (const value_type& uh) const; value_type derivative_solve (const value_type& mrh) const; Float dual_space_norm (const value_type& mrh) const; };
The value_type
could be a field
. The Newton method could also be applied when value_type
is a simple Float
scalar. Conversely, it supports multi-field extensions.
The update_derivative
and derivative_solver
members are called at each step of the Newton algorithm.
The dual_space_norm
member function returns a scalar from the weighted residual field term mrh
returned by the residue
function: this scalar is used as the stopping criterion of the algorithm.
See the p_laplacian_newton.cc example and the User's guide for more.
This documentation has been generated from file main/lib/newton.h