Rheolef
7.2
an efficient C++ finite element environment
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This function implements a generic damped Newton method for the resolution of the following problem:
F(u) = 0
Recall that the damped Newton method is more robust than the basic Newton one: it converges from any initial value.
A simple call to the algorithm writes:
my_problem P; field uh (Xh); damped_newton (P, uh, tol, max_iter);
In addition to the members required for the newton
method, two additional members are required for the damped variant:
class my_problem { public: ... value_type derivative_trans_mult (const value_type& mrh) const; Float space_norm (const value_type& uh) const; };
The derivative_trans_mult
is used for computing the damping coefficient. The space_norm
represents usually a L2 norm e.g. formally:
/ space_norm(uh) = sqrt | |uh(x)|^2 dx / Omega
See the p_laplacian_damped_newton.cc example and the User's guide for more.
This documentation has been generated from file main/lib/damped_newton.h