newton(5)
NAME
newton -- Newton nonlinear algorithm
DESCRIPTION
- Nonlinear Newton algorithm for the resolution of the following problem:
- F(u) = 0
- A simple call to the algorithm writes:
my_problem P;
field uh (Vh);
newton (P, uh, tol, max_iter);- The my_problem class may contains methods for the evaluation of F (aka residue) and its derivative:
class my_problem {
public:my_problem();
field residue (const field& uh) const;
void update_derivative (const field& uh) const;
field derivative_solve (const field& mrh) const;
Float norm (const field& uh) const;
Float dual_norm (const field& Muh) const;- };
- See the example p-laplacian.h in the user's documentation for more.
IMPLEMENTATION
- template <class Problem, class Field>
int newton (Problem P, Field& uh, Float& tol, size_t& max_iter, std::ostream *p_cerr = 0) { - if (p_cerr) *p_cerr << "# Newton: n r" << std::endl;
for (size_t n = 0; true; n++) {Field rh = P.residue(uh);
Float r = P.dual_norm(rh);
if (p_cerr) *p_cerr << n << " " << r << std::endl;
if (r <= tol) { tol = r; max_iter = n; return 0; }
if (n == max_iter) { tol = r; return 1; }
P.update_derivative (uh);
Field delta_uh = P.derivative_solve (-rh);
uh += delta_uh; - }
- }