catchmark(4rheolef) rheolef-6.1 catchmark(4rheolef)NAME
catchmark - iostream manipulator
DESCRIPTION
The catchmark is used for building labels used for input-output of vector-valued fields (see field(2)):
cin >> catchmark("f") >> fh;
cout << catchmark("u") << uh
<< catchmark("w") << wh
<< catchmark("psi") << psih;
Assuming its value for output is "u", the corresponding labels will be "#u0", "#u1", "#u2", ...
IMPLEMENTATION
class catchmark {
public:
catchmark(const std::string& x);
const std::string& mark() const { return _mark; }
friend std::istream& operator >> (std::istream& is, const catchmark& m);
friend std::ostream& operator << (std::ostream& os, const catchmark& m);
protected:
std::string _mark;
};
SEE ALSOfield(2)rheolef-6.1 rheolef-6.1 catchmark(4rheolef)
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newton(4rheolef) rheolef-6.1 newton(4rheolef)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, odiststream *p_derr = 0) {
if (p_derr) *p_derr << "# 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_derr) *p_derr << 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;
}
}
rheolef-6.1 rheolef-6.1 newton(4rheolef)
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