sphere.icc

The level set function for the sphere geometry

struct p {
Float operator() (const point& x) const {
if (d == 2) return 26*(pow(x[0],5) - 10*pow(x[0],3)*sqr(x[1])
+ 5*x[0]*pow(x[1],4));
else return 3*sqr(x[0])*x[1] - pow(x[1],3);
}
p (size_t d1) : d(d1) {}
protected: size_t d;
};
struct f {
Float operator() (const point& x) const {
if (d == 2) return _p(x)/pow(norm(x),5);
else return alpha*_p(x);
}
f (size_t d1) : d(d1), _p(d1), alpha(0) {
Float pi = acos(Float(-1));
alpha = -(13./8.)*sqrt(35./pi);
}
protected: size_t d; p _p; Float alpha;
};
struct u_exact {
Float operator() (const point& x) const {
if (d == 2) return _f(x)/(25+sqr(norm(x)));
else return sqr(norm(x))/(12+sqr(norm(x)))*_f(x);
}
u_exact (size_t d1) : d(d1), _f(d1) {}
protected: size_t d; f _f;
};
Float phi (const point& x) { return norm(x) - 1; }
p::p
p(size_t d1)
Definition: sphere.icc:31
f::_p
p _p
Definition: sphere.icc:43
f::d
size_t d
Definition: cosinusprod_dirichlet.h:30
u_exact::d
size_t d
Definition: interpolate_RTk_polynom.icc:145
p::d
size_t d
Definition: sphere.icc:32
rheolef::pow
space_mult_list< T, M > pow(const space_basic< T, M > &X, size_t n)
Definition: space_mult.h:120
rheolef::norm
T norm(const vec< T, M > &x)
norm(x): see the expression page for the full documentation
Definition: vec.h:387
f::alpha
Float alpha
Definition: sphere.icc:43
p
Definition: sphere.icc:25
u_exact::operator()
point operator()(const point &x) const
Definition: interpolate_RTk_polynom.icc:126
f::operator()
point operator()(const point &x) const
Definition: cavity_dg.h:30
u_exact::u_exact
u_exact(size_t d1, Float w1=acos(Float(-1)))
Definition: interpolate_RTk_polynom.icc:144
phi
Float phi(const point &x)
Definition: sphere.icc:53
Float
see the Float page for the full documentation
f::f
f()
Definition: taylor.h:34
u_exact
Definition: interpolate_RTk_polynom.icc:125
point
see the point page for the full documentation
p::operator()
Float operator()(const point &x) const
Definition: sphere.icc:26
f::pi
const Float pi
Definition: cosinusprod_dirichlet.h:30
f
Definition: cavity_dg.h:29
u_exact::_f
f _f
Definition: sphere.icc:51