Rheolef  7.2
an efficient C++ finite element environment
 
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p_laplacian1.icc

The p-Laplacian problem by the Newton method – class body.

The p-Laplacian problem by the Newton method – class body

#include "eta.h"
#include "nu.h"
#include "dirichlet.icc"
p_laplacian::p_laplacian (Float p1, const geo& omega, string approx)
: p(p1), Xh(), lh(), m(), pm(), a1(), pa1() {
Xh = space (omega, approx);
Xh.block ("boundary");
trial u (Xh); test v (Xh);
lh = integrate (v);
m = integrate (u*v);
pm = problem (m);
}
field uh (Xh, 0);
dirichlet (lh, uh);
return uh;
}
field p_laplacian::residue (const field& uh) const {
trial u (Xh); test v (Xh);
field mrh = a*uh - lh;
mrh.set_b() = 0;
return mrh;
}
void p_laplacian::update_derivative (const field& uh) const {
size_t d = Xh.get_geo().dimension();
trial u (Xh); test v (Xh);
pa1 = problem (a1);
}
field delta_uh (Xh,0);
pa1.solve (rh, delta_uh);
return delta_uh;
}
field lh(Float epsilon, Float t, const test &v)
see the Float page for the full documentation
see the field page for the full documentation
see the form page for the full documentation
see the geo page for the full documentation
field derivative_solve(const field &mrh) const
problem pa1
Definition p_laplacian.h:43
p_laplacian(Float p, const geo &omega, string approx)
field initial() const
void update_derivative(const field &uh) const
field residue(const field &uh) const
see the problem page for the full documentation
see the space page for the full documentation
see the test page for the full documentation
see the test page for the full documentation
The Poisson problem with homogeneous Dirichlet boundary condition – solver function.
void dirichlet(const field &lh, field &uh)
Definition dirichlet.icc:25
The p-Laplacian problem – the eta function.
class rheolef::details::field_expr_v2_nonlinear_node_unary compose
rheolef::details::is_vec dot
std::enable_if< details::has_field_rdof_interface< Expr >::value, details::field_expr_v2_nonlinear_terminal_field< typenameExpr::scalar_type, typenameExpr::memory_type, details::differentiate_option::gradient > >::type grad(const Expr &expr)
grad(uh): see the expression page for the full documentation
T norm2(const vec< T, M > &x)
norm2(x): see the expression page for the full documentation
Definition vec.h:379
std::enable_if< details::is_field_expr_v2_nonlinear_arg< Expr >::value &&!is_undeterminated< Result >::value, Result >::type integrate(const geo_basic< T, M > &omega, const Expr &expr, const integrate_option &iopt, Result dummy=Result())
see the integrate page for the full documentation
Definition integrate.h:211
The p-Laplacian problem – the nu function.
Definition eta.h:25
Definition nu.h:26
Definition sphere.icc:25
Definition leveque.h:25