Vector valued right-hand side for the mean curvature equation. More...

#include <secOrd_op_rhs_impl.h>

Inheritance diagram for Esfem::Impl::Vec_rhs_fun:

Collaboration diagram for Esfem::Impl::Vec_rhs_fun:

Public Types
using	Base = Esfem::Grid::Grid_and_time::Vec_Function_space
	Template argument.

using	Domain = Base::DomainType
	$\R^3$

using	Range = Base::RangeType
	$\R^3$

Public Member Functions
	Vec_rhs_fun (const Dune::Fem::TimeProviderBase &)
	Get time and time step. More...

	Vec_rhs_fun (const Vec_rhs_fun &)=delete
	No copy construct.

Vec_rhs_fun &	operator= (const Vec_rhs_fun &)=delete
	No copy assignment.

void	evaluate (const Domain &, Range &) const
	y = f(x)

Range	operator() (const Domain &) const
	y = f(x)

Private Member Functions
void	update_cache () const
	Conditional update member `cache` More...

Private Attributes
const Dune::Fem::TimeProviderBase &	tp
	Time and time step.

double	alpha
	$\alpha \Delta v$

double	epsilon
	$\varepsilon \Delta X$

double	r_start
	Initial size of sphere.

double	r_end
	Final size of sphere.

double	k
	Steepness of logistic growh.

double	delta
	$\delta u$

double	cache [4]
	Helper variable, which save computations.

Detailed Description

Vector valued right-hand side for the mean curvature equation.

This is my right-hand function:

$\biggl[ k \Bigl( 1 - \frac{r(t)}{r_{end}}\Bigr) \lvert X \rvert + 2 \Bigl(\alpha k \Bigl( 1 - \frac{r(t)}{r_{end}}\Bigr) + \varepsilon \Bigr) \frac{1}{\lvert X \rvert} - \delta xy e^{-6t}\biggr]$

Currently I am testing. So, I use an easier right-hand side. I am doing classic mean curvature flow on the sphere. Right-hand side must be zero for this example. Also I expect unit sphere as starting value, alpha = 0 and epsilon = 1.

Old test, which I want to check again later:

$\surface_0 = S^2$
Exact flow: $\Phi(x,t) = e^{-t} x$
Velocity:
Normal:
Mean curvature:
$\delta = \varepsilon = 0$ , hence the operator is
$v - \alpha \Delta v = g(x,t) = -(1 + \alpha 2/ |x|^2) x.$

Todo:
Finish test and clean up comments.