A solution to the Poisson equation with a discontinuous first derivative. More...

#include <Moustache.hpp>

Public Types
using	options = implementation defined

Public Member Functions
	Moustache (const Moustache &)=default

Moustache &	operator= (const Moustache &)=default

	Moustache (Moustache &&)=default

Moustache &	operator= (Moustache &&)=default

std::unique_ptr< elliptic::analytic_data::AnalyticSolution >	get_clone () const override

template<typename DataType , typename... RequestedTags>
tuples::TaggedTuple< RequestedTags... >	variables (const tnsr::I< DataType, Dim > &x, tmpl::list< RequestedTags... >) const

virtual std::unique_ptr< AnalyticSolution >	get_clone () const =0

Static Public Attributes
static constexpr Options::String	help

Detailed Description

template<size_t Dim>
class Poisson::Solutions::Moustache< Dim >

A solution to the Poisson equation with a discontinuous first derivative.

Details

This implements the solution $u (x, y) = x (1 - x) y (1 - y) {({(x - \frac{1}{2})}^{2} + {(y - \frac{1}{2})}^{2})}^{\frac{3}{2}}$ to the Poisson equation in two dimensions, and $u (x) = x (1 - x) {| x - \frac{1}{2} |}^{3}$ in one dimension. Their boundary conditions vanish on the square $[0, 1]^{2}$ or interval $[0, 1]$ , respectively.

The corresponding source $f = - Δ u$ has a discontinuous first derivative at $\frac{1}{2}$ . This accomplishes two things:

It makes it useful to test the convergence behaviour of our elliptic DG solver.
It makes it look like a moustache (at least in 1D).

This solution is taken from [185].

Member Function Documentation

◆ get_clone()

template<size_t Dim>

std::unique_ptr< elliptic::analytic_data::AnalyticSolution > Poisson::Solutions::Moustache< Dim >::get_clone ( ) const

inlineoverridevirtual

Implements elliptic::analytic_data::AnalyticSolution.

Member Data Documentation

◆ help

template<size_t Dim>

constexpr Options::String Poisson::Solutions::Moustache< Dim >::help

staticconstexpr

Initial value:

{
      "A solution with a discontinuous first derivative of its source at 1/2 "
      "that also happens to look like a moustache. It vanishes at zero and one "
      "in each dimension"}

The documentation for this class was generated from the following file:

src/PointwiseFunctions/AnalyticSolutions/Poisson/Moustache.hpp

Public Types

Public Member Functions