Poisson::Solutions::Lorentzian< Dim, DataType > Class Template Reference

A Lorentzian solution to the Poisson equation. More...

#include <Lorentzian.hpp>

Classes
struct	PlusConstant
struct	ComplexPhase

Public Types
using	options

Public Member Functions
	Lorentzian (const Lorentzian &)=default
Lorentzian &	operator= (const Lorentzian &)=default
	Lorentzian (Lorentzian &&)=default
Lorentzian &	operator= (Lorentzian &&)=default
	Lorentzian (const double constant, const double complex_phase=0.)
double	constant () const
double	complex_phase () const
std::unique_ptr< elliptic::analytic_data::AnalyticSolution >	get_clone () const override
template<typename... RequestedTags>
tuples::TaggedTuple< RequestedTags... >	variables (const tnsr::I< DataVector, Dim > &x, tmpl::list< RequestedTags... >) const
void	pup (PUP::er &p) override

Static Public Attributes
static constexpr Options::String	help

Detailed Description

template<size_t Dim, typename DataType = DataVector>
class Poisson::Solutions::Lorentzian< Dim, DataType >

A Lorentzian solution to the Poisson equation.

Details

This implements the Lorentzian solution \(u(\boldsymbol{x})=\left(1+r^2\right)^{-\frac{1}{2}}\) to the three-dimensional Poisson equation \(-\Delta u(\boldsymbol{x})=f(\boldsymbol{x})\), where \(r^2=x^2+y^2+z^2\). The corresponding source is \(f(\boldsymbol{x})=3\left(1+r^2\right)^{-\frac{5}{2}}\).

If DataType is ComplexDataVector, the solution is multiplied by exp(i * complex_phase) to rotate it in the complex plane. This allows to use this solution for the complex Poisson equation.

Note

Corresponding 1D and 2D solutions are not implemented yet.

Member Typedef Documentation

options

template<size_t Dim, typename DataType = DataVector>

using Poisson::Solutions::Lorentzian< Dim, DataType >::options

Initial value:

tmpl::flatten<tmpl::list<
     PlusConstant,
     tmpl::conditional_t<std::is_same_v<DataType, ComplexDataVector>,
                         ComplexPhase, tmpl::list<>>>>

Member Function Documentation

get_clone()

template<size_t Dim, typename DataType = DataVector>

std::unique_ptr< elliptic::analytic_data::AnalyticSolution > Poisson::Solutions::Lorentzian< Dim, DataType >::get_clone ( ) const

inlineoverridevirtual

Implements elliptic::analytic_data::AnalyticSolution.

Member Data Documentation

help

template<size_t Dim, typename DataType = DataVector>

Options::String Poisson::Solutions::Lorentzian< Dim, DataType >::help

staticconstexpr

Initial value:

{
      "A Lorentzian solution to the Poisson equation."}

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

• src/PointwiseFunctions/AnalyticSolutions/Poisson/Lorentzian.hpp