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

#include <Lorentzian.hpp>

Classes
struct	ComplexPhase

struct	PlusConstant

Public Types
using	options = tmpl::flatten< tmpl::list< PlusConstant, tmpl::conditional_t< std::is_same_v< DataType, ComplexDataVector >, ComplexPhase, tmpl::list<> > > >

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

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

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 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>

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

staticconstexpr

Initial value:

{

"A Lorentzian solution to the Poisson equation."}

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

src/PointwiseFunctions/AnalyticSolutions/Poisson/Lorentzian.hpp

Classes

Public Types

Public Member Functions