ScalarWave::Solutions::PlaneWave< Dim > Class Template Reference

A plane wave solution to the Euclidean wave equation. More...

#include <PlaneWave.hpp>

Classes
struct	Center
struct	Profile
struct	WaveVector

Public Types
using	options = tmpl::list<WaveVector, Center, Profile>
using	tags

Public Member Functions
	PlaneWave (std::array< double, Dim > wave_vector, std::array< double, Dim > center, std::unique_ptr< MathFunction< 1, Frame::Inertial > > profile)
	PlaneWave (const PlaneWave &)
PlaneWave &	operator= (const PlaneWave &)
	PlaneWave (PlaneWave &&)=default
PlaneWave &	operator= (PlaneWave &&)=default
auto	get_clone () const -> std::unique_ptr< evolution::initial_data::InitialData > override
template<typename T>
Scalar< T >	psi (const tnsr::I< T, Dim > &x, double t) const
	The value of the scalar field.
template<typename T>
Scalar< T >	dpsi_dt (const tnsr::I< T, Dim > &x, double t) const
	The time derivative of the scalar field.
template<typename T>
tnsr::i< T, Dim >	dpsi_dx (const tnsr::I< T, Dim > &x, double t) const
	The spatial derivatives of the scalar field.
template<typename T>
Scalar< T >	d2psi_dt2 (const tnsr::I< T, Dim > &x, double t) const
	The second time derivative of the scalar field.
template<typename T>
tnsr::i< T, Dim >	d2psi_dtdx (const tnsr::I< T, Dim > &x, double t) const
	The second mixed derivatives of the scalar field.
template<typename T>
tnsr::ii< T, Dim >	d2psi_dxdx (const tnsr::I< T, Dim > &x, double t) const
	The second spatial derivatives of the scalar field.
tuples::TaggedTuple< Tags::Psi, Tags::Pi, Tags::Phi< Dim, Frame::Inertial > >	variables (const tnsr::I< DataVector, Dim > &x, double t, tmpl::list< Tags::Psi, Tags::Pi, Tags::Phi< Dim, Frame::Inertial > >) const
	Retrieve the evolution variables at time t and spatial coordinates x
tuples::TaggedTuple<::Tags::dt< Tags::Psi >, ::Tags::dt< Tags::Pi >, ::Tags::dt< Tags::Phi< Dim, Frame::Inertial > > >	variables (const tnsr::I< DataVector, Dim > &x, double t, tmpl::list<::Tags::dt< Tags::Psi >, ::Tags::dt< Tags::Pi >, ::Tags::dt< Tags::Phi< Dim, Frame::Inertial > > >) const
	Retrieve the time derivative of the evolution variables at time t and spatial coordinates x
void	pup (PUP::er &p) override
Public Member Functions inherited from evolution::initial_data::InitialData
virtual const InitialData &	unwrap () const
	Unwrap wrapper types (e.g. WithNoise, which wraps analytic initial data and adds random noise) to reach the underlying analytic solution or data.

Static Public Attributes
static constexpr size_t	volume_dim = Dim
static constexpr Options::String	help

Friends
template<size_t LocalDim>
bool	operator== (const PlaneWave< LocalDim > &lhs, const PlaneWave< LocalDim > &rhs)
template<size_t LocalDim>
bool	operator!= (const PlaneWave< LocalDim > &lhs, const PlaneWave< LocalDim > &rhs)

Detailed Description

template<size_t Dim>
class ScalarWave::Solutions::PlaneWave< Dim >

A plane wave solution to the Euclidean wave equation.

The solution is given by \(\Psi(\vec{x},t) = F(u(\vec{x},t))\) where the profile \(F\) of the plane wave is an arbitrary one-dimensional function of \(u = \vec{k} \cdot (\vec{x} - \vec{x_o}) - \omega t\) with the wave vector \(\vec{k}\), the frequency \(\omega = ||\vec{k}||\) and initial center of the profile \(\vec{x_o}\).

Template Parameters

Dim	the spatial dimension of the solution

Member Typedef Documentation

tags

template<size_t Dim>

using ScalarWave::Solutions::PlaneWave< Dim >::tags

Initial value:

 tmpl::list<Tags::Psi, Tags::Pi, Tags::Phi<Dim, Frame::Inertial>,
                          ::Tags::dt<Tags::Psi>, ::Tags::dt<Tags::Pi>,
                          ::Tags::dt<Tags::Phi<Dim, Frame::Inertial>>>

Member Function Documentation

get_clone()

template<size_t Dim>

auto ScalarWave::Solutions::PlaneWave< Dim >::get_clone ( ) const -> std::unique_ptr< evolution::initial_data::InitialData >

overridevirtual

Implements evolution::initial_data::InitialData.

variables()

template<size_t Dim>

tuples::TaggedTuple<::Tags::dt< Tags::Psi >, ::Tags::dt< Tags::Pi >, ::Tags::dt< Tags::Phi< Dim, Frame::Inertial > > > ScalarWave::Solutions::PlaneWave< Dim >::variables	(	const tnsr::I< DataVector, Dim > &	x,
		double	t,
		tmpl::list<::Tags::dt< Tags::Psi >, ::Tags::dt< Tags::Pi >, ::Tags::dt< Tags::Phi< Dim, Frame::Inertial > > >	) const

Retrieve the time derivative of the evolution variables at time t and spatial coordinates x

Note

This function's expected use case is setting the past time derivative values for Adams-Bashforth-like steppers.

Member Data Documentation

help

template<size_t Dim>

Options::String ScalarWave::Solutions::PlaneWave< Dim >::help

staticconstexpr

Initial value:

= {
      "A plane wave solution of the Euclidean wave equation"}

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

• src/PointwiseFunctions/AnalyticSolutions/WaveEquation/PlaneWave.hpp