Namespaces | Classes | Enumerations
Spectral

Namespaces

 Spectral::Swsh
 Namespace for spin-weighted spherical harmonic utilities.
 
 Spectral
 Functionality associated with a particular choice of basis functions and quadrature for spectral operations.
 

Classes

class  SpherepackIterator
 Iterates over spectral coefficients stored in SPHEREPACK format. More...
 
class  YlmSpherepack
 C++ interface to SPHEREPACK. More...
 

Enumerations

enum  Spectral::Basis { Chebyshev, Legendre }
 The choice of basis functions for computing collocation points and weights. More...
 
enum  Spectral::Quadrature { Gauss, GaussLobatto }
 The choice of quadrature method to compute integration weights. More...
 
template<size_t Dim>
void to_modal_coefficients (gsl::not_null< ModalVector *> modal_coefficients, const DataVector &nodal_coefficients, const Mesh< Dim > &mesh) noexcept
 Compute the modal coefficients from the nodal coefficients. More...
 
template<size_t Dim>
ModalVector to_modal_coefficients (const DataVector &nodal_coefficients, const Mesh< Dim > &mesh) noexcept
 Compute the modal coefficients from the nodal coefficients. More...
 
template<size_t Dim>
void to_nodal_coefficients (gsl::not_null< DataVector *> nodal_coefficients, const ModalVector &modal_coefficients, const Mesh< Dim > &mesh) noexcept
 Compute the nodal coefficients from the modal coefficients. More...
 
template<size_t Dim>
DataVector to_nodal_coefficients (const ModalVector &modal_coefficients, const Mesh< Dim > &mesh) noexcept
 Compute the nodal coefficients from the modal coefficients. More...
 

Detailed Description

Things related to spectral transformations.

Enumeration Type Documentation

◆ Basis

enum Spectral::Basis
strong

The choice of basis functions for computing collocation points and weights.

Details

Choose Legendre for a general-purpose DG mesh, unless you have a particular reason for choosing another basis.

◆ Quadrature

enum Spectral::Quadrature
strong

The choice of quadrature method to compute integration weights.

Details

Integrals using \(N\) collocation points with Gauss quadrature are exact to polynomial order \(p=2N-1\). Gauss-Lobatto quadrature is exact only to polynomial order \(p=2N-3\), but includes collocation points at the domain boundary.

Function Documentation

◆ to_modal_coefficients() [1/2]

template<size_t Dim>
void to_modal_coefficients ( gsl::not_null< ModalVector *>  modal_coefficients,
const DataVector nodal_coefficients,
const Mesh< Dim > &  mesh 
)
noexcept

Compute the modal coefficients from the nodal coefficients.

See also
Spectral::grid_points_to_spectral_matrix

◆ to_modal_coefficients() [2/2]

template<size_t Dim>
ModalVector to_modal_coefficients ( const DataVector nodal_coefficients,
const Mesh< Dim > &  mesh 
)
noexcept

Compute the modal coefficients from the nodal coefficients.

See also
Spectral::grid_points_to_spectral_matrix

◆ to_nodal_coefficients() [1/2]

template<size_t Dim>
void to_nodal_coefficients ( gsl::not_null< DataVector *>  nodal_coefficients,
const ModalVector modal_coefficients,
const Mesh< Dim > &  mesh 
)
noexcept

Compute the nodal coefficients from the modal coefficients.

See also
Spectral::spectral_to_grid_points_matrix

◆ to_nodal_coefficients() [2/2]

template<size_t Dim>
DataVector to_nodal_coefficients ( const ModalVector modal_coefficients,
const Mesh< Dim > &  mesh 
)
noexcept

Compute the nodal coefficients from the modal coefficients.

See also
Spectral::spectral_to_grid_points_matrix