dg Namespace Reference

Functionality related to discontinuous Galerkin schemes. More...

Classes
struct	SimpleBoundaryData
	Distinguishes between field data, which can be projected to a mortar, and extra data, which will not be projected. More...
class	SimpleMortarData
	Storage of boundary data on two sides of a mortar. More...

Typedefs
template<size_t VolumeDim>
using	MortarId = DirectionalId< VolumeDim >
template<size_t MortarDim>
using	MortarSize = std::array< Spectral::MortarSize, MortarDim >
template<size_t VolumeDim, typename ValueType >
using	MortarMap = DirectionalIdMap< VolumeDim, ValueType >

Enumerations
enum class	Formulation { StrongInertial , WeakInertial , StrongLogical }
	The DG formulation to use. More...

Functions
std::ostream &	operator<< (std::ostream &os, Formulation t)
template<typename InboxTag , size_t Dim, typename TemporalIdType , typename... InboxTags>
bool	has_received_from_all_mortars (const TemporalIdType &temporal_id, const Element< Dim > &element, const tuples::TaggedTuple< InboxTags... > &inboxes)
	Determines if data on all mortars has been received for the InboxTag at time temporal_id. More...
template<size_t Dim, typename DtTagsList >
void	interpolate_dt_terms_gauss_points (const gsl::not_null< Variables< DtTagsList > * > dt_vars, const Mesh< Dim > &volume_mesh, const Direction< Dim > &direction, const Variables< DtTagsList > &dt_corrections)
	Interpolate the Bjorhus/time derivative corrections to the volume time derivatives in the specified direction. More...
template<size_t Dim, typename DtTagsList , typename BoundaryCorrectionTagsList >
void	lift_boundary_terms_gauss_points (const gsl::not_null< Variables< DtTagsList > * > dt_vars, const Scalar< DataVector > &volume_det_inv_jacobian, const Mesh< Dim > &volume_mesh, const Direction< Dim > &direction, const Variables< BoundaryCorrectionTagsList > &boundary_corrections, const Scalar< DataVector > &magnitude_of_face_normal, const Scalar< DataVector > &face_det_jacobian)
	Lift the boundary corrections to the volume time derivatives in the specified direction. More...
template<size_t Dim, typename DtTagsList , typename BoundaryCorrectionTagsList >
void	lift_boundary_terms_gauss_points (const gsl::not_null< Variables< DtTagsList > * > dt_vars, const Scalar< DataVector > &volume_det_inv_jacobian, const Mesh< Dim > &volume_mesh, const size_t dimension, const Variables< BoundaryCorrectionTagsList > &upper_boundary_corrections, const Scalar< DataVector > &upper_magnitude_of_face_normal, const Scalar< DataVector > &upper_face_det_jacobian, const Variables< BoundaryCorrectionTagsList > &lower_boundary_corrections, const Scalar< DataVector > &lower_magnitude_of_face_normal, const Scalar< DataVector > &lower_face_det_jacobian)
	Lift both the upper and lower (in logical coordinates) boundary corrections to the volume time derivatives in the specified logical dimension. More...
template<size_t Dim, typename... VolumeTags, typename... BoundaryCorrectionTags>
void	lift_boundary_terms_gauss_points (const gsl::not_null< Variables< tmpl::list< VolumeTags... > > * > volume_data, const Variables< tmpl::list< BoundaryCorrectionTags... > > &boundary_corrections, const Mesh< Dim > &volume_mesh, const Direction< Dim > &direction)
	Lift the boundary corrections from the face to the volume for Gauss points in the direction perpendicular to the face. More...
template<size_t Dim>
void	metric_identity_det_jac_times_inv_jac (gsl::not_null< InverseJacobian< DataVector, Dim, Frame::ElementLogical, Frame::Inertial > * > det_jac_times_inverse_jacobian, const Mesh< Dim > &mesh, const tnsr::I< DataVector, Dim, Frame::Inertial > &inertial_coords, const Jacobian< DataVector, Dim, Frame::ElementLogical, Frame::Inertial > &jacobian)
	Compute the Jacobian determinant times the inverse Jacobian so that the result is divergence-free. More...
template<size_t Dim>
void	metric_identity_jacobian_quantities (gsl::not_null< InverseJacobian< DataVector, Dim, Frame::ElementLogical, Frame::Inertial > * > det_jac_times_inverse_jacobian, gsl::not_null< InverseJacobian< DataVector, Dim, Frame::ElementLogical, Frame::Inertial > * > inverse_jacobian, gsl::not_null< Jacobian< DataVector, Dim, Frame::ElementLogical, Frame::Inertial > * > jacobian, gsl::not_null< Scalar< DataVector > * > det_jacobian, const Mesh< Dim > &mesh, const tnsr::I< DataVector, Dim, Frame::Inertial > &inertial_coords)
	Compute the Jacobian, inverse Jacobian, and determinant of the Jacobian so that they satisfy the metric identities. More...
template<size_t Dim>
Mesh< Dim >	mortar_mesh (const Mesh< Dim > &face_mesh1, const Mesh< Dim > &face_mesh2)
	Find a mesh for a mortar capable of representing data from either of two faces. More...
template<size_t Dim>
MortarSize< Dim - 1 >	mortar_size (const ElementId< Dim > &self, const ElementId< Dim > &neighbor, size_t dimension, const OrientationMap< Dim > &orientation)
	Determine the size of the mortar (i.e., the part of the face it covers) for communicating with a neighbor. This is the size relative to the size of self, and will not generally agree with that determined by neighbor.
template<typename VolumeVarsTagsList , typename FaceVarsTagsList , size_t Dim>
void	project_contiguous_data_to_boundary (const gsl::not_null< Variables< FaceVarsTagsList > * > face_fields, const Variables< VolumeVarsTagsList > &volume_fields, const Mesh< Dim > &volume_mesh, const Direction< Dim > &direction)
	Projects a Variables of volume data to a contiguous subset of a boundary Variables More...
template<typename TagsToProjectList , typename VolumeVarsTagsList , typename FaceVarsTagsList , size_t Dim>
void	project_tensors_to_boundary (const gsl::not_null< Variables< FaceVarsTagsList > * > face_fields, const Variables< VolumeVarsTagsList > &volume_fields, const Mesh< Dim > &volume_mesh, const Direction< Dim > &direction)
	Projects a subset of the tensors in the volume_fields onto the face. More...
template<typename DataType , size_t Dim>
void	apply_mass_matrix (const gsl::not_null< DataType * > data, const Mesh< Dim > &mesh)
	Apply the DG mass matrix to the data, in the diagonal mass-matrix approximation ("mass-lumping") More...
template<size_t Dim, typename TagsList >
void	apply_mass_matrix (const gsl::not_null< Variables< TagsList > * > data, const Mesh< Dim > &mesh)
	Apply the DG mass matrix to the data, in the diagonal mass-matrix approximation ("mass-lumping") More...
template<typename DataType , size_t Dim>
void	apply_inverse_mass_matrix (const gsl::not_null< DataType * > data, const Mesh< Dim > &mesh)
	Apply the inverse DG mass matrix to the data. More...
template<size_t Dim, typename TagsList >
void	apply_inverse_mass_matrix (const gsl::not_null< Variables< TagsList > * > data, const Mesh< Dim > &mesh)
	Apply the inverse DG mass matrix to the data. More...
template<typename... BoundaryCorrectionTags>
void	lift_flux (const gsl::not_null< Variables< tmpl::list< BoundaryCorrectionTags... > > * > boundary_correction_terms, const size_t extent_perpendicular_to_boundary, const Scalar< DataVector > &magnitude_of_face_normal)
	Lifts the flux contribution from an interface to the volume. More...
template<typename... FluxTags>
auto	lift_flux (Variables< tmpl::list< FluxTags... > > flux, const size_t extent_perpendicular_to_boundary, const Scalar< DataVector > &magnitude_of_face_normal) -> Variables< tmpl::list< db::remove_tag_prefix< FluxTags >... > >
	Lifts the flux contribution from an interface to the volume. More...
template<typename Tags , size_t Dim>
void	project_to_mortar (const gsl::not_null< Variables< Tags > * > result, const Variables< Tags > &vars, const Mesh< Dim > &face_mesh, const Mesh< Dim > &mortar_mesh, const MortarSize< Dim > &mortar_size)
	Project variables from a face to a mortar.
template<typename Tags , size_t Dim>
Variables< Tags >	project_to_mortar (const Variables< Tags > &vars, const Mesh< Dim > &face_mesh, const Mesh< Dim > &mortar_mesh, const MortarSize< Dim > &mortar_size)
	Project variables from a face to a mortar.
template<typename Tags , size_t Dim>
void	project_from_mortar (const gsl::not_null< Variables< Tags > * > result, const Variables< Tags > &vars, const Mesh< Dim > &face_mesh, const Mesh< Dim > &mortar_mesh, const MortarSize< Dim > &mortar_size)
	Project variables from a mortar to a face.
template<typename Tags , size_t Dim>
Variables< Tags >	project_from_mortar (const Variables< Tags > &vars, const Mesh< Dim > &face_mesh, const Mesh< Dim > &mortar_mesh, const MortarSize< Dim > &mortar_size)
	Project variables from a mortar to a face.
template<typename Symm , typename IndexList , size_t Dim>
void	project_tensor_to_boundary (const gsl::not_null< Tensor< DataVector, Symm, IndexList > * > face_field, const Tensor< DataVector, Symm, IndexList > &volume_field, const Mesh< Dim > &volume_mesh, const Direction< Dim > &direction)
	Projects a tensor to the face. More...
template<typename Symm , typename IndexList , size_t Dim>
Tensor< DataVector, Symm, IndexList >	project_tensor_to_boundary (const Tensor< DataVector, Symm, IndexList > &volume_field, const Mesh< Dim > &volume_mesh, const Direction< Dim > &direction)
	Projects a tensor to the face. More...

Detailed Description

Functionality related to discontinuous Galerkin schemes.

Function Documentation

apply_inverse_mass_matrix() [1/2]

template<typename DataType , size_t Dim>

void dg::apply_inverse_mass_matrix	(	const gsl::not_null< DataType * >	data,
		const Mesh< Dim > &	mesh
	)

Apply the inverse DG mass matrix to the data.

See also

dg::apply_mass_matrix

apply_inverse_mass_matrix() [2/2]

template<size_t Dim, typename TagsList >

void dg::apply_inverse_mass_matrix	(	const gsl::not_null< Variables< TagsList > * >	data,
		const Mesh< Dim > &	mesh
	)

Apply the inverse DG mass matrix to the data.

See also

dg::apply_mass_matrix

apply_mass_matrix() [1/2]

template<typename DataType , size_t Dim>

void dg::apply_mass_matrix	(	const gsl::not_null< DataType * >	data,
		const Mesh< Dim > &	mesh
	)

Apply the DG mass matrix to the data, in the diagonal mass-matrix approximation ("mass-lumping")

The DG mass matrix is:

\begin{equation} M_{pq} = \int_{\Omega_k} \psi_p(\xi) \psi_q(\xi) \mathrm{d}V \end{equation}

where \(\psi_p(\xi)\) are the basis functions on the element \(\Omega_k\). In the diagonal mass-matrix approximation ("mass-lumping") we evaluate the integral directly on the collocation points, i.e. with a Gauss or Gauss-Lobatto quadrature determined by the element mesh. Then it reduces to:

\begin{equation} M_{pq} \approx \delta_{pq} \prod_{i=1}^d w_{p_i} \end{equation}

where \(d\) is the spatial dimension and \(w_{p_i}\) are the quadrature weights in dimension \(i\). To apply the mass matrix in coordinates different than logical, or to account for a curved background metric, the data can be pre-multiplied with the Jacobian determinant and/or a metric determinant.

Note

The mass-lumping is exact on Legendre-Gauss meshes, but omits a correction term on Legendre-Gauss-Lobatto meshes.

apply_mass_matrix() [2/2]

template<size_t Dim, typename TagsList >

void dg::apply_mass_matrix	(	const gsl::not_null< Variables< TagsList > * >	data,
		const Mesh< Dim > &	mesh
	)

Apply the DG mass matrix to the data, in the diagonal mass-matrix approximation ("mass-lumping")

The DG mass matrix is:

\begin{equation} M_{pq} = \int_{\Omega_k} \psi_p(\xi) \psi_q(\xi) \mathrm{d}V \end{equation}

where \(\psi_p(\xi)\) are the basis functions on the element \(\Omega_k\). In the diagonal mass-matrix approximation ("mass-lumping") we evaluate the integral directly on the collocation points, i.e. with a Gauss or Gauss-Lobatto quadrature determined by the element mesh. Then it reduces to:

\begin{equation} M_{pq} \approx \delta_{pq} \prod_{i=1}^d w_{p_i} \end{equation}

where \(d\) is the spatial dimension and \(w_{p_i}\) are the quadrature weights in dimension \(i\). To apply the mass matrix in coordinates different than logical, or to account for a curved background metric, the data can be pre-multiplied with the Jacobian determinant and/or a metric determinant.

Note

The mass-lumping is exact on Legendre-Gauss meshes, but omits a correction term on Legendre-Gauss-Lobatto meshes.

interpolate_dt_terms_gauss_points()

template<size_t Dim, typename DtTagsList >

void dg::interpolate_dt_terms_gauss_points	(	const gsl::not_null< Variables< DtTagsList > * >	dt_vars,
		const Mesh< Dim > &	volume_mesh,
		const Direction< Dim > &	direction,
		const Variables< DtTagsList > &	dt_corrections
	)

Interpolate the Bjorhus/time derivative corrections to the volume time derivatives in the specified direction.

The general interpolation term (for the \(+\xi\)-dimension) is:

\begin{align*} \partial_t u_{\alpha\breve{\imath}\breve{\jmath}\breve{k}}=\cdots +\ell^{\mathrm{Gauss-Lobatto}}_{N} \left(\xi_{\breve{\imath}}^{\mathrm{Gauss}}\right) \partial_t u^{\mathrm{BC}}_{\alpha\breve{\jmath}\breve{k}}, \end{align*}

where \(\breve{\imath}\), \(\breve{\jmath}\), and \(\breve{k}\) are indices in the logical \(\xi\), \(\eta\), and \(\zeta\) dimensions. \(\partial_t u^{\mathrm{BC}}\) is the time derivative correction, and the function Spectral::boundary_interpolation_term() is used to compute and cache the terms from the lifting terms.

lift_boundary_terms_gauss_points() [1/3]

template<size_t Dim, typename DtTagsList , typename BoundaryCorrectionTagsList >

void dg::lift_boundary_terms_gauss_points	(	const gsl::not_null< Variables< DtTagsList > * >	dt_vars,
		const Scalar< DataVector > &	volume_det_inv_jacobian,
		const Mesh< Dim > &	volume_mesh,
		const Direction< Dim > &	direction,
		const Variables< BoundaryCorrectionTagsList > &	boundary_corrections,
		const Scalar< DataVector > &	magnitude_of_face_normal,
		const Scalar< DataVector > &	face_det_jacobian
	)

Lift the boundary corrections to the volume time derivatives in the specified direction.

The general lifting term (for the \(\xi\)-dimension) is:

\begin{align*} \partial_t u_{\alpha\breve{\imath}\breve{\jmath}\breve{k}}=\cdots -\frac{\ell_{\breve{\imath}}\left(\xi=1\right)} {w_{\breve{\imath}}J_{\breve{\imath}\breve{\jmath}\breve{k}}} \left[J\sqrt{ \frac{\partial\xi}{\partial x^i} \gamma^{ij} \frac{\partial\xi}{\partial x^j}} \left(G_{\alpha} + D_{\alpha}\right) \right]_{\breve{\jmath}\breve{k}}\left(\xi=1\right), \end{align*}

where \(\breve{\imath}\), \(\breve{\jmath}\), and \(\breve{k}\) are indices in the logical \(\xi\), \(\eta\), and \(\zeta\) dimensions. The \(G+D\) terms correspond to the boundary_corrections function argument, and the function Spectral::boundary_lifting_term() is used to compute and cache the terms from the lifting terms \(\ell_{\breve{\imath}}(\xi=\pm1)/w_{\breve{\imath}}\).

Note

that normal vectors are pointing out of the element.

Parameters

dt_vars	The volume time derivatives \(\partial_t u_{\alpha\breve{\imath}\breve{\jmath}\breve{k}}\) to be updated
volume_det_inv_jacobian	The inverse Jacobian determinant in the volume \(J^{-1}_{\breve{\imath}\breve{\jmath}\breve{k}}\)
volume_mesh	The mesh of the volume
direction	The direction of the face on which the boundary corrections are defined
boundary_corrections	The boundary corrections \(\left(G_{\alpha} + D_{\alpha}\right)\)
magnitude_of_face_normal	The term \(\sqrt{ \frac{\partial\xi}{\partial x^i} \gamma^{ij} \frac{\partial\xi}{\partial x^j}}\)
face_det_jacobian	The volume Jacobian determinant \(J\) evaluated on the face (not the surface Jacobian determinant)

lift_boundary_terms_gauss_points() [2/3]

template<size_t Dim, typename DtTagsList , typename BoundaryCorrectionTagsList >

void dg::lift_boundary_terms_gauss_points	(	const gsl::not_null< Variables< DtTagsList > * >	dt_vars,
		const Scalar< DataVector > &	volume_det_inv_jacobian,
		const Mesh< Dim > &	volume_mesh,
		const size_t	dimension,
		const Variables< BoundaryCorrectionTagsList > &	upper_boundary_corrections,
		const Scalar< DataVector > &	upper_magnitude_of_face_normal,
		const Scalar< DataVector > &	upper_face_det_jacobian,
		const Variables< BoundaryCorrectionTagsList > &	lower_boundary_corrections,
		const Scalar< DataVector > &	lower_magnitude_of_face_normal,
		const Scalar< DataVector > &	lower_face_det_jacobian
	)

Lift both the upper and lower (in logical coordinates) boundary corrections to the volume time derivatives in the specified logical dimension.

The upper and lower boundary corrections in the logical dimension are lifted together in order to reduce the amount of striding through data that is needed and to improve cache-friendliness.

The general lifting term (for the \(\xi\)-dimension) is:

\begin{align*} \partial_t u_{\alpha\breve{\imath}\breve{\jmath}\breve{k}}=\cdots -\frac{\ell_{\breve{\imath}}\left(\xi=1\right)} {w_{\breve{\imath}}J_{\breve{\imath}\breve{\jmath}\breve{k}}} \left[J\sqrt{ \frac{\partial\xi}{\partial x^i} \gamma^{ij} \frac{\partial\xi}{\partial x^j}} \left(G_{\alpha} + D_{\alpha}\right) \right]_{\breve{\jmath}\breve{k}}\left(\xi=1\right) - \frac{\ell_{\breve{\imath}}\left(\xi=-1\right)} {w_{\breve{\imath}}J_{\breve{\imath}\breve{\jmath}\breve{k}}} \left[J\sqrt{ \frac{\partial\xi}{\partial x^i} \gamma^{ij} \frac{\partial\xi}{\partial x^j}} \left(G_{\alpha} + D_{\alpha}\right) \right]_{\breve{\jmath}\breve{k}}\left(\xi=-1\right), \end{align*}

where \(\breve{\imath}\), \(\breve{\jmath}\), and \(\breve{k}\) are indices in the logical \(\xi\), \(\eta\), and \(\zeta\) dimensions. The \(G+D\) terms correspond to the upper_boundary_corrections and lower_boundary_corrections function arguments, and the function Spectral::boundary_lifting_term() is used to compute and cache the terms from the lifting terms \(\ell_{\breve{\imath}}(\xi=\pm1)/w_{\breve{\imath}}\).

Note

that normal vectors are pointing out of the element and therefore both terms have the same sign.

lift_boundary_terms_gauss_points() [3/3]

template<size_t Dim, typename... VolumeTags, typename... BoundaryCorrectionTags>

void dg::lift_boundary_terms_gauss_points	(	const gsl::not_null< Variables< tmpl::list< VolumeTags... > > * >	volume_data,
		const Variables< tmpl::list< BoundaryCorrectionTags... > > &	boundary_corrections,
		const Mesh< Dim > &	volume_mesh,
		const Direction< Dim > &	direction
	)

Lift the boundary corrections from the face to the volume for Gauss points in the direction perpendicular to the face.

This function doesn't apply any Jacobians or quadrature weights. It only applies the lifting matrix \(\ell_{\breve{\imath}}(\xi=\pm1)\) to the boundary_corrections and adds the result to the volume_data.

project_contiguous_data_to_boundary()

template<typename VolumeVarsTagsList , typename FaceVarsTagsList , size_t Dim>

void dg::project_contiguous_data_to_boundary	(	const gsl::not_null< Variables< FaceVarsTagsList > * >	face_fields,
		const Variables< VolumeVarsTagsList > &	volume_fields,
		const Mesh< Dim > &	volume_mesh,
		const Direction< Dim > &	direction
	)

Projects a Variables of volume data to a contiguous subset of a boundary Variables

The volume_fields are all projected into the face_fields in the direction direction. The tags in VolumeVarsTagsList must be a contiguous subset of the tags in FaceVarsTagsList. That is, FaceVarsTagsList must be equivalent to tmpl::append<Before, VolumeVarsTagsList, After> where Before and After are tmpl::lists of arbitrary size. This is because the projection is applied on all of the tensor components of the volume variables and is written into contiguous memory on the boundary.

In general, this function will be used for projecting all the evolved variables or all the volume fluxes to the faces. The function dg::project_tensors_to_boundary() should be used for projecting individual tensors to the face.

Note

This function works for both Gauss and Gauss-Lobatto uniform meshes.

project_tensor_to_boundary() [1/2]

template<typename Symm , typename IndexList , size_t Dim>

void dg::project_tensor_to_boundary	(	const gsl::not_null< Tensor< DataVector, Symm, IndexList > * >	face_field,
		const Tensor< DataVector, Symm, IndexList > &	volume_field,
		const Mesh< Dim > &	volume_mesh,
		const Direction< Dim > &	direction
	)

Projects a tensor to the face.

Note

This function works for both Gauss and Gauss-Lobatto uniform meshes.

project_tensor_to_boundary() [2/2]

template<typename Symm , typename IndexList , size_t Dim>

Tensor< DataVector, Symm, IndexList > dg::project_tensor_to_boundary	(	const Tensor< DataVector, Symm, IndexList > &	volume_field,
		const Mesh< Dim > &	volume_mesh,
		const Direction< Dim > &	direction
	)

Projects a tensor to the face.

Note

This function works for both Gauss and Gauss-Lobatto uniform meshes.

project_tensors_to_boundary()

template<typename TagsToProjectList , typename VolumeVarsTagsList , typename FaceVarsTagsList , size_t Dim>

void dg::project_tensors_to_boundary	(	const gsl::not_null< Variables< FaceVarsTagsList > * >	face_fields,
		const Variables< VolumeVarsTagsList > &	volume_fields,
		const Mesh< Dim > &	volume_mesh,
		const Direction< Dim > &	direction
	)

Projects a subset of the tensors in the volume_fields onto the face.

The tensors to project are listed in the TagsToProjectList.

Note

This function works for both Gauss and Gauss-Lobatto uniform meshes.