An exponential spectral filter applied in each logical direction of a tensor-product (line, square, cube, ...) element. More...

#include <Hypercube.hpp>

Classes
struct	BlocksToFilter
	Which blocks and block groups the filter should be applied to. More...
struct	BoundaryCorrectionFilterEveryNSteps
	Apply the boundary correction filter once every N steps. None (std::nullopt) disables the every-N-steps trigger. More...
struct	BoundaryCorrectionFilterOnSubstep
	Apply the boundary correction filter inside every substep instead of only at step boundaries. More...
struct	Enable
	Enable the filter. More...
struct	HalfPower
	Half of the exponent in the exponential. More...
struct	VolumeFilterEveryNSteps
	Apply the volume filter once every N steps. None (std::nullopt) disables the every-N-steps trigger. More...
struct	VolumeFilterOnSubstep
	Apply the volume filter inside every substep instead of only at step boundaries. More...

Public Types
using	options

Public Member Functions
	Hypercube (unsigned half_power, bool enable, const std::optional< std::vector< std::string > > &blocks_to_filter, bool volume_filter_on_substep, bool boundary_filter_on_substep, std::optional< size_t > volume_filter_every_n_steps, std::optional< size_t > boundary_filter_every_n_steps, const Options::Context &context={})
	WRAPPED_PUPable_decl_base_template (SINGLE_ARG(Filter< Dim, TagList >), Hypercube)
	Hypercube (CkMigrateMessage *msg)
void	pup (PUP::er &p) override
std::unique_ptr< Filter< Dim, TagList > >	get_clone () const override
	Return a heap-allocated deep copy of this filter.
bool	apply_volume_filter_on_substep () const override
	Whether the volume filter should be applied inside every Runge-Kutta substep.
bool	apply_volume_filter_on_this_step (size_t step_number) const override
	Whether the volume filter should be applied at the given step_number.
bool	apply_boundary_filter_on_substep () const override
	Whether the boundary filter should be applied inside every Runge-Kutta substep.
bool	apply_boundary_filter_on_this_step (size_t step_number) const override
	Whether the boundary filter should be applied at the given step_number.
bool	need_jacobians () const override
	Whether the filter needs the grid-to-inertial Jacobian and its inverse.
bool	supports_mesh (const Mesh< Dim > &mesh) const override
	Returns true if this filter can filter the mesh.
const std::optional< std::vector< size_t > > &	blocks_to_filter () const override
	The set of block (or block group) names the filter applies to.
void	set_blocks_to_filter (const std::vector< std::string > &all_block_names, const std::unordered_map< std::string, std::unordered_set< std::string > > &block_groups) override
	Used after construction to change blocks and groups labeled by strings to size_ts, which is what is used throughout the code.
void	apply_in_volume (gsl::not_null< Variables< TagList > * > vars, const Mesh< Dim > &mesh, const std::optional< InverseJacobian< DataVector, Dim, Frame::Grid, Frame::Inertial > > &inv_jac_grid_to_inertial, const std::optional< Jacobian< DataVector, Dim, Frame::Grid, Frame::Inertial > > &jac_grid_to_inertial) const override
	Apply the filter in place to the volume vars on the Dim-dimensional mesh.
void	apply_on_boundary (gsl::not_null< Variables< TagList > * > vars, const Mesh< Dim - 1 > &mesh, const std::optional< InverseJacobian< DataVector, Dim, Frame::Grid, Frame::Inertial > > &inv_jac_grid_to_inertial, const std::optional< Jacobian< DataVector, Dim, Frame::Grid, Frame::Inertial > > &jac_grid_to_inertial) const override
	Apply the filter in place to face vars on the Dim - 1 face mesh.
bool	is_equal (const Filter< Dim, TagList > &other) const override
	Returns true if other is the same concrete filter type and is equivalent to *this.
Public Member Functions inherited from Filters::Filter< Dim, TagList >
	WRAPPED_PUPable_abstract (Filter)
	Filter (CkMigrateMessage *m)

Static Public Attributes
static constexpr Options::String	help

Friends
template<size_t LocalDim, typename LocalTagList>
bool	operator== (const Hypercube< LocalDim, LocalTagList > &lhs, const Hypercube< LocalDim, LocalTagList > &rhs)

Detailed Description

template<size_t Dim, typename TagList>
class Filters::Hypercube< Dim, TagList >

An exponential spectral filter applied in each logical direction of a tensor-product (line, square, cube, ...) element.

Concrete implementation of Filters::Filter for tensor-product (hypercube) elements, driven by the DG filtering action. See Filters::Filter for the framing of volume vs. boundary application, the substep / every-N-steps cadence controls, and the blocks_to_filter semantics.

For each component of the tensors in TagList, the filter rescales the 1-D modal coefficients \(c_i\) in each logical direction as

\begin{align*} c_i \to c_i \exp\!\left[-36 \left(\frac{i}{N}\right)^{2m}\right], \end{align*}

where \(N\) is the basis degree (number of grid points per element per dimension minus one) and \(m\) is the HalfPower option. The same coefficient and HalfPower are used in every logical direction. With the fixed coefficient 36 the highest mode is rescaled by approximately machine epsilon, i.e. effectively zeroed. For a discussion of filtering see section 5.3 of [101].

Design decision:

The exponential coefficient is hardcoded to 36 since this is what has worked well in practice for several decades in SpEC. If we ever use quad or double-double types, we may want to try 72, but that is unlikely to be necessary since 36 decreases the highest coefficient by 1e-16. I.e., this is not relative to the largest coefficient.

Member Typedef Documentation

◆ options

template<size_t Dim, typename TagList>

using Filters::Hypercube< Dim, TagList >::options

Initial value:

 
      tmpl::list<HalfPower, Enable, BlocksToFilter, VolumeFilterOnSubstep,
                 BoundaryCorrectionFilterOnSubstep, VolumeFilterEveryNSteps,
                 BoundaryCorrectionFilterEveryNSteps>

Member Function Documentation

◆ apply_boundary_filter_on_substep()

template<size_t Dim, typename TagList>

bool Filters::Hypercube< Dim, TagList >::apply_boundary_filter_on_substep ( ) const

overridevirtual

Whether the boundary filter should be applied inside every Runge-Kutta substep.

Implements Filters::Filter< Dim, TagList >.

◆ apply_boundary_filter_on_this_step()

template<size_t Dim, typename TagList>

bool Filters::Hypercube< Dim, TagList >::apply_boundary_filter_on_this_step ( size_t step_number ) const

overridevirtual

Whether the boundary filter should be applied at the given step_number.

Implements Filters::Filter< Dim, TagList >.

◆ apply_in_volume()

template<size_t Dim, typename TagList>

void Filters::Hypercube< Dim, TagList >::apply_in_volume	(	gsl::not_null< Variables< TagList > * >	vars,
		const Mesh< Dim > &	mesh,
		const std::optional< InverseJacobian< DataVector, Dim, Frame::Grid, Frame::Inertial > > &	inv_jac_grid_to_inertial,
		const std::optional< Jacobian< DataVector, Dim, Frame::Grid, Frame::Inertial > > &	jac_grid_to_inertial ) const

overridevirtual

Apply the filter in place to the volume vars on the Dim-dimensional mesh.

The grid-to-inertial Jacobian jac_grid_to_inertial and its inverse inv_jac_grid_to_inertial are populated only when need_jacobians() returns true; otherwise both arguments are std::nullopt.

Implements Filters::Filter< Dim, TagList >.

◆ apply_on_boundary()

template<size_t Dim, typename TagList>

void Filters::Hypercube< Dim, TagList >::apply_on_boundary	(	gsl::not_null< Variables< TagList > * >	vars,
		const Mesh< Dim - 1 > &	mesh,
		const std::optional< InverseJacobian< DataVector, Dim, Frame::Grid, Frame::Inertial > > &	inv_jac_grid_to_inertial,
		const std::optional< Jacobian< DataVector, Dim, Frame::Grid, Frame::Inertial > > &	jac_grid_to_inertial ) const

overridevirtual

Apply the filter in place to face vars on the Dim - 1 face mesh.

Used to filter the lifted boundary corrections produced by the DG numerical flux before they enter the volume right-hand side. The grid-to-inertial Jacobian jac_grid_to_inertial and its inverse inv_jac_grid_to_inertial are populated only when need_jacobians() returns true; otherwise both arguments are std::nullopt.

Implements Filters::Filter< Dim, TagList >.

◆ apply_volume_filter_on_substep()

template<size_t Dim, typename TagList>

bool Filters::Hypercube< Dim, TagList >::apply_volume_filter_on_substep ( ) const

overridevirtual

Whether the volume filter should be applied inside every Runge-Kutta substep.

Implements Filters::Filter< Dim, TagList >.

◆ apply_volume_filter_on_this_step()

template<size_t Dim, typename TagList>

bool Filters::Hypercube< Dim, TagList >::apply_volume_filter_on_this_step ( size_t step_number ) const

overridevirtual

Whether the volume filter should be applied at the given step_number.

Implements Filters::Filter< Dim, TagList >.

◆ blocks_to_filter()

template<size_t Dim, typename TagList>

const std::optional< std::vector< size_t > > & Filters::Hypercube< Dim, TagList >::blocks_to_filter ( ) const

overridevirtual

The set of block (or block group) names the filter applies to.

std::nullopt means the filter applies to every block in the domain.

Implements Filters::Filter< Dim, TagList >.

◆ get_clone()

template<size_t Dim, typename TagList>

std::unique_ptr< Filter< Dim, TagList > > Filters::Hypercube< Dim, TagList >::get_clone ( ) const

overridevirtual

Return a heap-allocated deep copy of this filter.

Implements Filters::Filter< Dim, TagList >.

◆ is_equal()

template<size_t Dim, typename TagList>

bool Filters::Hypercube< Dim, TagList >::is_equal ( const Filter< Dim, TagList > & other ) const

overridevirtual

Returns true if other is the same concrete filter type and is equivalent to *this.

Implements Filters::Filter< Dim, TagList >.

◆ need_jacobians()

template<size_t Dim, typename TagList>

bool Filters::Hypercube< Dim, TagList >::need_jacobians ( ) const

inlineoverridevirtual

Whether the filter needs the grid-to-inertial Jacobian and its inverse.

When false, the driving action passes std::nullopt for the Jacobian arguments of apply_in_volume and apply_on_boundary and avoids constructing them.

Implements Filters::Filter< Dim, TagList >.

◆ set_blocks_to_filter()

template<size_t Dim, typename TagList>

void Filters::Hypercube< Dim, TagList >::set_blocks_to_filter	(	const std::vector< std::string > &	all_block_names,
		const std::unordered_map< std::string, std::unordered_set< std::string > > &	block_groups )

overridevirtual

Used after construction to change blocks and groups labeled by strings to size_ts, which is what is used throughout the code.

Implements Filters::Filter< Dim, TagList >.

◆ supports_mesh()

template<size_t Dim, typename TagList>

bool Filters::Hypercube< Dim, TagList >::supports_mesh ( const Mesh< Dim > & mesh ) const

overridevirtual

Returns true if this filter can filter the mesh.

Implements Filters::Filter< Dim, TagList >.

Member Data Documentation

◆ help

template<size_t Dim, typename TagList>

Options::String Filters::Hypercube< Dim, TagList >::help

staticconstexpr

Initial value:

= {
      "An exponential filter applied in each direction of a line, square, or "
      "cube (hypercube)."}

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

src/NumericalAlgorithms/LinearOperators/Filters/Hypercube.hpp

Classes

Public Types

Public Member Functions

Static Public Attributes

Friends

Detailed Description

Design decision:

Member Typedef Documentation

◆ options

Member Function Documentation

◆ apply_boundary_filter_on_substep()

◆ apply_boundary_filter_on_this_step()

◆ apply_in_volume()

◆ apply_on_boundary()

◆ apply_volume_filter_on_substep()

◆ apply_volume_filter_on_this_step()

◆ blocks_to_filter()

◆ get_clone()

◆ is_equal()

◆ need_jacobians()

◆ set_blocks_to_filter()

◆ supports_mesh()

Member Data Documentation

◆ help