A modal filter for hollow-cylinder elements: independent exponential roll-offs in the radial, angular (Fourier), and axial directions plus an optional top-mode Heaviside cutoff in the angular direction. More...

#include <HollowCylinder.hpp>

Classes
struct	AngularHalfPower
	Half of the exponent \(m\) in the smooth exponential roll-off applied to the angular (Fourier) modal coefficients. More...
struct	BlocksToFilter
	Which blocks 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 Runge-Kutta substep instead of only at whole-step boundaries. More...
struct	Enable
	Enable (true) or disable (false) the filter. More...
struct	NumModesToKill
	The number of top angular (Fourier) \(m\)-modes to set to zero. More...
struct	RadialHalfPower
	Half of the exponent \(m\) in the smooth exponential roll-off applied to the radial modal coefficients (logical dimension 0). If None, the radial direction is not filtered. 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 Runge-Kutta substep instead of only at whole-step boundaries. More...
struct	ZHalfPower
	Half of the exponent \(m\) in the smooth exponential roll-off applied to the axial \(z\) modal coefficients (logical dimension 2). If None, the axial direction is not filtered. More...

Public Types
using	options

Public Member Functions
	HollowCylinder (size_t num_modes_to_kill, std::optional< size_t > angular_half_power, std::optional< size_t > radial_half_power, std::optional< size_t > z_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< 3, TagList >), HollowCylinder)
	HollowCylinder (CkMigrateMessage *msg)
void	pup (PUP::er &p) override
std::unique_ptr< Filter< 3, 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< 3 > &mesh) const override
std::string	name () const override
	A human-readable name for the concrete filter type, used in diagnostics.
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< 3 > &mesh, const std::optional< InverseJacobian< DataVector, 3, Frame::Grid, Frame::Inertial > > &inv_jac_grid_to_inertial, const std::optional< Jacobian< DataVector, 3, Frame::Grid, Frame::Inertial > > &jac_grid_to_inertial) const override
void	apply_on_boundary (gsl::not_null< Variables< TagList > * > vars, const Mesh< 2 > &mesh, const std::optional< InverseJacobian< DataVector, 3, Frame::Grid, Frame::Inertial > > &inv_jac_grid_to_inertial, const std::optional< Jacobian< DataVector, 3, Frame::Grid, Frame::Inertial > > &jac_grid_to_inertial) const override
bool	is_equal (const Filter< 3, TagList > &other) const override
Public Member Functions inherited from Filters::Filter< 3, TagList >
	WRAPPED_PUPable_abstract (Filter)
virtual bool	supports_mesh (const Mesh< Dim > &mesh) const=0
	Returns true if this filter can filter the mesh.
virtual bool	is_equal (const Filter &other) const=0
	Returns true if other is the same concrete filter type and is equivalent to *this.
virtual 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=0
	Apply the filter in place to the volume vars on the Dim-dimensional mesh.
virtual 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=0
	Apply the filter in place to face vars on the Dim - 1 face mesh.

Static Public Attributes
static constexpr Options::String	help

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

Detailed Description

template<typename TagList>
class Filters::HollowCylinder< TagList >

A modal filter for hollow-cylinder elements: independent exponential roll-offs in the radial, angular (Fourier), and axial directions plus an optional top-mode Heaviside cutoff in the angular direction.

Concrete implementation of Filters::Filter for the hollow-cylinder shells created by domain::creators::AngularCylinder, 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.

A hollow-cylinder shell element uses a Legendre/Chebyshev basis in the radial direction (logical dimension 0), a Fourier basis in the angular direction (logical dimension 1), and a Legendre/Chebyshev basis in the axial \(z\) direction (logical dimension 2).

For each component of the tensors in TagList, the filter rescales the 1-D modal coefficients in a given logical direction by a smooth exponential roll-off. For the radial and axial (Legendre/Chebyshev) directions the coefficient \(c_i\) of the \(i\)-th modal basis function is rescaled 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 half-power option for that direction (RadialHalfPower or ZHalfPower). For the angular (Fourier) direction the roll-off is applied in the angular mode number \(k\) instead, with the maximum resolved mode \(K = (N_\mathrm{pts} - 1) / 2\) taking the role of \(N\):

\begin{align*} c_k \to c_k \exp\!\left[-36 \left(\frac{k}{K}\right)^{2m}\right], \end{align*}

where \(m\) is AngularHalfPower and both the \(\cos\) and \(\sin\) contributions to a given mode \(k\) are weighted identically. Any direction whose half-power is None is left untouched. When NumModesToKill is nonzero, the top NumModesToKill angular modes are additionally set to zero by a Heaviside cutoff.

Note: The angular (Fourier) direction is periodic and therefore has no boundary faces: a hollow-cylinder element only has radial and axial boundaries. Consequently apply_on_boundary is only ever valid on a face obtained by slicing away the radial direction (a (angular, z) face) or the axial direction (a (radial, angular) face); both of these retain the angular direction. A face that sliced away the angular direction would have no Fourier direction and cannot occur, so apply_on_boundary errors if handed one.

Member Typedef Documentation

◆ options

template<typename TagList>

using Filters::HollowCylinder< TagList >::options

Initial value:

 
      tmpl::list<NumModesToKill, AngularHalfPower, RadialHalfPower, ZHalfPower,
                 Enable, BlocksToFilter, VolumeFilterOnSubstep,
                 BoundaryCorrectionFilterOnSubstep, VolumeFilterEveryNSteps,
                 BoundaryCorrectionFilterEveryNSteps>

Member Function Documentation

◆ apply_boundary_filter_on_substep()

template<typename TagList>

bool Filters::HollowCylinder< TagList >::apply_boundary_filter_on_substep ( ) const

overridevirtual

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

Implements Filters::Filter< 3, TagList >.

◆ apply_boundary_filter_on_this_step()

template<typename TagList>

bool Filters::HollowCylinder< 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.

Note: Currently the check for whether to filter on every N steps is done relative to the start of the current Slab. This means that for GTS, independent of the value of N for every N steps, every step has a filter applied since GTS has one step per slab.

Implements Filters::Filter< 3, TagList >.

◆ apply_volume_filter_on_substep()

template<typename TagList>

bool Filters::HollowCylinder< TagList >::apply_volume_filter_on_substep ( ) const

overridevirtual

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

Implements Filters::Filter< 3, TagList >.

◆ apply_volume_filter_on_this_step()

template<typename TagList>

bool Filters::HollowCylinder< 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.

Note: Currently the check for whether to filter on every N steps is done relative to the start of the current Slab. This means that for GTS, independent of the value of N for every N steps, every step has a filter applied since GTS has one step per slab.

Implements Filters::Filter< 3, TagList >.

◆ blocks_to_filter()

template<typename TagList>

const std::optional< std::vector< size_t > > & Filters::HollowCylinder< 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< 3, TagList >.

◆ get_clone()

template<typename TagList>

std::unique_ptr< Filter< 3, TagList > > Filters::HollowCylinder< TagList >::get_clone ( ) const

overridevirtual

Return a heap-allocated deep copy of this filter.

Implements Filters::Filter< 3, TagList >.

◆ name()

template<typename TagList>

std::string Filters::HollowCylinder< TagList >::name ( ) const

inlineoverridevirtual

A human-readable name for the concrete filter type, used in diagnostics.

Implements Filters::Filter< 3, TagList >.

◆ need_jacobians()

template<typename TagList>

bool Filters::HollowCylinder< 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< 3, TagList >.

◆ set_blocks_to_filter()

template<typename TagList>

void Filters::HollowCylinder< 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< 3, TagList >.

Member Data Documentation

◆ help

template<typename TagList>

Options::String Filters::HollowCylinder< TagList >::help

staticconstexpr

Initial value:

= {
      "A hollow-cylinder filter applying independent exponential roll-offs in "
      "the radial, angular (Fourier), and axial directions with an optional "
      "top-mode Heaviside cutoff in the angular direction."}

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

src/NumericalAlgorithms/LinearOperators/Filters/HollowCylinder.hpp

Classes

Public Types

Public Member Functions

Static Public Attributes

Friends

Detailed Description

Member Typedef Documentation

◆ options

Member Function Documentation

◆ apply_boundary_filter_on_substep()

◆ apply_boundary_filter_on_this_step()

◆ apply_volume_filter_on_substep()

◆ apply_volume_filter_on_this_step()

◆ blocks_to_filter()

◆ get_clone()

◆ name()

◆ need_jacobians()

◆ set_blocks_to_filter()

Member Data Documentation

◆ help