A modal filter for spherical-shell elements: a top- \(\ell\) Heaviside cutoff in the angular direction plus optional smooth exponential roll-offs in both the angular \(\ell\) direction and the radial direction. More...

#include <SphericalShell.hpp>

Classes
struct	NumModesToKill
	The number of top \(\ell\) modes to set to zero. More...
struct	AngularHalfPower
	Half of the exponent \(\sigma_a\) in the smooth exponential roll-off applied to the angular \(\ell\) modes below the top- \(\ell\) cutoff. More...
struct	RadialHalfPower
	Half of the exponent \(\sigma_r\) in the smooth exponential roll-off applied to the radial modal coefficients. More...
struct	Enable
	Enable (true) or disable (false) the filter. More...
struct	BlocksToFilter
	Which blocks the filter should be applied to. More...
struct	VolumeFilterOnSubstep
	Apply the volume filter inside every Runge-Kutta substep instead of only at whole-step boundaries. More...
struct	BoundaryCorrectionFilterOnSubstep
	Apply the boundary correction filter inside every Runge-Kutta substep instead of only at whole-step boundaries. More...
struct	VolumeFilterEveryNSteps
	Apply the volume filter once every N steps. None (std::nullopt) disables the every-N-steps trigger. More...
struct	BoundaryCorrectionFilterEveryNSteps
	Apply the boundary correction filter once every N steps. None (std::nullopt) disables the every-N-steps trigger. More...

Public Types
using	options

Public Member Functions
	SphericalShell (size_t num_modes_to_kill, std::optional< size_t > angular_half_power, std::optional< size_t > radial_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 >), SphericalShell)
	SphericalShell (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 SphericalShell< LocalTagList > &lhs, const SphericalShell< LocalTagList > &rhs)

Detailed Description

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

A modal filter for spherical-shell elements: a top- \(\ell\) Heaviside cutoff in the angular direction plus optional smooth exponential roll-offs in both the angular \(\ell\) direction and the radial direction.

Concrete implementation of Filters::Filter for spherical-shell 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 Spherepack-normalized angular modal coefficients \(c_{\ell'}\) as

\begin{align*} c_{\ell'} \to c_{\ell'} \exp\!\left[-36 \left(\frac{\ell'} {\ell^+_{\mathrm{cut}}+1}\right)^{2\sigma_a}\right], \end{align*}

where \(\ell^+_{\mathrm{cut}} = \ell_{\mathrm{max}} -\) NumModesToKill is the largest angular mode that is retained and \(\sigma_a\) is the AngularHalfPower option. With the fixed coefficient 36 and \(\sigma_a\) in the typical range 28-32 the angular filter is smooth below \(\ell^+_{\mathrm{cut}}\) and reduces to a sharp Heaviside cutoff as \(\sigma_a \to \infty\). When AngularHalfPower is None, only the Heaviside cutoff is applied. See ylm::TensorYlm for the derivation of the underlying angular filter.

When RadialHalfPower has a value \(\sigma_r\), an additional 1D exponential filter is applied independently along each radial column. The radial nodal coefficients \(c_i\) are rescaled in modal space as

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

where \(N_r\) is the radial basis degree (radial extent minus one). When RadialHalfPower is None, the radial direction is left untouched.

Design decision:

The exponential coefficient is hardcoded to 36, matching the choice in Hypercube. SphericalShell is the Filters::Filter-based implementation that plugs into the filtering action and supports per-block selection together with independent volume- and boundary-filtering cadences. It is intended for spherical-shell blocks, which store Spherepack-normalized spherical-harmonic modes.

Member Typedef Documentation

◆ options

template<typename TagList>

using Filters::SphericalShell< TagList >::options

Initial value:

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

Member Function Documentation

◆ apply_boundary_filter_on_substep()

template<typename TagList>

bool Filters::SphericalShell< 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::SphericalShell< 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::SphericalShell< 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::SphericalShell< 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::SphericalShell< 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::SphericalShell< 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::SphericalShell< 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::SphericalShell< 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::SphericalShell< 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::SphericalShell< TagList >::help

staticconstexpr

Initial value:

                                  = {
"A spherical-shell filter applying a top-ell Heaviside cutoff in the "
"angular direction with optional smooth exponential roll-offs in both "
"the angular ell direction and the radial direction."}

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

src/NumericalAlgorithms/LinearOperators/Filters/SphericalShell.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_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