Items for assessing truncation error in spectral methods. More...

Classes
struct	ConvergenceInfo
	Holds convergence rate and pile up modes of a power monitor. More...

Functions
template<typename VectorType, size_t Dim>
std::array< double, Dim >	relative_truncation_error (const VectorType &tensor_component, const Mesh< Dim > &mesh)
	The relative truncation error in each logical direction of the grid.
ConvergenceInfo	convergence_rate_and_number_of_pile_up_modes (const DataVector &power_monitor, size_t number_of_filtered_modes=0)
	Returns the convergence rate and the number of pile up modes of a power monitor as a ConvergenceInfo.

template<typename VectorType, size_t Dim>
void	power_monitors (gsl::not_null< std::array< DataVector, Dim > * > result, const VectorType &u, const Mesh< Dim > &mesh)
	Returns array of power monitors in each spatial dimension.
template<typename VectorType, size_t Dim>
std::array< DataVector, Dim >	power_monitors (const VectorType &u, const Mesh< Dim > &mesh)
	Returns array of power monitors in each spatial dimension.

double	relative_truncation_error (const DataVector &power_monitor, size_t num_modes_to_use)
	Compute the relative truncation error.

template<typename VectorType, size_t Dim>
std::array< double, Dim >	absolute_truncation_error (const VectorType &tensor_component, const Mesh< Dim > &mesh)
	Returns an estimate of the absolute truncation error in each dimension.

void	spherical_shell_radial_power_monitor (gsl::not_null< DataVector * > result, const DataVector &tensor_component, const Mesh< 3 > &mesh)
	Return the radial power monitor for a tensor component on a spherical shell.
DataVector	spherical_shell_radial_power_monitor (const DataVector &tensor_component, const Mesh< 3 > &mesh)
	Return the radial power monitor for a tensor component on a spherical shell.

void	spherical_shell_angular_power_monitor (gsl::not_null< DataVector * > result, const DataVector &tensor_ylm_component, const Mesh< 3 > &mesh, int spin_weight, bool zero_m_is_real)
	Return the angular power monitor for one TensorYlm component on a spherical shell.
DataVector	spherical_shell_angular_power_monitor (const DataVector &tensor_ylm_component, const Mesh< 3 > &mesh, int spin_weight, bool zero_m_is_real)
	Return the angular power monitor for one TensorYlm component on a spherical shell.

Detailed Description

Items for assessing truncation error in spectral methods.

Function Documentation

◆ relative_truncation_error()

template<typename VectorType, size_t Dim>

std::array< double, Dim > PowerMonitors::relative_truncation_error	(	const VectorType &	tensor_component,
		const Mesh< Dim > &	mesh )

The relative truncation error in each logical direction of the grid.

This overload is intended for visualization purposes only. It takes a tensor component as input, so it can be used as a kernel to post-process volume data with Python bindings (see TransformVolumeData.py).

◆ spherical_shell_angular_power_monitor() [1/2]

DataVector PowerMonitors::spherical_shell_angular_power_monitor	(	const DataVector &	tensor_ylm_component,
		const Mesh< 3 > &	mesh,
		int	spin_weight,
		bool	zero_m_is_real )

Return the angular power monitor for one TensorYlm component on a spherical shell.

The mesh dimensions are assumed to be ordered (radial, theta, phi), with l_max == m_max. TensorYlm coefficients use the radial dimension as the fastest-moving extent. As reviewed in Sec. II of [31], spin-weighted spherical harmonics with l < |spin_weight| vanish, so these modes are omitted from both the sum and its normalization. Set zero_m_is_real for real scalar coefficients, which have no imaginary m=0 coefficients in Spherepack storage.

◆ spherical_shell_angular_power_monitor() [2/2]

void PowerMonitors::spherical_shell_angular_power_monitor	(	gsl::not_null< DataVector * >	result,
		const DataVector &	tensor_ylm_component,
		const Mesh< 3 > &	mesh,
		int	spin_weight,
		bool	zero_m_is_real )

Return the angular power monitor for one TensorYlm component on a spherical shell.

The mesh dimensions are assumed to be ordered (radial, theta, phi), with l_max == m_max. TensorYlm coefficients use the radial dimension as the fastest-moving extent. As reviewed in Sec. II of [31], spin-weighted spherical harmonics with l < |spin_weight| vanish, so these modes are omitted from both the sum and its normalization. Set zero_m_is_real for real scalar coefficients, which have no imaginary m=0 coefficients in Spherepack storage.

◆ spherical_shell_radial_power_monitor() [1/2]

DataVector PowerMonitors::spherical_shell_radial_power_monitor	(	const DataVector &	tensor_component,
		const Mesh< 3 > &	mesh )

Return the radial power monitor for a tensor component on a spherical shell.

The mesh dimensions are assumed to be ordered (radial, theta, phi). The radial grid points are contiguous, so each angular point supplies one radial slice to the one-dimensional modal transform.

◆ spherical_shell_radial_power_monitor() [2/2]

void PowerMonitors::spherical_shell_radial_power_monitor	(	gsl::not_null< DataVector * >	result,
		const DataVector &	tensor_component,
		const Mesh< 3 > &	mesh )