ElementMap< Dim, TargetFrame > Class Template Reference

The CoordinateMap for the Element from the Logical frame to the TargetFrame More...

#include <ElementMap.hpp>

Public Types
using	source_frame = Frame::ElementLogical
using	target_frame = TargetFrame

Public Member Functions
	ElementMap (const ElementId< Dim > &element_id, std::unique_ptr< domain::CoordinateMapBase< Frame::BlockLogical, TargetFrame, Dim > > block_map)
	ElementMap (const ElementId< Dim > &element_id, const Block< Dim > &block)
	Construct from an element_id within the block. The (affine) ElementLogical to BlockLogical map is determined by the element_id. The BlockLogical to TargetFrame map is determined by the block:
const domain::CoordinateMapBase< Frame::BlockLogical, TargetFrame, Dim > &	block_map () const
template<typename T>
tnsr::I< T, Dim, TargetFrame >	operator() (const tnsr::I< T, Dim, Frame::ElementLogical > &source_point, const double time=std::numeric_limits< double >::signaling_NaN(), const domain::FunctionsOfTimeMap &functions_of_time={}) const
template<typename T>
tnsr::I< T, Dim, Frame::ElementLogical >	inverse (tnsr::I< T, Dim, TargetFrame > target_point, const double time=std::numeric_limits< double >::signaling_NaN(), const domain::FunctionsOfTimeMap &functions_of_time={}) const
template<typename T>
InverseJacobian< T, Dim, Frame::ElementLogical, TargetFrame >	inv_jacobian (const tnsr::I< T, Dim, Frame::ElementLogical > &source_point, const double time=std::numeric_limits< double >::signaling_NaN(), const domain::FunctionsOfTimeMap &functions_of_time={}) const
template<typename T>
Jacobian< T, Dim, Frame::ElementLogical, TargetFrame >	jacobian (const tnsr::I< T, Dim, Frame::ElementLogical > &source_point, const double time=std::numeric_limits< double >::signaling_NaN(), const domain::FunctionsOfTimeMap &functions_of_time={}) const
template<typename T>
InverseHessian< T, Dim, Frame::ElementLogical, TargetFrame >	inv_hessian (const tnsr::I< T, Dim, Frame::ElementLogical > &source_point, const double time=std::numeric_limits< double >::signaling_NaN(), const domain::FunctionsOfTimeMap &functions_of_time={}) const
	The inverse Hessian of the element map.
void	pup (PUP::er &p)

Static Public Attributes
static constexpr size_t	dim = Dim

Detailed Description

template<size_t Dim, typename TargetFrame>
class ElementMap< Dim, TargetFrame >

The CoordinateMap for the Element from the Logical frame to the TargetFrame

An ElementMap takes a CoordinateMap for a Block and an ElementId as input, and then "prepends" the correct affine map to the CoordinateMap so that the map corresponds to the coordinate map for the Element rather than the Block. This allows DomainCreators to only specify the maps for the Blocks without worrying about how the domain may be decomposed beyond that.

Constructor & Destructor Documentation

ElementMap()

template<size_t Dim, typename TargetFrame>

ElementMap< Dim, TargetFrame >::ElementMap	(	const ElementId< Dim > &	element_id,
		const Block< Dim > &	block )

Construct from an element_id within the block. The (affine) ElementLogical to BlockLogical map is determined by the element_id. The BlockLogical to TargetFrame map is determined by the block:

• If the block is time-independent: the block.stationary_map() is used.
• If the block is time-dependent: The block.moving_mesh_*_map() maps are used. Which maps are used depends on the TargetFrame.

Member Function Documentation

inv_hessian()

template<size_t Dim, typename TargetFrame>

template<typename T>

InverseHessian< T, Dim, Frame::ElementLogical, TargetFrame > ElementMap< Dim, TargetFrame >::inv_hessian ( const tnsr::I< T, Dim, Frame::ElementLogical > & source_point, const double time = std::numeric_limits<double>::signaling_NaN(), const domain::FunctionsOfTimeMap & functions_of_time = {} ) const

inline

The inverse Hessian of the element map.

Let \( \xi^i \) be the element logical coordinates, \( x^i \) be the block logical coordinates, and \( y^i \) be the inertial coordinates. The element map maps \( \xi^i \rightarrow x^i \rightarrow y^i \). Thus, the inverse Hessian is

\[\frac{\partial^2\xi^i}{\partial y^j \partial y^k} = \frac{\partial}{\partial y^j}\frac{\partial x^l}{\partial y^k} \frac{\partial \xi^i}{\partial x^l}} = \frac{\partial^2 x^l}{\partial y^j \partial y^k} \frac{\partial \xi^i}{\partial x^l} \]

where we have used the fact

\[\frac{\partial^2 \xi^i}{\partial x^l \partial x^n} = 0. \]

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

• src/Domain/ElementMap.hpp