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PHiLiP::GridRefinement::Element< dim, real > Class Template Referenceabstract

Element class. More...

#include <field.h>

Inheritance diagram for PHiLiP::GridRefinement::Element< dim, real >:
Collaboration diagram for PHiLiP::GridRefinement::Element< dim, real >:

Public Types

using VertexList = std::array< dealii::Tensor< 1, dim, real >, dealii::GeometryInfo< dim >::vertices_per_cell >
 Type alias for array of vertex coordinates for element.
 
using ChordList = std::array< dealii::Tensor< 1, dim, real >, dim >
 Type alias for array of chord veectors (face center to face center) in Deal.II ordering.
 

Public Member Functions

virtual ~Element ()=default
 Destructor.
 
virtual real & scale ()=0
 Reference for element size. More...
 
virtual void set_scale (const real val)=0
 Set the scale for the element.
 
virtual real get_scale () const =0
 Get the scale for the element.
 
virtual void set_anisotropic_ratio (const std::array< real, dim > &ratio)=0
 Set the anisotropic ratio for each reference axis. More...
 
virtual std::array< real, dim > get_anisotropic_ratio ()=0
 Get the anisotropic ratio of each reference axis as an array. More...
 
virtual real get_anisotropic_ratio (const unsigned int j)=0
 Get the anisotropic ratio corresponding to the \(j^{th}\) reference axis. More...
 
virtual void set_unit_axis (const std::array< dealii::Tensor< 1, dim, real >, dim > &unit_axis)=0
 Set the unit axes of the element. More...
 
virtual std::array< dealii::Tensor< 1, dim, real >, dim > get_unit_axis ()=0
 Get unit axis directions as an array.
 
virtual dealii::Tensor< 1, dim, real > get_unit_axis (const unsigned int j)=0
 Get the \(j^{th}\) reference axis.
 
virtual void set_axis (const std::array< dealii::Tensor< 1, dim, real >, dim > &axis)=0
 Set the scaled local frame axes based on vector set (length and direction) More...
 
virtual std::array< dealii::Tensor< 1, dim, real >, dim > get_axis ()=0
 Get the array of axes of the local frame field \((v_1,v_2,v_3)\).
 
virtual dealii::Tensor< 1, dim, real > get_axis (const unsigned int j)=0
 Get the vector corresponding to the \(j^{th}\) frame axis \(v_j\).
 
virtual dealii::Tensor< 2, dim, real > get_metric ()=0
 Get metric matrix at point describing mapping from reference element. More...
 
virtual dealii::Tensor< 2, dim, real > get_inverse_metric ()=0
 . Get inverse metric matrix for the reference element More...
 
template<typename DoFCellAccessorType >
void set_cell (const DoFCellAccessorType &cell)
 Set the Element based on the input cell (from current mesh) More...
 
virtual void set_anisotropy (const std::array< real, dim > &derivative_value, const std::array< dealii::Tensor< 1, dim, real >, dim > &derivative_direction, const unsigned int order)=0
 Set anisotropy from reconstructed directional derivatives. More...
 
virtual void apply_anisotropic_limit (const real anisotropic_ratio_min, const real anisotropic_ratio_max)=0
 Limits the anisotropic ratios to a given bandwidth. More...
 

Protected Member Functions

ChordList get_chord_list (const VertexList &vertices)
 Get the chord list from an input set of vertices.
 
virtual void set_cell_internal (const VertexList &vertices)=0
 Set element to match geometry of input vertex set. More...
 

Detailed Description

template<int dim, typename real>
class PHiLiP::GridRefinement::Element< dim, real >

Element class.

This provides a base class for incorporating both isotropic (size) and anisotropic (size, anisotropy orientation) in controlling unstructured mesh adaptation methods. Provides functions for setting and accesing the local values for a given cell. A collection of elements is contained in the corresponding Field class (with respective extensions for anisotropy). Note: setting anisotropic properties in the isotropic case will assert(0) and make no changes.

Definition at line 23 of file field.h.

Member Function Documentation

◆ apply_anisotropic_limit()

template<int dim, typename real>
virtual void PHiLiP::GridRefinement::Element< dim, real >::apply_anisotropic_limit ( const real  anisotropic_ratio_min,
const real  anisotropic_ratio_max 
)
pure virtual

Limits the anisotropic ratios to a given bandwidth.

First finds ratio above max, redistributes length change to maintain constant volume and scale. Then the process is repeated with a lower bound. Note: does nothing in the isotropic case.

Implemented in PHiLiP::GridRefinement::ElementAnisotropic< dim, real >, and PHiLiP::GridRefinement::ElementIsotropic< dim, real >.

◆ get_anisotropic_ratio() [1/2]

template<int dim, typename real>
virtual std::array<real,dim> PHiLiP::GridRefinement::Element< dim, real >::get_anisotropic_ratio ( )
pure virtual

Get the anisotropic ratio of each reference axis as an array.

Note: equals 1 for each axis in isotropic case.

Implemented in PHiLiP::GridRefinement::ElementAnisotropic< dim, real >, and PHiLiP::GridRefinement::ElementIsotropic< dim, real >.

◆ get_anisotropic_ratio() [2/2]

template<int dim, typename real>
virtual real PHiLiP::GridRefinement::Element< dim, real >::get_anisotropic_ratio ( const unsigned int  j)
pure virtual

Get the anisotropic ratio corresponding to the \(j^{th}\) reference axis.

Note: equals 1 for each axis in isotropic case.

Implemented in PHiLiP::GridRefinement::ElementAnisotropic< dim, real >, and PHiLiP::GridRefinement::ElementIsotropic< dim, real >.

◆ get_inverse_metric()

template<int dim, typename real>
virtual dealii::Tensor<2,dim,real> PHiLiP::GridRefinement::Element< dim, real >::get_inverse_metric ( )
pure virtual

. Get inverse metric matrix for the reference element

In 2D orthogonal case, \(V = 1/h * \mathrm{diag}{\rho,1/\rho} * R(-\theta)\).

Implemented in PHiLiP::GridRefinement::ElementAnisotropic< dim, real >, and PHiLiP::GridRefinement::ElementIsotropic< dim, real >.

◆ get_metric()

template<int dim, typename real>
virtual dealii::Tensor<2,dim,real> PHiLiP::GridRefinement::Element< dim, real >::get_metric ( )
pure virtual

Get metric matrix at point describing mapping from reference element.

In 2D orthorgonal case, \(V = [v,w] = h * R(\theta) * \mathrm{diag}{\rho,1/\rho}\). Under transformation, order of axes is maintained with \((i,j,k)\) vectors mapping to \((v_1,v_2,v_3)\)

Implemented in PHiLiP::GridRefinement::ElementAnisotropic< dim, real >, and PHiLiP::GridRefinement::ElementIsotropic< dim, real >.

◆ scale()

template<int dim, typename real>
virtual real& PHiLiP::GridRefinement::Element< dim, real >::scale ( )
pure virtual

Reference for element size.

Allows direct read/write of scale of mean element axis. Measure of element (length, area, volume) will be \(scale^{dim}\)

Implemented in PHiLiP::GridRefinement::ElementAnisotropic< dim, real >, and PHiLiP::GridRefinement::ElementIsotropic< dim, real >.

◆ set_anisotropic_ratio()

template<int dim, typename real>
virtual void PHiLiP::GridRefinement::Element< dim, real >::set_anisotropic_ratio ( const std::array< real, dim > &  ratio)
pure virtual

Set the anisotropic ratio for each reference axis.

Requires array of order matching axis definition. Each reference axis will have length \(l = \alpha * scale\). Note: does nothing in the isotropic case.

Implemented in PHiLiP::GridRefinement::ElementAnisotropic< dim, real >, and PHiLiP::GridRefinement::ElementIsotropic< dim, real >.

◆ set_anisotropy()

template<int dim, typename real>
virtual void PHiLiP::GridRefinement::Element< dim, real >::set_anisotropy ( const std::array< real, dim > &  derivative_value,
const std::array< dealii::Tensor< 1, dim, real >, dim > &  derivative_direction,
const unsigned int  order 
)
pure virtual

Set anisotropy from reconstructed directional derivatives.

Based on Dolejsi's method for simplices, uses values obtained from reconstructed polynomial on neighbouring cell patch.

Implemented in PHiLiP::GridRefinement::ElementAnisotropic< dim, real >, and PHiLiP::GridRefinement::ElementIsotropic< dim, real >.

◆ set_axis()

template<int dim, typename real>
virtual void PHiLiP::GridRefinement::Element< dim, real >::set_axis ( const std::array< dealii::Tensor< 1, dim, real >, dim > &  axis)
pure virtual

Set the scaled local frame axes based on vector set (length and direction)

Describe the axes of reference parrelogram or parrelopiped at point. Note: does nothing in the isotropic case.

Implemented in PHiLiP::GridRefinement::ElementAnisotropic< dim, real >, and PHiLiP::GridRefinement::ElementIsotropic< dim, real >.

◆ set_cell()

template<int dim, typename real>
template<typename DoFCellAccessorType >
void PHiLiP::GridRefinement::Element< dim, real >::set_cell ( const DoFCellAccessorType &  cell)
inline

Set the Element based on the input cell (from current mesh)

Templated on the mesh/dof type of the input cell from DoFHandler.

Definition at line 123 of file field.h.

◆ set_cell_internal()

template<int dim, typename real>
virtual void PHiLiP::GridRefinement::Element< dim, real >::set_cell_internal ( const VertexList &  vertices)
protectedpure virtual

Set element to match geometry of input vertex set.

Vertices describe the tensor product element in Deal.II ordering. Internal function used in handling of set_cell().

◆ set_unit_axis()

template<int dim, typename real>
virtual void PHiLiP::GridRefinement::Element< dim, real >::set_unit_axis ( const std::array< dealii::Tensor< 1, dim, real >, dim > &  unit_axis)
pure virtual

Set the unit axes of the element.

Requires an ordered array of dealii::Tensor with vector axes. If none unit values are provided, will be rescaled and factored in to anisotropic ratios. Note: does nothing in the isotropic case.

Implemented in PHiLiP::GridRefinement::ElementAnisotropic< dim, real >, and PHiLiP::GridRefinement::ElementIsotropic< dim, real >.

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