Kaskade::BoundaryInterpolationDisplacement< GridView > Class Template Reference

The BoundaryInterpolationDisplacement class provides a Kaskade WeakFunctionView on the displacement from grid to actual domain boundary (which is computed by boundary interpolation). More...

#include <boundaryInterpolation.hh>

Detailed Description

template<class GridView>
class Kaskade::BoundaryInterpolationDisplacement< GridView >

The BoundaryInterpolationDisplacement class provides a Kaskade WeakFunctionView on the displacement from grid to actual domain boundary (which is computed by boundary interpolation).

It does also implement the interface required for displacements to be used in the BoundaryLocator.

Definition at line 783 of file boundaryInterpolation.hh.

Public Types
using	Displacement = GlobalPosition< GridView >
using	DisplacementDerivative = Dune::FieldMatrix< ctype, dim, GridView::dimension >

Public Member Functions
	BoundaryInterpolationDisplacement (BoundaryInterpolationDisplacement &&)=default
	BoundaryInterpolationDisplacement (GridView const &gv, GridBoundaryTangents< GridView > const &tangents)
	Constructor precomputes for each level-0-cell data that is needed for boundary interpolation. More...
template<class VolumeDisplacement >
void	applyVolumeDisplacement (VolumeDisplacement const &u)
	Provides a \( G^1 \)-continuous boundary displacement of deformed grids. More...
Displacement	value (Cell< GridView > const &cell, LocalPosition< GridView > const &xiFine) const
	Provides the displacement for a point given by cell and local position \( \xi \). More...
DisplacementDerivative	derivative (Cell< GridView > const &cell, LocalPosition< GridView > const &xiFine) const
	Provides the global displacement derivative (w.r.t. global variable \( x \)) for a point given by cell and local position \( \xi \). More...

Related Functions
(Note that these are not member functions.)
template<class VolumeDisplacement >
auto	makeCompositeBoundaryInterpolation (VolumeDisplacement const &u, GeometricFeatureDetector< typename VolumeDisplacement::Space::Grid::LevelGridView::IndexSet::IndexType, typename VolumeDisplacement::Space::Grid::ctype, VolumeDisplacement::Space::Grid::dimension > const &features)
	Creates a composite boundary interpolation displacement from a volume displacement. More...

Member Typedef Documentation

Displacement

template<class GridView >

using Kaskade::BoundaryInterpolationDisplacement< GridView >::Displacement = GlobalPosition<GridView>

Definition at line 788 of file boundaryInterpolation.hh.

DisplacementDerivative

template<class GridView >

using Kaskade::BoundaryInterpolationDisplacement< GridView >::DisplacementDerivative = Dune::FieldMatrix<ctype,dim,GridView::dimension>

Definition at line 789 of file boundaryInterpolation.hh.

Constructor & Destructor Documentation

BoundaryInterpolationDisplacement() [1/2]

template<class GridView >

Kaskade::BoundaryInterpolationDisplacement< GridView >::BoundaryInterpolationDisplacement ( BoundaryInterpolationDisplacement< GridView > &&  )

default

BoundaryInterpolationDisplacement() [2/2]

template<class GridView >

Kaskade::BoundaryInterpolationDisplacement< GridView >::BoundaryInterpolationDisplacement ( GridView const &  gv, GridBoundaryTangents< GridView > const &  tangents  )

inline

Constructor precomputes for each level-0-cell data that is needed for boundary interpolation.

Parameters

gv	level 0 grid view (coarse level)
tangents	tangents on grid boundary

Definition at line 798 of file boundaryInterpolation.hh.

Member Function Documentation

applyVolumeDisplacement()

template<class GridView >

template<class VolumeDisplacement >

void Kaskade::BoundaryInterpolationDisplacement< GridView >::applyVolumeDisplacement ( VolumeDisplacement const &  u )

inline

Provides a \( G^1 \)-continuous boundary displacement of deformed grids.

Let a (volume) displacement \( u \) and the corresponding deformation \( \varphi \) on a simplicial grid with \( G^1 \)-continuous boundary displacement \( v \) be given. In principle, the composite boundary displacement would be

\[ x \mapsto \varphi(x+v(x))-x = u(x+v(x)) \approx u(x) + u_x(x)v(x). \]

Unfortunately, \( \varphi \) is in general not \( G^1 \)-continuous, such that the resulting composite boundary deformation is not \( G^1 \)-continuous.

Therefore we define the composite boundary interpolation by interpolating almost from scratch. We take the \( G^1 \)-continuous boundary edge tangents from the reference grid (which means that feaure edges are independent of the deformation) and rotate them according to \( t \mapsto t + u_x t \). Here, \( u_x \) at a vertex is computed by averaging the surrounding displacement derivatives, which yields a \( G^1 \)-continuous boundary interpolation.

Warning

As this works on the coarse grid and ignores the volume displacement between coarse grid vertices, this is mostly useful for P1 (if need be, P2) discretizations on a single level.

Definition at line 842 of file boundaryInterpolation.hh.

Referenced by Kaskade::BoundaryInterpolationDisplacement< GridView >::makeCompositeBoundaryInterpolation().

derivative()

template<class GridView >

DisplacementDerivative Kaskade::BoundaryInterpolationDisplacement< GridView >::derivative ( Cell< GridView > const &  cell, LocalPosition< GridView > const &  xiFine  ) const

inline

Provides the global displacement derivative (w.r.t. global variable \( x \)) for a point given by cell and local position \( \xi \).

Parameters

cell	any cell in the grid, can be leaf or any level below

Definition at line 934 of file boundaryInterpolation.hh.

value()

template<class GridView >

Displacement Kaskade::BoundaryInterpolationDisplacement< GridView >::value ( Cell< GridView > const &  cell, LocalPosition< GridView > const &  xiFine  ) const

inline

Provides the displacement for a point given by cell and local position \( \xi \).

Parameters

cell	any cell in the grid, can be leaf or any level below

Definition at line 898 of file boundaryInterpolation.hh.

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

• boundaryInterpolation.hh