dg::aRealGeometryX2d< real_type > Struct Template Reference

This is the abstract interface class for a two-dimensional RealGeometryX. More...

Inheritance diagram for dg::aRealGeometryX2d< real_type >:

Public Member Functions
SparseTensor< thrust::host_vector< real_type > >	jacobian () const
	The Jacobian of the coordinate transformation from physical to computational space. More...
SparseTensor< thrust::host_vector< real_type > >	metric () const
	The (inverse) metric tensor of the coordinate system. More...
std::vector< thrust::host_vector< real_type > >	map () const
	The coordinate map from computational to physical space. More...
virtual aRealGeometryX2d *	clone () const =0
	Geometries are cloneable. More...
virtual	~aRealGeometryX2d ()=default
	allow deletion through base class pointer More...
Public Member Functions inherited from dg::aRealTopologyX2d< real_type >
real_type	x0 () const
	Left boundary in x. More...
real_type	x1 () const
	Right boundary in x. More...
real_type	y0 () const
	left boundary in y More...
real_type	y1 () const
	Right boundary in y. More...
real_type	lx () const
	length of x More...
real_type	ly () const
	length of y More...
real_type	hx () const
	cell size in x More...
real_type	hy () const
	cell size in y More...
real_type	fx () const
	partition factor in x More...
real_type	fy () const
	partition factor in y More...
unsigned	n () const
	number of polynomial coefficients in x and y More...
unsigned	Nx () const
	number of cells in x More...
unsigned	inner_Nx () const
	number of topological cells in x More...
unsigned	outer_Nx () const
	number of smooth rows in x More...
unsigned	Ny () const
	number of cells in y More...
unsigned	inner_Ny () const
	number of cells in the inner region of y More...
unsigned	outer_Ny () const
	number of cells in one of the outer regions of y More...
bc	bcx () const
	boundary conditions in x More...
bc	bcy () const
	boundary conditions in y More...
RealGrid2d< real_type >	grid () const
	Return a copy without topology. More...
const DLT< real_type > &	dlt () const
	discrete legendre trafo More...
unsigned	size () const
	real_typehe total number of points More...
void	display (std::ostream &os=std::cout) const
	Display. More...
void	shift_topologic (real_type x0, real_type y0, real_type &x1, real_type &y1) const
	Shifts a point coordinate due to topology. More...
bool	contains (real_type x, real_type y) const
	Check if the grid contains a point. More...

Protected Member Functions
	aRealGeometryX2d (const aRealGeometryX2d &src)=default
aRealGeometryX2d &	operator= (const aRealGeometryX2d &src)=default
Protected Member Functions inherited from dg::aRealTopologyX2d< real_type >
	~aRealTopologyX2d ()=default
	disallow destruction through base class pointer More...
	aRealTopologyX2d (real_type x0, real_type x1, real_type y0, real_type y1, real_type fx, real_type fy, unsigned n, unsigned Nx, unsigned Ny, bc bcx, bc bcy)
	Construct a 2D X-point grid. More...
	aRealTopologyX2d (const aRealTopologyX2d &src)=default
aRealTopologyX2d &	operator= (const aRealTopologyX2d &src)=default

Additional Inherited Members
Public Types inherited from dg::aRealTopologyX2d< real_type >
using	value_type = real_type
using	host_vector = thrust::host_vector< real_type >
	The host vector type used by host functions like evaluate. More...
using	host_grid = RealGridX2d< real_type >

Detailed Description

template<class real_type>
struct dg::aRealGeometryX2d< real_type >

This is the abstract interface class for a two-dimensional RealGeometryX.

Constructor & Destructor Documentation

~aRealGeometryX2d()

template<class real_type >

virtual dg::aRealGeometryX2d< real_type >::~aRealGeometryX2d ( )

virtualdefault

allow deletion through base class pointer

aRealGeometryX2d()

template<class real_type >

dg::aRealGeometryX2d< real_type >::aRealGeometryX2d ( const aRealGeometryX2d< real_type > &  src )

protecteddefault

explicit copy constructor (default)

Parameters

src

source

Member Function Documentation

clone()

template<class real_type >

virtual aRealGeometryX2d * dg::aRealGeometryX2d< real_type >::clone ( ) const

pure virtual

Geometries are cloneable.

Implemented in dg::RealCartesianGridX2d< real_type >, and dg::RealCartesianRefinedGridX2d< real_type >.

jacobian()

template<class real_type >

SparseTensor< thrust::host_vector< real_type > > dg::aRealGeometryX2d< real_type >::jacobian ( ) const

inline

The Jacobian of the coordinate transformation from physical to computational space.

The elements of the Tensor are (if x,y are the coordinates in computational space and R,Z are the physical space coordinates)

\[ J = \begin{pmatrix} x_R(x,y) & x_Z(x,y) \\ y_R(x,y) & y_Z(x,y) \end{pmatrix} \]

Returns

Jacobian

Note

per default this will be the identity tensor

map()

template<class real_type >

std::vector< thrust::host_vector< real_type > > dg::aRealGeometryX2d< real_type >::map ( ) const

inline

The coordinate map from computational to physical space.

The elements of the map are (if x,y are the coordinates in computational space and R,Z are the physical space coordinates)

\[ R(x,y) \\ Z(x,y) \]

Returns

a vector of size 2

Note

per default this will be the identity map

metric()

template<class real_type >

SparseTensor< thrust::host_vector< real_type > > dg::aRealGeometryX2d< real_type >::metric ( ) const

inline

The (inverse) metric tensor of the coordinate system.

The elements of the inverse metric tensor are the contravariant elements of the metric \(g\). If x,y are the coordinates, then

\[ g^{-1} = \begin{pmatrix} g^{xx}(x,y) & g^{xy}(x,y) \\ & g^{yy}(x,y) \end{pmatrix} \]

Returns

symmetric tensor

Note

use the dg::tensor::volume2d function to compute the volume element from here

per default this will be the identity tensor

operator=()

template<class real_type >

aRealGeometryX2d & dg::aRealGeometryX2d< real_type >::operator= ( const aRealGeometryX2d< real_type > &  src )

protecteddefault

explicit assignment operator (default)

Parameters

src

source

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

• topology/base_geometryX.h