dg::aRealGeometry2d< real_type > Struct Template Reference

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

Inheritance diagram for dg::aRealGeometry2d< real_type >:

Public Member Functions
SparseTensor< thrust::host_vector< real_type > >	jacobian () const
	The Jacobian of the coordinate transformation from physical to computational space.
SparseTensor< thrust::host_vector< real_type > >	metric () const
	The (inverse) metric tensor of the coordinate system.
std::vector< thrust::host_vector< real_type > >	map () const
	The coordinate map from computational to physical space.
virtual aRealGeometry2d *	clone () const =0
	Geometries are cloneable.
virtual	~aRealGeometry2d ()=default
	allow deletion through base class pointer
Public Member Functions inherited from dg::aRealTopology< real_type, 2 >
unsigned	shape (unsigned u=0) const
	\( n_u N_u\) the total number of points of an axis
host_vector	abscissas (unsigned u=0) const
	Construct grid abscissas of the u axis.
host_vector	weights (unsigned u=0) const
	Get the weights of the u axis.
std::array< unsigned, Nd >	get_shape () const
	\( n_u N_u\) the total number of points of an axis
std::array< host_vector, Nd >	get_abscissas () const
	Construct abscissas for all axes.
std::array< host_vector, Nd >	get_weights () const
	Construct weights for all axes.
std::array< real_type, Nd >	get_p () const
	Get left boundary point \( \vec p\).
std::array< real_type, Nd >	get_q () const
	Get right boundary point \( \vec q\).
std::array< real_type, Nd >	get_l () const
	Get grid length \( l_u = q_u - p_u\) for all axes.
std::array< real_type, Nd >	get_h () const
	Get grid constant \( h_u = \frac{q_u - p_u}{N_u}\) for all axes.
std::array< unsigned, Nd >	get_N () const
	Get number of cells \( N_u\) for all axes.
std::array< unsigned, Nd >	get_n () const
	Get number of polynomial coefficients \( n_u\) for all axes.
std::array< dg::bc, Nd >	get_bc () const
	Get boundary condition \( b_u\) for all axes.
real_type	p (unsigned u=0) const
	Get left boundary point \( p_u\) for axis u.
real_type	q (unsigned u=0) const
	Get right boundary point \( q_u\) for axis u.
real_type	h (unsigned u=0) const
	Get grid constant \( h_u = \frac{q_u - p_u}{N_u}\) for axis u.
real_type	l (unsigned u=0) const
	Get grid length \( l_u = q_u - p_u\) for axis u.
unsigned	n (unsigned u=0) const
	Get number of polynomial coefficients \( n_u\) for axis u.
unsigned	N (unsigned u=0) const
	Get number of cells \( N_u\) for axis u.
dg::bc	bc (unsigned u=0) const
	Get boundary condition \( b_u\) for axis u.
RealGrid< real_type, 1 >	grid (unsigned u) const
	Get axis u as a 1d grid.
RealGrid< real_type, 1 >	axis (unsigned u) const
	An alias for "grid".
real_type	x0 () const
	Equivalent to p(0)
real_type	x1 () const
	Equivalent to p(1)
real_type	y0 () const
	Equivalent to p(2)
real_type	y1 () const
	Equivalent to q(0)
real_type	z0 () const
	Equivalent to q(1)
real_type	z1 () const
	Equivalent to q(2)
real_type	lx () const
	Equivalent to l(0)
real_type	ly () const
	Equivalent to l(1)
real_type	lz () const
	Equivalent to l(2)
real_type	hx () const
	Equivalent to h(0)
real_type	hy () const
	Equivalent to h(1)
real_type	hz () const
	Equivalent to h(2)
unsigned	nx () const
	Equivalent to n(0)
unsigned	ny () const
	Equivalent to n(1)
unsigned	nz () const
	Equivalent to n(2)
unsigned	Nx () const
	Equivalent to N(0)
unsigned	Ny () const
	Equivalent to N(1)
unsigned	Nz () const
	Equivalent to N(2)
dg::bc	bcx () const
	Equivalent to bc(0)
dg::bc	bcy () const
	Equivalent to bc(1)
dg::bc	bcz () const
	Equivalent to bc(2)
RealGrid< real_type, 1 >	gx () const
	Equivalent to grid(0)
RealGrid< real_type, 1 >	gy () const
	Equivalent to grid(1)
RealGrid< real_type, 1 >	gz () const
	Equivalent to grid(2)
std::array< unsigned, Nd >	start () const
	Start coordinate in C-order for dg::file::NcHyperslab.
std::array< unsigned, Nd >	count () const
	Count vector in C-order for dg::file::NcHyperslab.
std::enable_if_t<(Md >=2), void >	multiplyCellNumbers (real_type fx, real_type fy)
	Multiply the number of cells in the first two dimensions with a given factor.
std::enable_if_t<(Md==1), void >	set (unsigned new_n, unsigned new_Nx)
	Set n and N in a 1-dimensional grid.
std::enable_if_t<(Md==2), void >	set (unsigned new_n, unsigned new_Nx, unsigned new_Ny)
	Set n and N in a 2-dimensional grid.
std::enable_if_t<(Md==3), void >	set (unsigned new_n, unsigned new_Nx, unsigned new_Ny, unsigned new_Nz)
	Set n and N in a 3-dimensional grid.
void	set (unsigned new_n, std::array< unsigned, Nd > new_N)
	Same as set( {new_n, new_n,...}, new_N);
void	set (std::array< unsigned, Nd > new_n, std::array< unsigned, Nd > new_N)
	Set the number of polynomials and cells.
void	set (std::array< real_type, Nd > new_p, std::array< real_type, Nd > new_q, std::array< unsigned, Nd > new_n, std::array< unsigned, Nd > new_N, std::array< dg::bc, Nd > new_bcs)
	Reset the entire grid.
void	set_axis (unsigned coord, unsigned new_n, unsigned new_N)
	Set n and N for axis coord.
void	set_pq (std::array< real_type, Nd > new_p, std::array< real_type, Nd > new_q)
	Reset the boundaries of the grid.
void	set_bcs (std::array< dg::bc, Nd > new_bcs)
	Reset the boundary conditions of the grid.
unsigned	size () const
	The total number of points.
void	display (std::ostream &os=std::cout) const
	Display.
std::enable_if_t<(Md==1), bool >	contains (real_type x) const
	Check if the grid contains a point.
bool	contains (const Vector &x) const
	Check if the grid contains a point.

Protected Member Functions
	aRealGeometry2d (const aRealGeometry2d &src)=default
aRealGeometry2d &	operator= (const aRealGeometry2d &src)=default
Protected Member Functions inherited from dg::aRealTopology< real_type, 2 >
	~aRealTopology ()=default
	disallow deletion through base class pointer
	aRealTopology ()=default
	default constructor
	aRealTopology (std::array< real_type, Nd > p, std::array< real_type, Nd > q, std::array< unsigned, Nd > n, std::array< unsigned, Nd > N, std::array< dg::bc, Nd > bcs)
	Construct a topology directly from points and dimensions.
	aRealTopology (const std::array< RealGrid< real_type, 1 >, Nd > &axes)
	Construct a topology as the product of 1d axes grids.
	aRealTopology (const aRealTopology &src)=default
aRealTopology &	operator= (const aRealTopology &src)=default
virtual void	do_set (std::array< unsigned, Nd > new_n, std::array< unsigned, Nd > new_N)=0
	Set the number of polynomials and cells.
virtual void	do_set (std::array< dg::bc, Nd > new_bcs)=0
	Reset the boundary conditions of the grid.
virtual void	do_set_pq (std::array< real_type, Nd > new_p, std::array< real_type, Nd > new_q)=0
	Reset the boundaries of the grid.

Additional Inherited Members
Public Types inherited from dg::aRealTopology< real_type, 2 >
using	value_type
	value type of abscissas and weights
using	host_vector
using	host_grid
	Associated realisation.
Static Public Member Functions inherited from dg::aRealTopology< real_type, 2 >
static constexpr unsigned	ndim ()
	Dimensionality == Nd.

Detailed Description

template<class real_type>
struct dg::aRealGeometry2d< real_type >

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

Constructor & Destructor Documentation

~aRealGeometry2d()

template<class real_type >

virtual dg::aRealGeometry2d< real_type >::~aRealGeometry2d ( )

virtualdefault

allow deletion through base class pointer

aRealGeometry2d()

template<class real_type >

dg::aRealGeometry2d< real_type >::aRealGeometry2d ( const aRealGeometry2d< real_type > & src )

protecteddefault

explicit copy constructor (default)

Parameters

src

source

Member Function Documentation

clone()

template<class real_type >

virtual aRealGeometry2d * dg::aRealGeometry2d< real_type >::clone ( ) const

pure virtual

Geometries are cloneable.

Implemented in dg::RealCartesianGrid2d< real_type >, and dg::RealCartesianRefinedGrid2d< real_type >.

jacobian()

template<class real_type >

SparseTensor< thrust::host_vector< real_type > > dg::aRealGeometry2d< 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::aRealGeometry2d< 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::aRealGeometry2d< 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 >

aRealGeometry2d & dg::aRealGeometry2d< real_type >::operator= ( const aRealGeometry2d< 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_geometry.h