two-dimensional Grid with Cartesian metric More...

Inheritance diagram for dg::RealCartesianGrid2d< real_type >:

Public Member Functions
	RealCartesianGrid2d (real_type x0, real_type x1, real_type y0, real_type y1, unsigned n, unsigned Nx, unsigned Ny, bc bcx=PER, bc bcy=PER)
	Equal polynomial coefficients. More...

	RealCartesianGrid2d (RealGrid1d< real_type > gx, RealGrid1d< real_type > gy)
	Construct a 2d grid as the product of two 1d grids. More...

	RealCartesianGrid2d (const dg::RealGrid2d< real_type > &g)
	Construct from existing topology. More...

virtual RealCartesianGrid2d< real_type > *	clone () const override final
	Geometries are cloneable. More...

Public Member Functions inherited from dg::aRealGeometry2d< real_type >
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 aRealGeometry2d *	clone () const =0
	Geometries are cloneable. More...

virtual	~aRealGeometry2d ()=default
	allow deletion through base class pointer More...

Public Member Functions inherited from dg::aRealTopology2d< 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...

unsigned	n () const
	number of polynomial coefficients in x More...

unsigned	nx () const
	number of polynomial coefficients in x More...

unsigned	ny () const
	number of polynomial coefficients in y More...

unsigned	Nx () const
	number of cells in x More...

unsigned	Ny () const
	number of cells in y More...

bc	bcx () const
	boundary conditions in x More...

bc	bcy () const
	boundary conditions in y More...

const DLT< real_type > &	dltx () const
	discrete legendre trafo More...

const DLT< real_type > &	dlty () const
	discrete legendre transformation in y More...

const RealGrid1d< real_type > &	gx () const
	The x-axis grid. More...

const RealGrid1d< real_type > &	gy () const
	The y-axis grid. More...

void	multiplyCellNumbers (real_type fx, real_type fy)
	Multiply the number of cells with a given factor. More...

void	set (unsigned new_n, unsigned new_Nx, unsigned new_Ny)
	Set the number of polynomials and cells. More...

void	set (unsigned new_nx, unsigned new_Nx, unsigned new_ny, unsigned new_Ny)
	Set the number of polynomials and cells. More...

unsigned	size () const
	The total number of points. More...

void	display (std::ostream &os=std::cout) const
	Display. More...

void	shift (bool &negative, real_type &x, real_type &y) const
	Shift any point coordinate to a corresponding grid coordinate according to the boundary condition. More...

void	shift (bool &negative, real_type &x, real_type &y, bc bcx, bc bcy) const
	Shift any point coordinate to a corresponding grid coordinate according to the boundary condition. More...

bool	contains (real_type x, real_type y) const
	Check if the grid contains a point. More...

template<class Vector >
bool	contains (const Vector &x) const
	Shortcut for contains( x[0], x[1]) More...

Additional Inherited Members
Public Types inherited from dg::aRealTopology2d< 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 = RealGrid2d< real_type >

Protected Member Functions inherited from dg::aRealGeometry2d< real_type >
	aRealGeometry2d (const aRealGeometry2d &src)=default

aRealGeometry2d &	operator= (const aRealGeometry2d &src)=default

Protected Member Functions inherited from dg::aRealTopology2d< real_type >
	~aRealTopology2d ()=default
	disallow destruction through base class pointer More...

	aRealTopology2d (RealGrid1d< real_type > gx, RealGrid1d< real_type > gy)
	Construct a 2d grid as the product of two 1d grids. More...

	aRealTopology2d (const aRealTopology2d &src)=default

aRealTopology2d &	operator= (const aRealTopology2d &src)=default

virtual void	do_set (unsigned new_nx, unsigned new_Nx, unsigned new_ny, unsigned new_Ny)=0

Detailed Description

template<class real_type>
struct dg::RealCartesianGrid2d< real_type >

two-dimensional Grid with Cartesian metric

    // create a Cartesian grid on the domain [0,lx]x[0,ly]
    const dg::CartesianGrid2d grid( 0, lx, 0, ly, n, Nx, Ny, bcx, bcy);
 
    // evaluate left and right hand side on the grid
    const dg::DVec lhs = dg::construct<dg::DVec>( dg::evaluate( left, grid));
    const dg::DVec rhs = dg::construct<dg::DVec>( dg::evaluate( right, grid));
    dg::DVec jac(lhs);
 
    // create an Arakawa object
    dg::ArakawaX<dg::aGeometry2d, dg::DMatrix, dg::DVec> arakawa( grid);
 
    //apply arakawa scheme
    arakawa( lhs, rhs, jac);

Constructor & Destructor Documentation

◆ RealCartesianGrid2d() [1/3]

template<class real_type >

dg::RealCartesianGrid2d< real_type >::RealCartesianGrid2d	(	real_type	x0,
		real_type	x1,
		real_type	y0,
		real_type	y1,
		unsigned	n,
		unsigned	Nx,
		unsigned	Ny,
		bc	bcx = `PER`,
		bc	bcy = `PER`
	)

inline

Equal polynomial coefficients.

Parameters

x0	left boundary in x
x1	right boundary in x
y0	lower boundary in y
y1	upper boundary in y
n	# of polynomial coefficients for both x and y dimension (1<=n<=20)
Nx	# of points in x
Ny	# of points in y
bcx	boundary condition in x
bcy	boundary condition in y