The simplest implementation of aRealTopology2d. More...

Inheritance diagram for dg::RealGrid2d< real_type >:

Public Member Functions
	RealGrid2d (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...

	RealGrid2d (RealGrid1d< real_type > gx, RealGrid1d< real_type > gy)
	Construct a 2d grid as the product of two 1d grids. More...

	RealGrid2d (const aRealTopology2d< real_type > &src)
	allow explicit type conversion from any other topology 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::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::RealGrid2d< real_type >

The simplest implementation of aRealTopology2d.

This code snippet demonstrates how to discretize and compute the norm of a function on a shared memory system

// define the function to integrate
double function(double x, double y, double amp){
    return amp*exp(x)*exp(y);
}
 
// create a grid of the domain [0,2]x[0,2] with 20 cells in x and y and 3 polynomial coefficients
dg::Grid2d g2d( 0, 2, 0, 2, 3, 20, 20);
 
// create the Gaussian weights (volume form) for the integration
const dg::HVec w2d = dg::create::weights( g2d);
 
// our function needs to depend only on x and y so let's fix the amplitude to 2
using namespace std::placeholders; //for _1, _2
auto functor = std::bind( function, _1, _2, 2.);
 
// discretize the function on the grid
const dg::HVec vec = dg::evaluate( functor, g2d);
 
// now compute the scalar product (the L2 norm)
double norm = dg::blas2::dot( vec, w2d, vec);
 
// norm is now: (e^4-1)^2

Constructor & Destructor Documentation

◆ RealGrid2d() [1/3]

template<class real_type >

dg::RealGrid2d< real_type >::RealGrid2d	(	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