fluxfunctions.h File Reference

#include <functional>
#include "dg/algorithm.h"

Go to the source code of this file.

Classes
struct	dg::geo::RealCylindricalFunctor< real_type >
	Inject both 2d and 3d operator() to a 2d functor. More...
struct	dg::geo::aCylindricalFunctor< Derived >
	Represent functions written in cylindrical coordinates that are independent of the angle phi serving as both 2d and 3d functions. More...
struct	dg::geo::Constant
	\( f(x,y) = c\) More...
struct	dg::geo::ZCutter
	\( f(R,Z)= \begin{cases} 0 \text{ if } Z < Z_X \\ 1 \text{ else } \end{cases} \) More...
struct	dg::geo::Periodify
	This function extends another function beyond the grid boundaries. More...
struct	dg::geo::CylindricalFunctorsLvl1
	This struct bundles a function and its first derivatives. More...
struct	dg::geo::CylindricalFunctorsLvl2
	This struct bundles a function and its first and second derivatives. More...
struct	dg::geo::CylindricalSymmTensorLvl1
struct	dg::geo::CylindricalVectorLvl0
struct	dg::geo::CylindricalVectorLvl1
	This struct bundles a vector field and its divergence. More...
struct	dg::geo::ScalarProduct
	Return scalar product of two vector fields \( v_0w_0 + v_1w_1 + v_2w_2\). More...
struct	dg::geo::SquareNorm
	Return norm of scalar product of two vector fields \( \sqrt{v_0w_0 + v_1w_1 + v_2w_2}\). More...

Namespaces
namespace	dg
namespace	dg::geo

Typedefs
using	dg::geo::CylindricalFunctor = RealCylindricalFunctor<double>
	Most of the times we use double.

Functions
int	dg::geo::findCriticalPoint (const CylindricalFunctorsLvl2 &psi, double &RC, double &ZC)
	This function finds critical points of psi (any point with vanishing gradient, including the X-point or O-point) via Newton iteration applied to the gradient of psi.
int	dg::geo::findOpoint (const CylindricalFunctorsLvl2 &psi, double &RC, double &ZC)
	This function finds O-points of psi.
void	dg::geo::findXpoint (const CylindricalFunctorsLvl2 &psi, double &RC, double &ZC)
	This function finds X-points of psi.
template<class Geometry3d >
dg::SparseTensor< typename Geometry3d::host_vector >	dg::geo::createAlignmentTensor (const dg::geo::CylindricalVectorLvl0 &bhat, const Geometry3d &g)
	\( \chi^{ij} = b^ib^j\)
template<class Geometry3d >
dg::SparseTensor< typename Geometry3d::host_vector >	dg::geo::createProjectionTensor (const dg::geo::CylindricalVectorLvl0 &bhat, const Geometry3d &g)
	\( h^{ij} = g^{ij} - b^ib^j\)