\( h^{ij}\) More...

Collaboration diagram for 3.4. Utility functor functionality:

Classes
struct	dg::geo::WallFieldlineDistance
	Distance to wall along fieldline in phi or s coordinate More...

struct	dg::geo::WallFieldlineCoordinate
	Normalized coordinate relative to wall along fieldline in phi or s coordinate. More...

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 uses the dg::Grid2d::shift member to extend 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...

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

Functions
template<class Geometry3d >
dg::SparseTensor< dg::get_host_vector< Geometry3d > >	dg::geo::createAlignmentTensor (const dg::geo::CylindricalVectorLvl0 &bhat, const Geometry3d &g)
	\( \chi^{ij} = b^ib^j\) More...

template<class Geometry3d >
dg::SparseTensor< dg::get_host_vector< Geometry3d > >	dg::geo::createProjectionTensor (const dg::geo::CylindricalVectorLvl0 &bhat, const Geometry3d &g)
	\( h^{ij} = g^{ij} - b^ib^j\) More...

Detailed Description

\( h^{ij}\)

Typedef Documentation

Most of the times we use double.

template<class Geometry3d >

dg::SparseTensor< dg::get_host_vector< Geometry3d > > dg::geo::createAlignmentTensor	(	const dg::geo::CylindricalVectorLvl0 &	bhat,
		const Geometry3d &	g
	)

\( \chi^{ij} = b^ib^j\)

Creates the two times contravariant tensor that, when applied to a covariant vector, creates a vector aligned to b.

Parameters

bhat	The (unit) vector field `b` to align to
g	The vector field is pushed unto this grid

Template Parameters

Geometry3d A three-dimensional geometry

template<class Geometry3d >

dg::SparseTensor< dg::get_host_vector< Geometry3d > > dg::geo::createProjectionTensor	(	const dg::geo::CylindricalVectorLvl0 &	bhat,
		const Geometry3d &	g
	)

\( h^{ij} = g^{ij} - b^ib^j\)

Creates the two times contravariant tensor that, when applied to a covariant vector, creates a vector perpendicular to b.

Parameters

bhat	The (unit) vector field `b`
g	The vector field is pushed unto this grid

Template Parameters

Geometry3d A three-dimensional geometry