Create and manage interpolation matrices from fieldline integration. More...

Public Member Functions
	Fieldaligned ()
	do not allocate memory; no member call except construct is valid More...

template<class Limiter >
	Fieldaligned (const dg::geo::TokamakMagneticField &vec, const ProductGeometry &grid, dg::bc bcx=dg::NEU, dg::bc bcy=dg::NEU, Limiter limit=FullLimiter(), double eps=1e-5, unsigned mx=12, unsigned my=12, double deltaPhi=-1, std::string interpolation_method="linear-nearest", bool benchmark=true)
	Construct from a magnetic field and a grid. More...

template<class Limiter >
	Fieldaligned (const dg::geo::CylindricalVectorLvl1 &vec, const ProductGeometry &grid, dg::bc bcx=dg::NEU, dg::bc bcy=dg::NEU, Limiter limit=FullLimiter(), double eps=1e-5, unsigned mx=12, unsigned my=12, double deltaPhi=-1, std::string interpolation_method="linear-nearest", bool benchmark=true)
	Construct from a vector field and a grid. More...

template<class ... Params>
void	construct (Params &&...ps)
	Perfect forward parameters to one of the constructors. More...

dg::bc	bcx () const

dg::bc	bcy () const

void	set_boundaries (dg::bc bcz, double left, double right)
	Set boundary conditions in the limiter region. More...

void	set_boundaries (dg::bc bcz, const container &left, const container &right)
	Set boundary conditions in the limiter region. More...

void	set_boundaries (dg::bc bcz, const container &global, double scal_left, double scal_right)
	Set boundary conditions in the limiter region. More...

void	operator() (enum whichMatrix which, const container &in, container &out)
	Apply the interpolation to three-dimensional vectors. More...

double	deltaPhi () const

const container &	hbm () const
	Distance between the planes and the boundary \( (s_{k}-s_{b}^-) \). More...

const container &	hbp () const
	Distance between the planes \( (s_b^+-s_{k}) \). More...

const container &	sqrtG () const
	Volume form (including weights) \( \sqrt{G}_{k} \). More...

const container &	sqrtGm () const
	Volume form on minus plane (including weights) \( \sqrt{G}_{k-1} \). More...

const container &	sqrtGp () const
	Volume form on plus plane (including weights) \( \sqrt{G}_{k+1} \). More...

const container &	bphi () const
	bphi More...

const container &	bphiM () const
	bphi on minus plane More...

const container &	bphiP () const
	bphi on plus plane More...

const container &	bbm () const
	Mask minus, 1 if fieldline intersects wall in minus direction but not in plus direction, 0 else. More...

const container &	bbo () const
	Mask both, 1 if fieldline intersects wall in plus direction and in minus direction, 0 else. More...

const container &	bbp () const
	Mask plus, 1 if fieldline intersects wall in plus direction but not in minus direction, 0 else. More...

const ProductGeometry &	grid () const
	Grid used for construction. More...

container	interpolate_from_coarse_grid (const ProductGeometry &grid_coarse, const container &coarse)
	Interpolate along fieldlines from a coarse to a fine grid in phi. More...

void	integrate_between_coarse_grid (const ProductGeometry &grid_coarse, const container &coarse, container &out)
	Integrate a 2d function on the fine grid. More...

template<class BinaryOp , class UnaryOp >
container	evaluate (BinaryOp binary, UnaryOp unary, unsigned p0, unsigned rounds) const
	Evaluate a 2d functor and transform to all planes along the fieldline More...

std::string	method () const
	Return the `interpolation_method` string given in the constructor. More...

	Fieldaligned ()
	do not allocate memory; no member call except construct is valid More...

template<class Limiter >
	Fieldaligned (const dg::geo::TokamakMagneticField &vec, const ProductGeometry &grid, dg::bc bcx=dg::NEU, dg::bc bcy=dg::NEU, Limiter limit=FullLimiter(), double eps=1e-5, unsigned mx=10, unsigned my=10, double deltaPhi=-1, std::string interpolation_method="dg", bool benchmark=true)
	Construct from a magnetic field and a grid. More...

template<class Limiter >
	Fieldaligned (const dg::geo::CylindricalVectorLvl1 &vec, const ProductGeometry &grid, dg::bc bcx=dg::NEU, dg::bc bcy=dg::NEU, Limiter limit=FullLimiter(), double eps=1e-5, unsigned mx=10, unsigned my=10, double deltaPhi=-1, std::string interpolation_method="dg", bool benchmark=true)
	Construct from a vector field and a grid. More...

template<class ... Params>
void	construct (Params &&...ps)
	Perfect forward parameters to one of the constructors. More...

dg::bc	bcx () const

dg::bc	bcy () const

void	set_boundaries (dg::bc bcz, double left, double right)
	Set boundary conditions in the limiter region. More...

void	set_boundaries (dg::bc bcz, const container &left, const container &right)
	Set boundary conditions in the limiter region. More...

void	set_boundaries (dg::bc bcz, const container &global, double scal_left, double scal_right)
	Set boundary conditions in the limiter region. More...

void	operator() (enum whichMatrix which, const container &in, container &out)
	Apply the interpolation to three-dimensional vectors. More...

double	deltaPhi () const

const container &	hbm () const
	Distance between the planes and the boundary \( (s_{k}-s_{b}^-) \). More...

const container &	hbp () const
	Distance between the planes \( (s_b^+-s_{k}) \). More...

const container &	sqrtG () const
	Volume form (including weights) \( \sqrt{G}_{k} \). More...

const container &	sqrtGm () const
	Volume form on minus plane (including weights) \( \sqrt{G}_{k-1} \). More...

const container &	sqrtGp () const
	Volume form on plus plane (including weights) \( \sqrt{G}_{k+1} \). More...

const container &	bphi () const
	bphi More...

const container &	bphiM () const
	bphi on minus plane More...

const container &	bphiP () const
	bphi on plus plane More...

const container &	bbm () const
	Mask minus, 1 if fieldline intersects wall in minus direction but not in plus direction, 0 else. More...

const container &	bbo () const
	Mask both, 1 if fieldline intersects wall in plus direction and in minus direction, 0 else. More...

const container &	bbp () const
	Mask plus, 1 if fieldline intersects wall in plus direction but not in minus direction, 0 else. More...

const ProductGeometry &	grid () const
	Grid used for construction. More...

container	interpolate_from_coarse_grid (const ProductGeometry &grid_coarse, const container &coarse)
	Interpolate along fieldlines from a coarse to a fine grid in phi. More...

void	integrate_between_coarse_grid (const ProductGeometry &grid_coarse, const container &coarse, container &out)
	Integrate a 2d function on the fine grid. More...

template<class BinaryOp , class UnaryOp >
container	evaluate (BinaryOp binary, UnaryOp unary, unsigned p0, unsigned rounds) const
	Evaluate a 2d functor and transform to all planes along the fieldline More...

std::string	method () const

	Fieldaligned ()
	do not allocate memory; no member call except construct is valid More...

template<class Limiter >
	Fieldaligned (const dg::geo::TokamakMagneticField &vec, const ProductGeometry &grid, dg::bc bcx=dg::NEU, dg::bc bcy=dg::NEU, Limiter limit=FullLimiter(), double eps=1e-5, unsigned mx=10, unsigned my=10, double deltaPhi=-1, std::string interpolation_method="dg", bool benchmark=true)
	Construct from a magnetic field and a grid. More...

template<class Limiter >
	Fieldaligned (const dg::geo::CylindricalVectorLvl1 &vec, const ProductGeometry &grid, dg::bc bcx=dg::NEU, dg::bc bcy=dg::NEU, Limiter limit=FullLimiter(), double eps=1e-5, unsigned mx=10, unsigned my=10, double deltaPhi=-1, std::string interpolation_method="dg", bool benchmark=true)
	Construct from a vector field and a grid. More...

template<class ... Params>
void	construct (Params &&...ps)
	Perfect forward parameters to one of the constructors. More...

dg::bc	bcx () const

dg::bc	bcy () const

void	set_boundaries (dg::bc bcz, double left, double right)
	Set boundary conditions in the limiter region. More...

void	set_boundaries (dg::bc bcz, const container &left, const container &right)
	Set boundary conditions in the limiter region. More...

void	set_boundaries (dg::bc bcz, const container &global, double scal_left, double scal_right)
	Set boundary conditions in the limiter region. More...

void	operator() (enum whichMatrix which, const container &in, container &out)
	Apply the interpolation to three-dimensional vectors. More...

double	deltaPhi () const

const container &	hbm () const
	Distance between the planes and the boundary \( (s_{k}-s_{b}^-) \). More...

const container &	hbp () const
	Distance between the planes \( (s_b^+-s_{k}) \). More...

const container &	sqrtG () const
	Volume form (including weights) \( \sqrt{G}_{k} \). More...

const container &	sqrtGm () const
	Volume form on minus plane (including weights) \( \sqrt{G}_{k-1} \). More...

const container &	sqrtGp () const
	Volume form on plus plane (including weights) \( \sqrt{G}_{k+1} \). More...

const container &	bphi () const
	bphi More...

const container &	bphiM () const
	bphi on minus plane More...

const container &	bphiP () const
	bphi on plus plane More...

const container &	bbm () const
	Mask minus, 1 if fieldline intersects wall in minus direction but not in plus direction, 0 else. More...

const container &	bbo () const
	Mask both, 1 if fieldline intersects wall in plus direction and in minus direction, 0 else. More...

const container &	bbp () const
	Mask plus, 1 if fieldline intersects wall in plus direction but not in minus direction, 0 else. More...

const ProductGeometry &	grid () const
	Grid used for construction. More...

container	interpolate_from_coarse_grid (const ProductGeometry &grid_coarse, const container &coarse)
	Interpolate along fieldlines from a coarse to a fine grid in phi. More...

void	integrate_between_coarse_grid (const ProductGeometry &grid_coarse, const container &coarse, container &out)
	Integrate a 2d function on the fine grid. More...

template<class BinaryOp , class UnaryOp >
container	evaluate (BinaryOp binary, UnaryOp unary, unsigned p0, unsigned rounds) const
	Evaluate a 2d functor and transform to all planes along the fieldline More...

std::string	method () const

Detailed Description

template<class ProductGeometry, class IMatrix, class container>
struct dg::geo::Fieldaligned< ProductGeometry, IMatrix, container >

Create and manage interpolation matrices from fieldline integration.

    const dg::CylindricalGrid3d g3d( R_0-a, R_0+a, -a, a, 0, 2.*M_PI, n, Nx, Ny, Nz, dg::NEU, dg::NEU, dg::PER);
    //create magnetic field
    const dg::geo::TokamakMagneticField mag = dg::geo::createCircularField( R_0, I_0);
    auto bhat = dg::geo::createBHat(mag);
    //create Fieldaligned object and construct DS from it
    dg::geo::Fieldaligned<dg::aProductGeometry3d,dg::IDMatrix,dg::DVec>  dsFA(
            bhat, g3d, dg::NEU, dg::NEU, dg::geo::NoLimiter(), 1e-8, mx[0], mx[1],
            -1, method);
    dg::geo::DS<dg::aProductGeometry3d, dg::IDMatrix, dg::DMatrix, dg::DVec>
        ds( dsFA );

Template Parameters

ProductGeometry	must be either `dg::aProductGeometry3d` or `dg::aProductMPIGeometry3d` or any derivative
IMatrix	The type of the interpolation matrix `dg::IHMatrix`, or `dg::IDMatrix`, `dg::MIHMatrix`, or `dg::MIDMatrix`
container	The container-class on which the interpolation matrix operates on `dg::HVec`, or `dg::DVec`, `dg::MHVec`, or `dg::MDVec`

See also: The pdf parallel derivative writeup

Constructor & Destructor Documentation

◆ Fieldaligned() [1/9]

template<class ProductGeometry , class IMatrix , class container >

dg::geo::Fieldaligned< ProductGeometry, IMatrix, container >::Fieldaligned ( )

inline

do not allocate memory; no member call except construct is valid

◆ Fieldaligned() [2/9]

template<class ProductGeometry , class IMatrix , class container >

template<class Limiter >

dg::geo::Fieldaligned< ProductGeometry, IMatrix, container >::Fieldaligned	(	const dg::geo::TokamakMagneticField &	vec,
		const ProductGeometry &	grid,
		dg::bc	bcx = `dg::NEU`,
		dg::bc	bcy = `dg::NEU`,
		Limiter	limit = `FullLimiter()`,
		double	eps = `1e-5`,
		unsigned	mx = `12`,
		unsigned	my = `12`,
		double	deltaPhi = `-1`,
		std::string	interpolation_method = `"linear-nearest"`,
		bool	benchmark = `true`
	)

inline

Construct from a magnetic field and a grid.

Template Parameters

Limiter Class that can be evaluated on a 2d grid, returns 1 if there is a limiter and 0 if there isn't. If a field line crosses the limiter in the plane \( \phi=0\) then the limiter boundary conditions apply.

Parameters

vec	The vector field to integrate. Note that you can control how the boundary conditions are represented by changing vec outside the grid domain using e.g. the `periodify` function.
grid	The grid on which to integrate fieldlines.
bcx	This parameter is passed on to `dg::create::interpolation(const thrust::host_vector<real_type>&,const thrust::host_vector<real_type>&,const aRealTopology2d<real_type>&,dg::bc,dg::bc,std::string)` (see there for more details) function and deterimens what happens when the endpoint of the fieldline integration leaves the domain boundaries of `grid`. Note that `bcx` and `grid.bcx()` have to be either both periodic or both not periodic.
bcy	analogous to `bcx`, applies to y direction
limit	Instance of the limiter class (Note that if `grid.bcz()==dg::PER` this parameter is ignored, Default is a limiter everywhere)
eps	Desired accuracy of the fieldline integrator
mx	refinement factor in X of the fine grid relative to grid (Set to 1, if the x-component of `vec` vanishes, else as high as possible, 12 is a good start) If the projection method (parsed from `interpolation_method`) is not "dg" then `mx` must be a multiple of `nx`
my	analogous to `mx`, applies to y direction
deltaPhi	The angular distance that the fieldline-integrator will integrate. Per default this is the distance between planes, which is chosen automatically if you set it <=0, i.e. if deltaPhi <=0 then it will be overwritten to deltaPhi = grid.hz(). Sometimes however, you may want to set it to a different value from `grid.hz()` for example for 2d problems or for a staggered grid.

Note: deltaPhi influences the interpolation matrices and the parallel modulation in the evaluate() member function.; If there is a limiter, the boundary condition on the first/last plane is set by the grid.bcz() variable and can be changed by the set_boundaries function. If there is no limiter, the boundary condition is periodic.

Parameters

interpolation_method parsed according to

interpolation_method	interpolation	projection
"dg"	"dg"	"dg"
"linear"	"linear"	"dg"
"cubic"	"cubic"	"dg"
"nearest"	"nearest"	"dg"
"linear-nearest" (##)	"linear"	"nearest"
"cubic-nearest"	"cubic"	"nearest"
"nearest-nearest"	"nearest"	"nearest"
"dg-linear"	"dg"	"linear"
"linear-linear"	"linear"	"linear"
"cubic-linear"	"cubic"	"linear"
"nearest-linear"	"nearest"	"linear"

(##) Use "linear-nearest" if in doubt. The table yields one parameter passed to create::interpolation (from the given grid to the fine grid) and one parameter to create::projection (from the fine grid to the given grid)

Parameters

benchmark	If true write construction timings to std::cout
eps	Desired accuracy of the fieldline integrator
mx	refinement factor in X of the fine grid relative to grid (Set to 1, if the x-component of `vec` vanishes, else as high as possible, 10 is a good start)
my	analogous to `mx`, applies to y direction
deltaPhi	The angular distance that the fieldline-integrator will integrate. Per default this is the distance between planes, which is chosen automatically if you set it <=0, i.e. if deltaPhi <=0 then it will be overwritten to deltaPhi = grid.hz(). Sometimes however, you may want to set it to a different value from `grid.hz()` for example for 2d problems or for a staggered grid.

Note: deltaPhi influences the interpolation matrices and the parallel modulation in the evaluate() member function.; If there is a limiter, the boundary condition on the first/last plane is set by the grid.bcz() variable and can be changed by the set_boundaries function. If there is no limiter, the boundary condition is periodic.

Parameters

interpolation_method	Several interpolation methods are available: dg uses the native dG interpolation scheme given by the grid, nearest searches for the nearest point and copies its value, linear searches for the two (in 2d four, etc.) closest points and linearly interpolates their values, cubic searches for the four (in 2d 16, etc) closest points and interpolates a cubic polynomial
benchmark	If true write construction timings to std::cout

◆ Fieldaligned() [3/9]

template<class ProductGeometry , class IMatrix , class container >

template<class Limiter >

dg::geo::Fieldaligned< ProductGeometry, IMatrix, container >::Fieldaligned	(	const dg::geo::CylindricalVectorLvl1 &	vec,
		const ProductGeometry &	grid,
		dg::bc	bcx = `dg::NEU`,
		dg::bc	bcy = `dg::NEU`,
		Limiter	limit = `FullLimiter()`,
		double	eps = `1e-5`,
		unsigned	mx = `12`,
		unsigned	my = `12`,
		double	deltaPhi = `-1`,
		std::string	interpolation_method = `"linear-nearest"`,
		bool	benchmark = `true`
	)

Construct from a vector field and a grid.

Template Parameters

Limiter Class that can be evaluated on a 2d grid, returns 1 if there is a limiter and 0 if there isn't. If a field line crosses the limiter in the plane \( \phi=0\) then the limiter boundary conditions apply.

Parameters

vec	The vector field to integrate. Note that you can control how the boundary conditions are represented by changing vec outside the grid domain using e.g. the `periodify` function.
grid	The grid on which to integrate fieldlines.
bcx	This parameter is passed on to `dg::create::interpolation(const thrust::host_vector<real_type>&,const thrust::host_vector<real_type>&,const aRealTopology2d<real_type>&,dg::bc,dg::bc,std::string)` (see there for more details) function and deterimens what happens when the endpoint of the fieldline integration leaves the domain boundaries of `grid`. Note that `bcx` and `grid.bcx()` have to be either both periodic or both not periodic.
bcy	analogous to `bcx`, applies to y direction
limit	Instance of the limiter class (Note that if `grid.bcz()==dg::PER` this parameter is ignored, Default is a limiter everywhere)
eps	Desired accuracy of the fieldline integrator
mx	refinement factor in X of the fine grid relative to grid (Set to 1, if the x-component of `vec` vanishes, else as high as possible, 12 is a good start) If the projection method (parsed from `interpolation_method`) is not "dg" then `mx` must be a multiple of `nx`
my	analogous to `mx`, applies to y direction
deltaPhi	The angular distance that the fieldline-integrator will integrate. Per default this is the distance between planes, which is chosen automatically if you set it <=0, i.e. if deltaPhi <=0 then it will be overwritten to deltaPhi = grid.hz(). Sometimes however, you may want to set it to a different value from `grid.hz()` for example for 2d problems or for a staggered grid.

Note: deltaPhi influences the interpolation matrices and the parallel modulation in the evaluate() member function.; If there is a limiter, the boundary condition on the first/last plane is set by the grid.bcz() variable and can be changed by the set_boundaries function. If there is no limiter, the boundary condition is periodic.

Parameters

interpolation_method parsed according to

interpolation_method	interpolation	projection
"dg"	"dg"	"dg"
"linear"	"linear"	"dg"
"cubic"	"cubic"	"dg"
"nearest"	"nearest"	"dg"
"linear-nearest" (##)	"linear"	"nearest"
"cubic-nearest"	"cubic"	"nearest"
"nearest-nearest"	"nearest"	"nearest"
"dg-linear"	"dg"	"linear"
"linear-linear"	"linear"	"linear"
"cubic-linear"	"cubic"	"linear"
"nearest-linear"	"nearest"	"linear"

(##) Use "linear-nearest" if in doubt. The table yields one parameter passed to create::interpolation (from the given grid to the fine grid) and one parameter to create::projection (from the fine grid to the given grid)

Parameters

benchmark	If true write construction timings to std::cout
eps	Desired accuracy of the fieldline integrator
mx	refinement factor in X of the fine grid relative to grid (Set to 1, if the x-component of `vec` vanishes, else as high as possible, 10 is a good start)
my	analogous to `mx`, applies to y direction
deltaPhi	The angular distance that the fieldline-integrator will integrate. Per default this is the distance between planes, which is chosen automatically if you set it <=0, i.e. if deltaPhi <=0 then it will be overwritten to deltaPhi = grid.hz(). Sometimes however, you may want to set it to a different value from `grid.hz()` for example for 2d problems or for a staggered grid.

Note: deltaPhi influences the interpolation matrices and the parallel modulation in the evaluate() member function.; If there is a limiter, the boundary condition on the first/last plane is set by the grid.bcz() variable and can be changed by the set_boundaries function. If there is no limiter, the boundary condition is periodic.

Parameters

interpolation_method	Several interpolation methods are available: dg uses the native dG interpolation scheme given by the grid, nearest searches for the nearest point and copies its value, linear searches for the two (in 2d four, etc.) closest points and linearly interpolates their values, cubic searches for the four (in 2d 16, etc) closest points and interpolates a cubic polynomial
benchmark	If true write construction timings to std::cout

◆ Fieldaligned() [4/9]

template<class ProductGeometry , class IMatrix , class container >

dg::geo::Fieldaligned< ProductGeometry, IMatrix, container >::Fieldaligned ( )

inline

do not allocate memory; no member call except construct is valid

◆ Fieldaligned() [5/9]

template<class ProductGeometry , class IMatrix , class container >

template<class Limiter >

dg::geo::Fieldaligned< ProductGeometry, IMatrix, container >::Fieldaligned	(	const dg::geo::TokamakMagneticField &	vec,
		const ProductGeometry &	grid,
		dg::bc	bcx = `dg::NEU`,
		dg::bc	bcy = `dg::NEU`,
		Limiter	limit = `FullLimiter()`,
		double	eps = `1e-5`,
		unsigned	mx = `10`,
		unsigned	my = `10`,
		double	deltaPhi = `-1`,
		std::string	interpolation_method = `"dg"`,
		bool	benchmark = `true`
	)

inline

Construct from a magnetic field and a grid.

Template Parameters

Limiter Class that can be evaluated on a 2d grid, returns 1 if there is a limiter and 0 if there isn't. If a field line crosses the limiter in the plane \( \phi=0\) then the limiter boundary conditions apply.

Parameters

vec	The vector field to integrate. Note that you can control how the boundary conditions are represented by changing vec outside the grid domain using e.g. the `periodify` function.
grid	The grid on which to integrate fieldlines.
bcx	This parameter is passed on to `dg::create::interpolation(const thrust::host_vector<real_type>&,const thrust::host_vector<real_type>&,const aRealTopology2d<real_type>&,dg::bc,dg::bc,std::string)` (see there for more details) function and deterimens what happens when the endpoint of the fieldline integration leaves the domain boundaries of `grid`. Note that `bcx` and `grid.bcx()` have to be either both periodic or both not periodic.
bcy	analogous to `bcx`, applies to y direction
limit	Instance of the limiter class (Note that if `grid.bcz()==dg::PER` this parameter is ignored, Default is a limiter everywhere)
eps	Desired accuracy of the fieldline integrator
mx	refinement factor in X of the fine grid relative to grid (Set to 1, if the x-component of `vec` vanishes, else as high as possible, 12 is a good start) If the projection method (parsed from `interpolation_method`) is not "dg" then `mx` must be a multiple of `nx`
my	analogous to `mx`, applies to y direction
deltaPhi	The angular distance that the fieldline-integrator will integrate. Per default this is the distance between planes, which is chosen automatically if you set it <=0, i.e. if deltaPhi <=0 then it will be overwritten to deltaPhi = grid.hz(). Sometimes however, you may want to set it to a different value from `grid.hz()` for example for 2d problems or for a staggered grid.

Note: deltaPhi influences the interpolation matrices and the parallel modulation in the evaluate() member function.; If there is a limiter, the boundary condition on the first/last plane is set by the grid.bcz() variable and can be changed by the set_boundaries function. If there is no limiter, the boundary condition is periodic.

Parameters

interpolation_method parsed according to

interpolation_method	interpolation	projection
"dg"	"dg"	"dg"
"linear"	"linear"	"dg"
"cubic"	"cubic"	"dg"
"nearest"	"nearest"	"dg"
"linear-nearest" (##)	"linear"	"nearest"
"cubic-nearest"	"cubic"	"nearest"
"nearest-nearest"	"nearest"	"nearest"
"dg-linear"	"dg"	"linear"
"linear-linear"	"linear"	"linear"
"cubic-linear"	"cubic"	"linear"
"nearest-linear"	"nearest"	"linear"

(##) Use "linear-nearest" if in doubt. The table yields one parameter passed to create::interpolation (from the given grid to the fine grid) and one parameter to create::projection (from the fine grid to the given grid)

Parameters

benchmark	If true write construction timings to std::cout
eps	Desired accuracy of the fieldline integrator
mx	refinement factor in X of the fine grid relative to grid (Set to 1, if the x-component of `vec` vanishes, else as high as possible, 10 is a good start)
my	analogous to `mx`, applies to y direction
deltaPhi	The angular distance that the fieldline-integrator will integrate. Per default this is the distance between planes, which is chosen automatically if you set it <=0, i.e. if deltaPhi <=0 then it will be overwritten to deltaPhi = grid.hz(). Sometimes however, you may want to set it to a different value from `grid.hz()` for example for 2d problems or for a staggered grid.

Note: deltaPhi influences the interpolation matrices and the parallel modulation in the evaluate() member function.; If there is a limiter, the boundary condition on the first/last plane is set by the grid.bcz() variable and can be changed by the set_boundaries function. If there is no limiter, the boundary condition is periodic.

Parameters

interpolation_method	Several interpolation methods are available: dg uses the native dG interpolation scheme given by the grid, nearest searches for the nearest point and copies its value, linear searches for the two (in 2d four, etc.) closest points and linearly interpolates their values, cubic searches for the four (in 2d 16, etc) closest points and interpolates a cubic polynomial
benchmark	If true write construction timings to std::cout

◆ Fieldaligned() [6/9]

template<class ProductGeometry , class IMatrix , class container >

template<class Limiter >

dg::geo::Fieldaligned< ProductGeometry, IMatrix, container >::Fieldaligned	(	const dg::geo::CylindricalVectorLvl1 &	vec,
		const ProductGeometry &	grid,
		dg::bc	bcx = `dg::NEU`,
		dg::bc	bcy = `dg::NEU`,
		Limiter	limit = `FullLimiter()`,
		double	eps = `1e-5`,
		unsigned	mx = `10`,
		unsigned	my = `10`,
		double	deltaPhi = `-1`,
		std::string	interpolation_method = `"dg"`,
		bool	benchmark = `true`
	)

Construct from a vector field and a grid.

Template Parameters

Limiter Class that can be evaluated on a 2d grid, returns 1 if there is a limiter and 0 if there isn't. If a field line crosses the limiter in the plane \( \phi=0\) then the limiter boundary conditions apply.

Parameters

vec	The vector field to integrate. Note that you can control how the boundary conditions are represented by changing vec outside the grid domain using e.g. the `periodify` function.
grid	The grid on which to integrate fieldlines.
bcx	This parameter is passed on to `dg::create::interpolation(const thrust::host_vector<real_type>&,const thrust::host_vector<real_type>&,const aRealTopology2d<real_type>&,dg::bc,dg::bc,std::string)` (see there for more details) function and deterimens what happens when the endpoint of the fieldline integration leaves the domain boundaries of `grid`. Note that `bcx` and `grid.bcx()` have to be either both periodic or both not periodic.
bcy	analogous to `bcx`, applies to y direction
limit	Instance of the limiter class (Note that if `grid.bcz()==dg::PER` this parameter is ignored, Default is a limiter everywhere)
eps	Desired accuracy of the fieldline integrator
mx	refinement factor in X of the fine grid relative to grid (Set to 1, if the x-component of `vec` vanishes, else as high as possible, 12 is a good start) If the projection method (parsed from `interpolation_method`) is not "dg" then `mx` must be a multiple of `nx`
my	analogous to `mx`, applies to y direction
deltaPhi	The angular distance that the fieldline-integrator will integrate. Per default this is the distance between planes, which is chosen automatically if you set it <=0, i.e. if deltaPhi <=0 then it will be overwritten to deltaPhi = grid.hz(). Sometimes however, you may want to set it to a different value from `grid.hz()` for example for 2d problems or for a staggered grid.

Note: deltaPhi influences the interpolation matrices and the parallel modulation in the evaluate() member function.; If there is a limiter, the boundary condition on the first/last plane is set by the grid.bcz() variable and can be changed by the set_boundaries function. If there is no limiter, the boundary condition is periodic.

Parameters

interpolation_method parsed according to

interpolation_method	interpolation	projection
"dg"	"dg"	"dg"
"linear"	"linear"	"dg"
"cubic"	"cubic"	"dg"
"nearest"	"nearest"	"dg"
"linear-nearest" (##)	"linear"	"nearest"
"cubic-nearest"	"cubic"	"nearest"
"nearest-nearest"	"nearest"	"nearest"
"dg-linear"	"dg"	"linear"
"linear-linear"	"linear"	"linear"
"cubic-linear"	"cubic"	"linear"
"nearest-linear"	"nearest"	"linear"

(##) Use "linear-nearest" if in doubt. The table yields one parameter passed to create::interpolation (from the given grid to the fine grid) and one parameter to create::projection (from the fine grid to the given grid)

Parameters

benchmark	If true write construction timings to std::cout
eps	Desired accuracy of the fieldline integrator
mx	refinement factor in X of the fine grid relative to grid (Set to 1, if the x-component of `vec` vanishes, else as high as possible, 10 is a good start)
my	analogous to `mx`, applies to y direction
deltaPhi	The angular distance that the fieldline-integrator will integrate. Per default this is the distance between planes, which is chosen automatically if you set it <=0, i.e. if deltaPhi <=0 then it will be overwritten to deltaPhi = grid.hz(). Sometimes however, you may want to set it to a different value from `grid.hz()` for example for 2d problems or for a staggered grid.

Note: deltaPhi influences the interpolation matrices and the parallel modulation in the evaluate() member function.; If there is a limiter, the boundary condition on the first/last plane is set by the grid.bcz() variable and can be changed by the set_boundaries function. If there is no limiter, the boundary condition is periodic.

Parameters

interpolation_method	Several interpolation methods are available: dg uses the native dG interpolation scheme given by the grid, nearest searches for the nearest point and copies its value, linear searches for the two (in 2d four, etc.) closest points and linearly interpolates their values, cubic searches for the four (in 2d 16, etc) closest points and interpolates a cubic polynomial
benchmark	If true write construction timings to std::cout

◆ Fieldaligned() [7/9]

template<class ProductGeometry , class IMatrix , class container >

dg::geo::Fieldaligned< ProductGeometry, IMatrix, container >::Fieldaligned ( )

inline

do not allocate memory; no member call except construct is valid

◆ Fieldaligned() [8/9]

template<class ProductGeometry , class IMatrix , class container >

template<class Limiter >

dg::geo::Fieldaligned< ProductGeometry, IMatrix, container >::Fieldaligned	(	const dg::geo::TokamakMagneticField &	vec,
		const ProductGeometry &	grid,
		dg::bc	bcx = `dg::NEU`,
		dg::bc	bcy = `dg::NEU`,
		Limiter	limit = `FullLimiter()`,
		double	eps = `1e-5`,
		unsigned	mx = `10`,
		unsigned	my = `10`,
		double	deltaPhi = `-1`,
		std::string	interpolation_method = `"dg"`,
		bool	benchmark = `true`
	)

inline

Construct from a magnetic field and a grid.

Template Parameters

Limiter Class that can be evaluated on a 2d grid, returns 1 if there is a limiter and 0 if there isn't. If a field line crosses the limiter in the plane \( \phi=0\) then the limiter boundary conditions apply.

Parameters

vec	The vector field to integrate. Note that you can control how the boundary conditions are represented by changing vec outside the grid domain using e.g. the `periodify` function.
grid	The grid on which to integrate fieldlines.
bcx	This parameter is passed on to `dg::create::interpolation(const thrust::host_vector<real_type>&,const thrust::host_vector<real_type>&,const aRealTopology2d<real_type>&,dg::bc,dg::bc,std::string)` (see there for more details) function and deterimens what happens when the endpoint of the fieldline integration leaves the domain boundaries of `grid`. Note that `bcx` and `grid.bcx()` have to be either both periodic or both not periodic.
bcy	analogous to `bcx`, applies to y direction
limit	Instance of the limiter class (Note that if `grid.bcz()==dg::PER` this parameter is ignored, Default is a limiter everywhere)
eps	Desired accuracy of the fieldline integrator
mx	refinement factor in X of the fine grid relative to grid (Set to 1, if the x-component of `vec` vanishes, else as high as possible, 12 is a good start) If the projection method (parsed from `interpolation_method`) is not "dg" then `mx` must be a multiple of `nx`
my	analogous to `mx`, applies to y direction
deltaPhi	The angular distance that the fieldline-integrator will integrate. Per default this is the distance between planes, which is chosen automatically if you set it <=0, i.e. if deltaPhi <=0 then it will be overwritten to deltaPhi = grid.hz(). Sometimes however, you may want to set it to a different value from `grid.hz()` for example for 2d problems or for a staggered grid.

Note: deltaPhi influences the interpolation matrices and the parallel modulation in the evaluate() member function.; If there is a limiter, the boundary condition on the first/last plane is set by the grid.bcz() variable and can be changed by the set_boundaries function. If there is no limiter, the boundary condition is periodic.

Parameters

interpolation_method parsed according to

interpolation_method	interpolation	projection
"dg"	"dg"	"dg"
"linear"	"linear"	"dg"
"cubic"	"cubic"	"dg"
"nearest"	"nearest"	"dg"
"linear-nearest" (##)	"linear"	"nearest"
"cubic-nearest"	"cubic"	"nearest"
"nearest-nearest"	"nearest"	"nearest"
"dg-linear"	"dg"	"linear"
"linear-linear"	"linear"	"linear"
"cubic-linear"	"cubic"	"linear"
"nearest-linear"	"nearest"	"linear"

(##) Use "linear-nearest" if in doubt. The table yields one parameter passed to create::interpolation (from the given grid to the fine grid) and one parameter to create::projection (from the fine grid to the given grid)

Parameters

benchmark	If true write construction timings to std::cout
eps	Desired accuracy of the fieldline integrator
mx	refinement factor in X of the fine grid relative to grid (Set to 1, if the x-component of `vec` vanishes, else as high as possible, 10 is a good start)
my	analogous to `mx`, applies to y direction
deltaPhi	The angular distance that the fieldline-integrator will integrate. Per default this is the distance between planes, which is chosen automatically if you set it <=0, i.e. if deltaPhi <=0 then it will be overwritten to deltaPhi = grid.hz(). Sometimes however, you may want to set it to a different value from `grid.hz()` for example for 2d problems or for a staggered grid.

Note: deltaPhi influences the interpolation matrices and the parallel modulation in the evaluate() member function.; If there is a limiter, the boundary condition on the first/last plane is set by the grid.bcz() variable and can be changed by the set_boundaries function. If there is no limiter, the boundary condition is periodic.

Parameters

interpolation_method	Several interpolation methods are available: dg uses the native dG interpolation scheme given by the grid, nearest searches for the nearest point and copies its value, linear searches for the two (in 2d four, etc.) closest points and linearly interpolates their values, cubic searches for the four (in 2d 16, etc) closest points and interpolates a cubic polynomial
benchmark	If true write construction timings to std::cout

◆ Fieldaligned() [9/9]

template<class ProductGeometry , class IMatrix , class container >

template<class Limiter >

dg::geo::Fieldaligned< ProductGeometry, IMatrix, container >::Fieldaligned	(	const dg::geo::CylindricalVectorLvl1 &	vec,
		const ProductGeometry &	grid,
		dg::bc	bcx = `dg::NEU`,
		dg::bc	bcy = `dg::NEU`,
		Limiter	limit = `FullLimiter()`,
		double	eps = `1e-5`,
		unsigned	mx = `10`,
		unsigned	my = `10`,
		double	deltaPhi = `-1`,
		std::string	interpolation_method = `"dg"`,
		bool	benchmark = `true`
	)

Construct from a vector field and a grid.

Template Parameters

Limiter Class that can be evaluated on a 2d grid, returns 1 if there is a limiter and 0 if there isn't. If a field line crosses the limiter in the plane \( \phi=0\) then the limiter boundary conditions apply.

Parameters

vec	The vector field to integrate. Note that you can control how the boundary conditions are represented by changing vec outside the grid domain using e.g. the `periodify` function.
grid	The grid on which to integrate fieldlines.
bcx	This parameter is passed on to `dg::create::interpolation(const thrust::host_vector<real_type>&,const thrust::host_vector<real_type>&,const aRealTopology2d<real_type>&,dg::bc,dg::bc,std::string)` (see there for more details) function and deterimens what happens when the endpoint of the fieldline integration leaves the domain boundaries of `grid`. Note that `bcx` and `grid.bcx()` have to be either both periodic or both not periodic.
bcy	analogous to `bcx`, applies to y direction
limit	Instance of the limiter class (Note that if `grid.bcz()==dg::PER` this parameter is ignored, Default is a limiter everywhere)
eps	Desired accuracy of the fieldline integrator
mx	refinement factor in X of the fine grid relative to grid (Set to 1, if the x-component of `vec` vanishes, else as high as possible, 12 is a good start) If the projection method (parsed from `interpolation_method`) is not "dg" then `mx` must be a multiple of `nx`
my	analogous to `mx`, applies to y direction
deltaPhi	The angular distance that the fieldline-integrator will integrate. Per default this is the distance between planes, which is chosen automatically if you set it <=0, i.e. if deltaPhi <=0 then it will be overwritten to deltaPhi = grid.hz(). Sometimes however, you may want to set it to a different value from `grid.hz()` for example for 2d problems or for a staggered grid.

Note: deltaPhi influences the interpolation matrices and the parallel modulation in the evaluate() member function.; If there is a limiter, the boundary condition on the first/last plane is set by the grid.bcz() variable and can be changed by the set_boundaries function. If there is no limiter, the boundary condition is periodic.

Parameters

interpolation_method parsed according to

interpolation_method	interpolation	projection
"dg"	"dg"	"dg"
"linear"	"linear"	"dg"
"cubic"	"cubic"	"dg"
"nearest"	"nearest"	"dg"
"linear-nearest" (##)	"linear"	"nearest"
"cubic-nearest"	"cubic"	"nearest"
"nearest-nearest"	"nearest"	"nearest"
"dg-linear"	"dg"	"linear"
"linear-linear"	"linear"	"linear"
"cubic-linear"	"cubic"	"linear"
"nearest-linear"	"nearest"	"linear"

(##) Use "linear-nearest" if in doubt. The table yields one parameter passed to create::interpolation (from the given grid to the fine grid) and one parameter to create::projection (from the fine grid to the given grid)

Parameters

benchmark	If true write construction timings to std::cout
eps	Desired accuracy of the fieldline integrator
mx	refinement factor in X of the fine grid relative to grid (Set to 1, if the x-component of `vec` vanishes, else as high as possible, 10 is a good start)
my	analogous to `mx`, applies to y direction
deltaPhi	The angular distance that the fieldline-integrator will integrate. Per default this is the distance between planes, which is chosen automatically if you set it <=0, i.e. if deltaPhi <=0 then it will be overwritten to deltaPhi = grid.hz(). Sometimes however, you may want to set it to a different value from `grid.hz()` for example for 2d problems or for a staggered grid.

Note: deltaPhi influences the interpolation matrices and the parallel modulation in the evaluate() member function.; If there is a limiter, the boundary condition on the first/last plane is set by the grid.bcz() variable and can be changed by the set_boundaries function. If there is no limiter, the boundary condition is periodic.

Parameters

interpolation_method	Several interpolation methods are available: dg uses the native dG interpolation scheme given by the grid, nearest searches for the nearest point and copies its value, linear searches for the two (in 2d four, etc.) closest points and linearly interpolates their values, cubic searches for the four (in 2d 16, etc) closest points and interpolates a cubic polynomial
benchmark	If true write construction timings to std::cout

Member Function Documentation

◆ bbm() [1/3]

template<class ProductGeometry , class IMatrix , class container >

const container & dg::geo::Fieldaligned< ProductGeometry, IMatrix, container >::bbm ( ) const

inline

Mask minus, 1 if fieldline intersects wall in minus direction but not in plus direction, 0 else.

Returns: three-dimensional vector

◆ bbm() [2/3]

template<class ProductGeometry , class IMatrix , class container >

const container & dg::geo::Fieldaligned< ProductGeometry, IMatrix, container >::bbm ( ) const

inline

Mask minus, 1 if fieldline intersects wall in minus direction but not in plus direction, 0 else.

Returns: three-dimensional vector

◆ bbm() [3/3]

template<class ProductGeometry , class IMatrix , class container >

const container & dg::geo::Fieldaligned< ProductGeometry, IMatrix, container >::bbm ( ) const

inline

Mask minus, 1 if fieldline intersects wall in minus direction but not in plus direction, 0 else.

Returns: three-dimensional vector

◆ bbo() [1/3]

template<class ProductGeometry , class IMatrix , class container >

const container & dg::geo::Fieldaligned< ProductGeometry, IMatrix, container >::bbo ( ) const

inline

Mask both, 1 if fieldline intersects wall in plus direction and in minus direction, 0 else.

Returns: three-dimensional vector

◆ bbo() [2/3]

template<class ProductGeometry , class IMatrix , class container >

const container & dg::geo::Fieldaligned< ProductGeometry, IMatrix, container >::bbo ( ) const

inline

Mask both, 1 if fieldline intersects wall in plus direction and in minus direction, 0 else.

Returns: three-dimensional vector

◆ bbo() [3/3]

template<class ProductGeometry , class IMatrix , class container >

const container & dg::geo::Fieldaligned< ProductGeometry, IMatrix, container >::bbo ( ) const

inline

Mask both, 1 if fieldline intersects wall in plus direction and in minus direction, 0 else.

Returns: three-dimensional vector

◆ bbp() [1/3]

template<class ProductGeometry , class IMatrix , class container >

const container & dg::geo::Fieldaligned< ProductGeometry, IMatrix, container >::bbp ( ) const

inline

Mask plus, 1 if fieldline intersects wall in plus direction but not in minus direction, 0 else.

Returns: three-dimensional vector

◆ bbp() [2/3]

template<class ProductGeometry , class IMatrix , class container >

const container & dg::geo::Fieldaligned< ProductGeometry, IMatrix, container >::bbp ( ) const

inline

Mask plus, 1 if fieldline intersects wall in plus direction but not in minus direction, 0 else.

Returns: three-dimensional vector

◆ bbp() [3/3]

template<class ProductGeometry , class IMatrix , class container >

const container & dg::geo::Fieldaligned< ProductGeometry, IMatrix, container >::bbp ( ) const

inline

Mask plus, 1 if fieldline intersects wall in plus direction but not in minus direction, 0 else.

Returns: three-dimensional vector

◆ bcx() [1/3]

template<class ProductGeometry , class IMatrix , class container >

dg::bc dg::geo::Fieldaligned< ProductGeometry, IMatrix, container >::bcx ( ) const

inline

◆ bcx() [2/3]

template<class ProductGeometry , class IMatrix , class container >

dg::bc dg::geo::Fieldaligned< ProductGeometry, IMatrix, container >::bcx ( ) const

inline

◆ bcx() [3/3]

template<class ProductGeometry , class IMatrix , class container >

dg::bc dg::geo::Fieldaligned< ProductGeometry, IMatrix, container >::bcx ( ) const

inline

◆ bcy() [1/3]

template<class ProductGeometry , class IMatrix , class container >

dg::bc dg::geo::Fieldaligned< ProductGeometry, IMatrix, container >::bcy ( ) const

inline

◆ bcy() [2/3]

template<class ProductGeometry , class IMatrix , class container >

dg::bc dg::geo::Fieldaligned< ProductGeometry, IMatrix, container >::bcy ( ) const

inline

◆ bcy() [3/3]

template<class ProductGeometry , class IMatrix , class container >

dg::bc dg::geo::Fieldaligned< ProductGeometry, IMatrix, container >::bcy ( ) const

inline

◆ bphi() [1/3]

template<class ProductGeometry , class IMatrix , class container >

const container & dg::geo::Fieldaligned< ProductGeometry, IMatrix, container >::bphi ( ) const

inline

bphi

Returns: three-dimensional vector

◆ bphi() [2/3]

template<class ProductGeometry , class IMatrix , class container >

const container & dg::geo::Fieldaligned< ProductGeometry, IMatrix, container >::bphi ( ) const

inline

bphi

Returns: three-dimensional vector

◆ bphi() [3/3]

template<class ProductGeometry , class IMatrix , class container >

const container & dg::geo::Fieldaligned< ProductGeometry, IMatrix, container >::bphi ( ) const

inline

bphi

Returns: three-dimensional vector

◆ bphiM() [1/3]

template<class ProductGeometry , class IMatrix , class container >

const container & dg::geo::Fieldaligned< ProductGeometry, IMatrix, container >::bphiM ( ) const

inline

bphi on minus plane

Returns: three-dimensional vector

◆ bphiM() [2/3]

template<class ProductGeometry , class IMatrix , class container >

const container & dg::geo::Fieldaligned< ProductGeometry, IMatrix, container >::bphiM ( ) const

inline

bphi on minus plane

Returns: three-dimensional vector

◆ bphiM() [3/3]

template<class ProductGeometry , class IMatrix , class container >

const container & dg::geo::Fieldaligned< ProductGeometry, IMatrix, container >::bphiM ( ) const

inline

bphi on minus plane

Returns: three-dimensional vector

◆ bphiP() [1/3]

template<class ProductGeometry , class IMatrix , class container >

const container & dg::geo::Fieldaligned< ProductGeometry, IMatrix, container >::bphiP ( ) const

inline

bphi on plus plane

Returns: three-dimensional vector

◆ bphiP() [2/3]

template<class ProductGeometry , class IMatrix , class container >

const container & dg::geo::Fieldaligned< ProductGeometry, IMatrix, container >::bphiP ( ) const

inline

bphi on plus plane

Returns: three-dimensional vector

◆ bphiP() [3/3]

template<class ProductGeometry , class IMatrix , class container >

const container & dg::geo::Fieldaligned< ProductGeometry, IMatrix, container >::bphiP ( ) const

inline

bphi on plus plane

Returns: three-dimensional vector

◆ construct() [1/3]

template<class ProductGeometry , class IMatrix , class container >

template<class ... Params>

void dg::geo::Fieldaligned< ProductGeometry, IMatrix, container >::construct ( Params &&... ps )

inline

Perfect forward parameters to one of the constructors.

Template Parameters

Params deduced by the compiler

Parameters

ps	parameters forwarded to constructors

◆ construct() [2/3]

template<class ProductGeometry , class IMatrix , class container >

template<class ... Params>

void dg::geo::Fieldaligned< ProductGeometry, IMatrix, container >::construct ( Params &&... ps )

inline

Perfect forward parameters to one of the constructors.

Template Parameters

Params deduced by the compiler

Parameters

ps	parameters forwarded to constructors

◆ construct() [3/3]

template<class ProductGeometry , class IMatrix , class container >

template<class ... Params>

void dg::geo::Fieldaligned< ProductGeometry, IMatrix, container >::construct ( Params &&... ps )

inline

Perfect forward parameters to one of the constructors.

Template Parameters

Params deduced by the compiler

Parameters

ps	parameters forwarded to constructors

◆ deltaPhi() [1/3]

template<class ProductGeometry , class IMatrix , class container >

double dg::geo::Fieldaligned< ProductGeometry, IMatrix, container >::deltaPhi ( ) const

inline

◆ deltaPhi() [2/3]

template<class ProductGeometry , class IMatrix , class container >

double dg::geo::Fieldaligned< ProductGeometry, IMatrix, container >::deltaPhi ( ) const

inline

◆ deltaPhi() [3/3]

template<class ProductGeometry , class IMatrix , class container >

double dg::geo::Fieldaligned< ProductGeometry, IMatrix, container >::deltaPhi ( ) const

inline

◆ evaluate() [1/3]

template<class ProductGeometry , class IMatrix , class container >

template<class BinaryOp , class UnaryOp >

container dg::geo::Fieldaligned< ProductGeometry, IMatrix, container >::evaluate	(	BinaryOp	binary,
		UnaryOp	unary,
		unsigned	p0,
		unsigned	rounds
	)		const

Evaluate a 2d functor and transform to all planes along the fieldline

The algorithm does the equivalent of the following:

Evaluate the given BinaryOp on a 2d plane
Apply the plus and minus transformation each \( r N_z\) times where \( N_z\) is the number of planes in the global 3d grid and \( r\) is the number of rounds.
Scale the transformations with \( u ( \pm (iN_z + j)\Delta\varphi) \), where u is the given UnarayOp, i in [0..r] is the round index and j in [0. Nz] is the plane index and \(\Delta\varphi\) is the angular distance given in the constructor (can be different from the actual grid distance hz!).
Sum all transformations with the same plane index j , where the minus transformations get the inverted index \( N_z - j\).
Shift the index by \( p_0\)

Attention: This version of the algorithm is less exact but much faster than dg::geo::fieldaligned_evaluate

Template Parameters

BinaryOp	Binary Functor
UnaryOp	Unary Functor

Parameters

binary	Functor to evaluate in x-y
unary	Functor to evaluate in z

Note: unary is evaluated such that p0 corresponds to z=0, p0+1 corresponds to z=hz, p0-1 to z=-hz, ...

Parameters

p0	The index of the plane to start
rounds	The number of rounds `r` to follow a fieldline; can be zero, then the fieldlines are only followed within the current box ( no periodicity)

Attention: It is recommended to use mx>1 and my>1 when this function is used, else there might occur some unfavourable summation effects due to the repeated use of transformations especially for low perpendicular resolution.

Returns: 3d vector

◆ evaluate() [2/3]

template<class ProductGeometry , class IMatrix , class container >

template<class BinaryOp , class UnaryOp >

container dg::geo::Fieldaligned< ProductGeometry, IMatrix, container >::evaluate	(	BinaryOp	binary,
		UnaryOp	unary,
		unsigned	p0,
		unsigned	rounds
	)		const

Evaluate a 2d functor and transform to all planes along the fieldline

The algorithm does the equivalent of the following:

Evaluate the given BinaryOp on a 2d plane
Apply the plus and minus transformation each \( r N_z\) times where \( N_z\) is the number of planes in the global 3d grid and \( r\) is the number of rounds.
Scale the transformations with \( u ( \pm (iN_z + j)\Delta\varphi) \), where u is the given UnarayOp, i in [0..r] is the round index and j in [0. Nz] is the plane index and \(\Delta\varphi\) is the angular distance given in the constructor (can be different from the actual grid distance hz!).
Sum all transformations with the same plane index j , where the minus transformations get the inverted index \( N_z - j\).
Shift the index by \( p_0\)

Attention: This version of the algorithm is less exact but much faster than dg::geo::fieldaligned_evaluate

Template Parameters

BinaryOp	Binary Functor
UnaryOp	Unary Functor

Parameters

binary	Functor to evaluate in x-y
unary	Functor to evaluate in z

Note: unary is evaluated such that p0 corresponds to z=0, p0+1 corresponds to z=hz, p0-1 to z=-hz, ...

Parameters

p0	The index of the plane to start
rounds	The number of rounds `r` to follow a fieldline; can be zero, then the fieldlines are only followed within the current box ( no periodicity)

Attention: It is recommended to use mx>1 and my>1 when this function is used, else there might occur some unfavourable summation effects due to the repeated use of transformations especially for low perpendicular resolution.

Returns: 3d vector

◆ evaluate() [3/3]

template<class ProductGeometry , class IMatrix , class container >

template<class BinaryOp , class UnaryOp >

container dg::geo::Fieldaligned< ProductGeometry, IMatrix, container >::evaluate	(	BinaryOp	binary,
		UnaryOp	unary,
		unsigned	p0,
		unsigned	rounds
	)		const

Evaluate a 2d functor and transform to all planes along the fieldline

The algorithm does the equivalent of the following:

Evaluate the given BinaryOp on a 2d plane
Apply the plus and minus transformation each \( r N_z\) times where \( N_z\) is the number of planes in the global 3d grid and \( r\) is the number of rounds.
Scale the transformations with \( u ( \pm (iN_z + j)\Delta\varphi) \), where u is the given UnarayOp, i in [0..r] is the round index and j in [0. Nz] is the plane index and \(\Delta\varphi\) is the angular distance given in the constructor (can be different from the actual grid distance hz!).
Sum all transformations with the same plane index j , where the minus transformations get the inverted index \( N_z - j\).
Shift the index by \( p_0\)

Attention: This version of the algorithm is less exact but much faster than dg::geo::fieldaligned_evaluate

Template Parameters

BinaryOp	Binary Functor
UnaryOp	Unary Functor

Parameters

binary	Functor to evaluate in x-y
unary	Functor to evaluate in z

Note: unary is evaluated such that p0 corresponds to z=0, p0+1 corresponds to z=hz, p0-1 to z=-hz, ...

Parameters

p0	The index of the plane to start
rounds	The number of rounds `r` to follow a fieldline; can be zero, then the fieldlines are only followed within the current box ( no periodicity)

Attention: It is recommended to use mx>1 and my>1 when this function is used, else there might occur some unfavourable summation effects due to the repeated use of transformations especially for low perpendicular resolution.

Returns: 3d vector

◆ grid() [1/3]

template<class ProductGeometry , class IMatrix , class container >

const ProductGeometry & dg::geo::Fieldaligned< ProductGeometry, IMatrix, container >::grid ( ) const

inline

Grid used for construction.

◆ grid() [2/3]

template<class ProductGeometry , class IMatrix , class container >

const ProductGeometry & dg::geo::Fieldaligned< ProductGeometry, IMatrix, container >::grid ( ) const

inline

Grid used for construction.

◆ grid() [3/3]

template<class ProductGeometry , class IMatrix , class container >

const ProductGeometry & dg::geo::Fieldaligned< ProductGeometry, IMatrix, container >::grid ( ) const

inline

Grid used for construction.

◆ hbm() [1/3]

template<class ProductGeometry , class IMatrix , class container >

const container & dg::geo::Fieldaligned< ProductGeometry, IMatrix, container >::hbm ( ) const

inline

Distance between the planes and the boundary \( (s_{k}-s_{b}^-) \).

Returns: three-dimensional vector

◆ hbm() [2/3]

template<class ProductGeometry , class IMatrix , class container >

const container & dg::geo::Fieldaligned< ProductGeometry, IMatrix, container >::hbm ( ) const

inline

Distance between the planes and the boundary \( (s_{k}-s_{b}^-) \).

Returns: three-dimensional vector

◆ hbm() [3/3]

template<class ProductGeometry , class IMatrix , class container >

const container & dg::geo::Fieldaligned< ProductGeometry, IMatrix, container >::hbm ( ) const

inline

Distance between the planes and the boundary \( (s_{k}-s_{b}^-) \).

Returns: three-dimensional vector

◆ hbp() [1/3]

template<class ProductGeometry , class IMatrix , class container >

const container & dg::geo::Fieldaligned< ProductGeometry, IMatrix, container >::hbp ( ) const

inline

Distance between the planes \( (s_b^+-s_{k}) \).

Returns: three-dimensional vector

◆ hbp() [2/3]

template<class ProductGeometry , class IMatrix , class container >

const container & dg::geo::Fieldaligned< ProductGeometry, IMatrix, container >::hbp ( ) const

inline

Distance between the planes \( (s_b^+-s_{k}) \).

Returns: three-dimensional vector

◆ hbp() [3/3]

template<class ProductGeometry , class IMatrix , class container >

const container & dg::geo::Fieldaligned< ProductGeometry, IMatrix, container >::hbp ( ) const

inline

Distance between the planes \( (s_b^+-s_{k}) \).

Returns: three-dimensional vector

◆ integrate_between_coarse_grid() [1/3]

template<class ProductGeometry , class IMatrix , class container >

void dg::geo::Fieldaligned< ProductGeometry, IMatrix, container >::integrate_between_coarse_grid	(	const ProductGeometry &	grid_coarse,
		const container &	coarse,
		container &	out
	)

Integrate a 2d function on the fine grid.

\[ \frac{1}{\Delta\varphi} \int_{-\Delta\varphi}^{\Delta\varphi}d \varphi w(\varphi) f(R(\varphi), Z(\varphi) \]

Parameters

grid_coarse	The coarse grid (`coarse_grid.Nz()` must integer divide `Nz` from input grid). The x and y dimensions must be equal to the input grid.
coarse	the 2d input vector
out	the integral (2d vector, may alias coarse)

◆ integrate_between_coarse_grid() [2/3]

template<class ProductGeometry , class IMatrix , class container >

void dg::geo::Fieldaligned< ProductGeometry, IMatrix, container >::integrate_between_coarse_grid	(	const ProductGeometry &	grid_coarse,
		const container &	coarse,
		container &	out
	)

Integrate a 2d function on the fine grid.

\[ \frac{1}{\Delta\varphi} \int_{-\Delta\varphi}^{\Delta\varphi}d \varphi w(\varphi) f(R(\varphi), Z(\varphi) \]

Parameters

grid_coarse	The coarse grid (`coarse_grid.Nz()` must integer divide `Nz` from input grid). The x and y dimensions must be equal to the input grid.
coarse	the 2d input vector
out	the integral (2d vector)

◆ integrate_between_coarse_grid() [3/3]

template<class ProductGeometry , class IMatrix , class container >

void dg::geo::Fieldaligned< ProductGeometry, IMatrix, container >::integrate_between_coarse_grid	(	const ProductGeometry &	grid_coarse,
		const container &	coarse,
		container &	out
	)

Integrate a 2d function on the fine grid.

\[ \frac{1}{\Delta\varphi} \int_{-\Delta\varphi}^{\Delta\varphi}d \varphi w(\varphi) f(R(\varphi), Z(\varphi) \]

Parameters

grid_coarse	The coarse grid (`coarse_grid.Nz()` must integer divide `Nz` from input grid). The x and y dimensions must be equal to the input grid.
coarse	the 2d input vector
out	the integral (2d vector)

◆ interpolate_from_coarse_grid() [1/3]

template<class ProductGeometry , class IMatrix , class container >

container dg::geo::Fieldaligned< ProductGeometry, IMatrix, container >::interpolate_from_coarse_grid	(	const ProductGeometry &	grid_coarse,
		const container &	coarse
	)

Interpolate along fieldlines from a coarse to a fine grid in phi.

In this function we assume that the Fieldaligned object lives on the fine grid and we now want to interpolate values from a vector living on a coarse grid along the fieldlines onto the fine grid. Here, coarse and fine are with respect to the phi direction. The perpendicular directions need to have the same resolution in both input and output, i.e. there is no interpolation in those directions.

Parameters

grid_coarse	The coarse grid (`coarse_grid.Nz()` must integer divide `Nz` from input grid) The x and y dimensions must be equal
coarse	the coarse input vector

Returns: the input interpolated onto the grid given in the constructor

Note: the interpolation weights are taken in the phi distance not the s-distance, which makes the interpolation linear in phi

◆ interpolate_from_coarse_grid() [2/3]

template<class ProductGeometry , class IMatrix , class container >

container dg::geo::Fieldaligned< ProductGeometry, IMatrix, container >::interpolate_from_coarse_grid	(	const ProductGeometry &	grid_coarse,
		const container &	coarse
	)

Interpolate along fieldlines from a coarse to a fine grid in phi.

In this function we assume that the Fieldaligned object lives on the fine grid and we now want to interpolate values from a vector living on a coarse grid along the fieldlines onto the fine grid. Here, coarse and fine are with respect to the phi direction. The perpendicular directions need to have the same resolution in both input and output, i.e. there is no interpolation in those directions.

Parameters

grid_coarse	The coarse grid (`coarse_grid.Nz()` must integer divide `Nz` from input grid) The x and y dimensions must be equal
coarse	the coarse input vector

Returns: the input interpolated onto the grid given in the constructor

Note: the interpolation weights are taken in the phi distance not the s-distance, which makes the interpolation linear in phi

◆ interpolate_from_coarse_grid() [3/3]

template<class ProductGeometry , class IMatrix , class container >

container dg::geo::Fieldaligned< ProductGeometry, IMatrix, container >::interpolate_from_coarse_grid	(	const ProductGeometry &	grid_coarse,
		const container &	coarse
	)

Interpolate along fieldlines from a coarse to a fine grid in phi.

In this function we assume that the Fieldaligned object lives on the fine grid and we now want to interpolate values from a vector living on a coarse grid along the fieldlines onto the fine grid. Here, coarse and fine are with respect to the phi direction. The perpendicular directions need to have the same resolution in both input and output, i.e. there is no interpolation in those directions.

Parameters

grid_coarse	The coarse grid (`coarse_grid.Nz()` must integer divide `Nz` from input grid) The x and y dimensions must be equal
coarse	the coarse input vector

Returns: the input interpolated onto the grid given in the constructor

Note: the interpolation weights are taken in the phi distance not the s-distance, which makes the interpolation linear in phi

◆ method() [1/3]

template<class ProductGeometry , class IMatrix , class container >

std::string dg::geo::Fieldaligned< ProductGeometry, IMatrix, container >::method ( ) const

inline

Return the interpolation_method string given in the constructor.

◆ method() [2/3]

template<class ProductGeometry , class IMatrix , class container >

std::string dg::geo::Fieldaligned< ProductGeometry, IMatrix, container >::method ( ) const

inline

◆ method() [3/3]

template<class ProductGeometry , class IMatrix , class container >

std::string dg::geo::Fieldaligned< ProductGeometry, IMatrix, container >::method ( ) const

inline

◆ operator()() [1/3]

template<class ProductGeometry , class IMatrix , class container >

void dg::geo::Fieldaligned< ProductGeometry, IMatrix, container >::operator()	(	enum whichMatrix	which,
		const container &	in,
		container &	out
	)

Apply the interpolation to three-dimensional vectors.

computes \( y = 1^\pm \otimes \mathcal T x\)

Parameters

which	specify what interpolation should be applied
in	input
out	output may not equal input

◆ operator()() [2/3]

template<class ProductGeometry , class IMatrix , class container >

void dg::geo::Fieldaligned< ProductGeometry, IMatrix, container >::operator()	(	enum whichMatrix	which,
		const container &	in,
		container &	out
	)

Apply the interpolation to three-dimensional vectors.

computes \( y = 1^\pm \otimes \mathcal T x\)

Parameters

which	specify what interpolation should be applied
in	input
out	output may not equal input

◆ operator()() [3/3]

template<class ProductGeometry , class IMatrix , class container >

void dg::geo::Fieldaligned< ProductGeometry, IMatrix, container >::operator()	(	enum whichMatrix	which,
		const container &	in,
		container &	out
	)

Apply the interpolation to three-dimensional vectors.

computes \( y = 1^\pm \otimes \mathcal T x\)

Parameters

which	specify what interpolation should be applied
in	input
out	output may not equal input

◆ set_boundaries() [1/9]

template<class ProductGeometry , class IMatrix , class container >

void dg::geo::Fieldaligned< ProductGeometry, IMatrix, container >::set_boundaries	(	dg::bc	bcz,
		const container &	global,
		double	scal_left,
		double	scal_right
	)

inline

Set boundary conditions in the limiter region.

if Dirichlet boundaries are used the left value is the left function value, if Neumann boundaries are used the left value is the left derivative value

Parameters

bcz	boundary condition
global	3D vector containing boundary values
scal_left	left scaling factor
scal_right	right scaling factor

◆ set_boundaries() [2/9]

template<class ProductGeometry , class IMatrix , class container >

void dg::geo::Fieldaligned< ProductGeometry, IMatrix, container >::set_boundaries	(	dg::bc	bcz,
		const container &	global,
		double	scal_left,
		double	scal_right
	)

inline

Set boundary conditions in the limiter region.

if Dirichlet boundaries are used the left value is the left function value, if Neumann boundaries are used the left value is the left derivative value

Parameters

bcz	boundary condition
global	3D vector containing boundary values
scal_left	left scaling factor
scal_right	right scaling factor

◆ set_boundaries() [3/9]

template<class ProductGeometry , class IMatrix , class container >

void dg::geo::Fieldaligned< ProductGeometry, IMatrix, container >::set_boundaries	(	dg::bc	bcz,
		const container &	global,
		double	scal_left,
		double	scal_right
	)

inline

Set boundary conditions in the limiter region.

if Dirichlet boundaries are used the left value is the left function value, if Neumann boundaries are used the left value is the left derivative value

Parameters

bcz	boundary condition
global	3D vector containing boundary values
scal_left	left scaling factor
scal_right	right scaling factor

◆ set_boundaries() [4/9]

template<class ProductGeometry , class IMatrix , class container >

void dg::geo::Fieldaligned< ProductGeometry, IMatrix, container >::set_boundaries	(	dg::bc	bcz,
		const container &	left,
		const container &	right
	)

inline

Set boundary conditions in the limiter region.

if Dirichlet boundaries are used the left value is the left function value, if Neumann boundaries are used the left value is the left derivative value

Parameters

bcz	boundary condition
left	spatially variable left boundary value (2d size)
right	spatially variable right boundary value (2d size)

◆ set_boundaries() [5/9]

template<class ProductGeometry , class IMatrix , class container >

void dg::geo::Fieldaligned< ProductGeometry, IMatrix, container >::set_boundaries	(	dg::bc	bcz,
		const container &	left,
		const container &	right
	)

inline

Set boundary conditions in the limiter region.

if Dirichlet boundaries are used the left value is the left function value, if Neumann boundaries are used the left value is the left derivative value

Parameters

bcz	boundary condition
left	spatially variable left boundary value (2d size)
right	spatially variable right boundary value (2d size)

◆ set_boundaries() [6/9]

template<class ProductGeometry , class IMatrix , class container >

void dg::geo::Fieldaligned< ProductGeometry, IMatrix, container >::set_boundaries	(	dg::bc	bcz,
		const container &	left,
		const container &	right
	)

inline

Set boundary conditions in the limiter region.

if Dirichlet boundaries are used the left value is the left function value, if Neumann boundaries are used the left value is the left derivative value

Parameters

bcz	boundary condition
left	spatially variable left boundary value (2d size)
right	spatially variable right boundary value (2d size)

◆ set_boundaries() [7/9]

template<class ProductGeometry , class IMatrix , class container >

void dg::geo::Fieldaligned< ProductGeometry, IMatrix, container >::set_boundaries	(	dg::bc	bcz,
		double	left,
		double	right
	)

inline

Set boundary conditions in the limiter region.

if Dirichlet boundaries are used the left value is the left function value, if Neumann boundaries are used the left value is the left derivative value

Parameters

bcz	boundary condition
left	constant left boundary value
right	constant right boundary value

◆ set_boundaries() [8/9]

template<class ProductGeometry , class IMatrix , class container >

void dg::geo::Fieldaligned< ProductGeometry, IMatrix, container >::set_boundaries	(	dg::bc	bcz,
		double	left,
		double	right
	)

inline

Set boundary conditions in the limiter region.

if Dirichlet boundaries are used the left value is the left function value, if Neumann boundaries are used the left value is the left derivative value

Parameters

bcz	boundary condition
left	constant left boundary value
right	constant right boundary value

◆ set_boundaries() [9/9]

template<class ProductGeometry , class IMatrix , class container >

void dg::geo::Fieldaligned< ProductGeometry, IMatrix, container >::set_boundaries	(	dg::bc	bcz,
		double	left,
		double	right
	)

inline

Set boundary conditions in the limiter region.

if Dirichlet boundaries are used the left value is the left function value, if Neumann boundaries are used the left value is the left derivative value

Parameters

bcz	boundary condition
left	constant left boundary value
right	constant right boundary value

◆ sqrtG() [1/3]

template<class ProductGeometry , class IMatrix , class container >

const container & dg::geo::Fieldaligned< ProductGeometry, IMatrix, container >::sqrtG ( ) const

inline

Volume form (including weights) \( \sqrt{G}_{k} \).

Returns: three-dimensional vector

◆ sqrtG() [2/3]

template<class ProductGeometry , class IMatrix , class container >

const container & dg::geo::Fieldaligned< ProductGeometry, IMatrix, container >::sqrtG ( ) const

inline

Volume form (including weights) \( \sqrt{G}_{k} \).

Returns: three-dimensional vector

◆ sqrtG() [3/3]

template<class ProductGeometry , class IMatrix , class container >

const container & dg::geo::Fieldaligned< ProductGeometry, IMatrix, container >::sqrtG ( ) const

inline

Volume form (including weights) \( \sqrt{G}_{k} \).

Returns: three-dimensional vector

◆ sqrtGm() [1/3]

template<class ProductGeometry , class IMatrix , class container >

const container & dg::geo::Fieldaligned< ProductGeometry, IMatrix, container >::sqrtGm ( ) const

inline

Volume form on minus plane (including weights) \( \sqrt{G}_{k-1} \).

Returns: three-dimensional vector

◆ sqrtGm() [2/3]

template<class ProductGeometry , class IMatrix , class container >

const container & dg::geo::Fieldaligned< ProductGeometry, IMatrix, container >::sqrtGm ( ) const

inline

Volume form on minus plane (including weights) \( \sqrt{G}_{k-1} \).

Returns: three-dimensional vector

◆ sqrtGm() [3/3]

template<class ProductGeometry , class IMatrix , class container >

const container & dg::geo::Fieldaligned< ProductGeometry, IMatrix, container >::sqrtGm ( ) const

inline

Volume form on minus plane (including weights) \( \sqrt{G}_{k-1} \).

Returns: three-dimensional vector

◆ sqrtGp() [1/3]

template<class ProductGeometry , class IMatrix , class container >

const container & dg::geo::Fieldaligned< ProductGeometry, IMatrix, container >::sqrtGp ( ) const

inline

Volume form on plus plane (including weights) \( \sqrt{G}_{k+1} \).

Returns: three-dimensional vector

◆ sqrtGp() [2/3]

template<class ProductGeometry , class IMatrix , class container >

const container & dg::geo::Fieldaligned< ProductGeometry, IMatrix, container >::sqrtGp ( ) const

inline

Volume form on plus plane (including weights) \( \sqrt{G}_{k+1} \).

Returns: three-dimensional vector

◆ sqrtGp() [3/3]

template<class ProductGeometry , class IMatrix , class container >

const container & dg::geo::Fieldaligned< ProductGeometry, IMatrix, container >::sqrtGp ( ) const

inline

Volume form on plus plane (including weights) \( \sqrt{G}_{k+1} \).

Returns: three-dimensional vector

The documentation for this struct was generated from the following files:

Public Member Functions

Detailed Description

Constructor & Destructor Documentation

◆ Fieldaligned() [1/9]

◆ Fieldaligned() [2/9]

◆ Fieldaligned() [3/9]

◆ Fieldaligned() [4/9]

◆ Fieldaligned() [5/9]

◆ Fieldaligned() [6/9]

◆ Fieldaligned() [7/9]

◆ Fieldaligned() [8/9]

◆ Fieldaligned() [9/9]

Member Function Documentation

◆ bbm() [1/3]

◆ bbm() [2/3]

◆ bbm() [3/3]

◆ bbo() [1/3]

◆ bbo() [2/3]

◆ bbo() [3/3]

◆ bbp() [1/3]

◆ bbp() [2/3]

◆ bbp() [3/3]

◆ bcx() [1/3]

◆ bcx() [2/3]

◆ bcx() [3/3]

◆ bcy() [1/3]

◆ bcy() [2/3]

◆ bcy() [3/3]

◆ bphi() [1/3]

◆ bphi() [2/3]

◆ bphi() [3/3]

◆ bphiM() [1/3]

◆ bphiM() [2/3]

◆ bphiM() [3/3]

◆ bphiP() [1/3]

◆ bphiP() [2/3]

◆ bphiP() [3/3]

◆ construct() [1/3]

◆ construct() [2/3]

◆ construct() [3/3]

◆ deltaPhi() [1/3]

◆ deltaPhi() [2/3]

◆ deltaPhi() [3/3]

◆ evaluate() [1/3]

◆ evaluate() [2/3]

◆ evaluate() [3/3]

◆ grid() [1/3]

◆ grid() [2/3]

◆ grid() [3/3]

◆ hbm() [1/3]

◆ hbm() [2/3]

◆ hbm() [3/3]

◆ hbp() [1/3]

◆ hbp() [2/3]

◆ hbp() [3/3]

◆ integrate_between_coarse_grid() [1/3]

◆ integrate_between_coarse_grid() [2/3]

◆ integrate_between_coarse_grid() [3/3]

◆ interpolate_from_coarse_grid() [1/3]

◆ interpolate_from_coarse_grid() [2/3]

◆ interpolate_from_coarse_grid() [3/3]

◆ method() [1/3]

◆ method() [2/3]

◆ method() [3/3]

◆ operator()() [1/3]

◆ operator()() [2/3]

◆ operator()() [3/3]

◆ set_boundaries() [1/9]

◆ set_boundaries() [2/9]

◆ set_boundaries() [3/9]

◆ set_boundaries() [4/9]

◆ set_boundaries() [5/9]

◆ set_boundaries() [6/9]

◆ set_boundaries() [7/9]

◆ set_boundaries() [8/9]

◆ set_boundaries() [9/9]

◆ sqrtG() [1/3]

◆ sqrtG() [2/3]

◆ sqrtG() [3/3]

◆ sqrtGm() [1/3]