dg::geo::Hector< IMatrix, Matrix, container > Struct Template Reference

The High PrEcision Conformal grid generaTOR. More...

Inheritance diagram for dg::geo::Hector< IMatrix, Matrix, container >:

Public Member Functions
	Hector (const CylindricalFunctorsLvl2 &psi, double psi0, double psi1, double X0, double Y0, unsigned n=13, unsigned Nx=2, unsigned Ny=10, double eps_u=1e-10, bool verbose=false)
	Construct a conformal grid.
	Hector (const CylindricalFunctorsLvl2 &psi, const CylindricalFunctorsLvl1 &chi, double psi0, double psi1, double X0, double Y0, unsigned n=13, unsigned Nx=2, unsigned Ny=10, double eps_u=1e-10, bool verbose=false)
	Construct an orthogonal grid with adaption.
	Hector (const CylindricalFunctorsLvl2 &psi, const CylindricalSymmTensorLvl1 &chi, double psi0, double psi1, double X0, double Y0, unsigned n=13, unsigned Nx=2, unsigned Ny=10, double eps_u=1e-10, bool verbose=false)
	Construct a curvilinear grid with monitor metric.
const dg::geo::CurvilinearGrid2d &	internal_grid () const
	Return the internally used orthogonal grid.
virtual Hector *	clone () const override final
	Abstract clone method that returns a copy on the heap.
bool	isConformal () const
Public Member Functions inherited from dg::geo::aRealGenerator2d< real_type >
real_type	width () const
	length in \( \zeta\) of the computational space
real_type	height () const
	length in \( \eta\) of the computational space
bool	isOrthogonal () const
	sparsity pattern for metric
void	generate (const thrust::host_vector< real_type > &zeta1d, const thrust::host_vector< real_type > &eta1d, thrust::host_vector< real_type > &x, thrust::host_vector< real_type > &y, thrust::host_vector< real_type > &zetaX, thrust::host_vector< real_type > &zetaY, thrust::host_vector< real_type > &etaX, thrust::host_vector< real_type > &etaY) const
	Generate grid points and elements of the Jacobian.
virtual	~aRealGenerator2d ()

Additional Inherited Members
Protected Member Functions inherited from dg::geo::aRealGenerator2d< real_type >
	aRealGenerator2d ()
	empty
	aRealGenerator2d (const aRealGenerator2d &)
	empty
aRealGenerator2d &	operator= (const aRealGenerator2d &)
	return *this

Detailed Description

template<class IMatrix = dg::IHMatrix, class Matrix = dg::HMatrix, class container = dg::HVec>
struct dg::geo::Hector< IMatrix, Matrix, container >

The High PrEcision Conformal grid generaTOR.

Note

implements the algorithm described in M. Wiesenberger, M. Held, L. Einkemmer Streamline integration as a method for two-dimensional elliptic grid generation Journal of Computational Physics 340, 435-450 (2017)

        unsigned nGrid = js["grid"]["generator"]["initial"]["n"].asUInt();
        unsigned NxGrid = js["grid"]["generator"]["initial"]["Nx"].asUInt();
        unsigned NyGrid = js["grid"]["generator"]["initial"]["Ny"].asUInt();
        double epsHector = js["grid"]["generator"]["eps"].asDouble();
        if( mode == 0)
        {
            std::cout << " ... of type conformal ...\n";
            generator = std::make_unique< dg::geo::Hector<dg::IDMatrix,
                      dg::DMatrix, dg::DVec>>( mag.get_psip(), psi_0, psi_1,
                              mag.R0(), 0., nGrid, NxGrid, NyGrid, epsHector,
                              true);
        }
        else if( mode == 1)
        {
            std::cout << " ... of type adaption ...\n";
            dg::geo::CylindricalFunctorsLvl1 nc =
                dg::geo::make_NablaPsiInvCollective( mag.get_psip());
            generator = std::make_unique< dg::geo::Hector<dg::IDMatrix,
                      dg::DMatrix, dg::DVec>>( mag.get_psip(), nc, psi_0,
                              psi_1, mag.R0(), 0., nGrid, NxGrid, NyGrid,
                              epsHector, true);
        }
        else
        {
            std::cout << " ... of type monitor metric ...\n";
            dg::geo::CylindricalSymmTensorLvl1 lc =
                dg::geo::make_LiseikinCollective( mag.get_psip(), 0.1, 0.001);
            generator = std::make_unique< dg::geo::Hector<dg::IDMatrix,
                      dg::DMatrix, dg::DVec>>( mag.get_psip(), lc, psi_0,
                              psi_1, mag.R0(), 0., nGrid, NxGrid, NyGrid,
                              epsHector, true);
        }

Template Parameters

IMatrix

The interpolation matrix type

Template Parameters

Matrix

A class for which the blas2 functions are callable in connection with the container class. The Matrix type can be one of: container: A container acts as a diagonal matrix. dg::HMatrix and dg::IHMatrix with dg::HVec or std::vector<dg::HVec> dg::DMatrix and dg::IDMatrix with dg::DVec or std::vector<dg::DVec> dg::MHMatrix with dg::MHVec or std::vector<dg::MHVec> dg::MDMatrix with dg::MDVec or std::vector<dg::MDVec> Any type that has the SelfMadeMatrixTag specified in a corresponding TensorTraits class (e.g. Elliptic). In this case only those blas2 functions that have a corresponding member function in the Matrix class (e.g. symv( const container&, container&); ) can be called. If the container is a std::vector, then the Matrix is applied to each of the elements.

Template Parameters

container

A data container class for which the blas1 functionality is overloaded. We assume that container is copyable/assignable and has a swap member function. Currently this is one of dg::HVec, dg::DVec, dg::MHVec or dg::MDVec std::vector<dg::HVec>, std::vector<dg::DVec>, std::vector<dg::MHVec> or std::vector<dg::MDVec> .

Constructor & Destructor Documentation

Hector() [1/3]

template<class IMatrix = dg::IHMatrix, class Matrix = dg::HMatrix, class container = dg::HVec>

dg::geo::Hector< IMatrix, Matrix, container >::Hector ( const CylindricalFunctorsLvl2 & psi, double psi0, double psi1, double X0, double Y0, unsigned n = 13, unsigned Nx = 2, unsigned Ny = 10, double eps_u = 1e-10, bool verbose = false )

inline

Construct a conformal grid.

Parameters

psi	\( \psi(x,y)\) the flux function and its derivatives in Cartesian coordinates (x,y)
psi0	first boundary
psi1	second boundary
X0	a point in the inside of the ring bounded by psi0 (shouldn't be the O-point)
Y0	a point in the inside of the ring bounded by psi0 (shouldn't be the O-point)
n	number of polynomials used for the internal grid
Nx	initial number of points in zeta for the internal grid
Ny	initial number of points in eta for the internal grid
eps_u	the accuracy of u
verbose	If true convergence details are printed to std::cout

Hector() [2/3]

template<class IMatrix = dg::IHMatrix, class Matrix = dg::HMatrix, class container = dg::HVec>

dg::geo::Hector< IMatrix, Matrix, container >::Hector ( const CylindricalFunctorsLvl2 & psi, const CylindricalFunctorsLvl1 & chi, double psi0, double psi1, double X0, double Y0, unsigned n = 13, unsigned Nx = 2, unsigned Ny = 10, double eps_u = 1e-10, bool verbose = false )

inline

Construct an orthogonal grid with adaption.

Parameters

psi	\( \psi(x,y)\) the flux function and its derivatives in Cartesian coordinates (x,y)
chi	\( \chi(x,y)\) the adaption function and its derivatives in Cartesian coordinates (x,y)
psi0	first boundary
psi1	second boundary
X0	a point in the inside of the ring bounded by psi0 (shouldn't be the O-point)
Y0	a point in the inside of the ring bounded by psi0 (shouldn't be the O-point)
n	number of polynomials used for the internal grid
Nx	initial number of points in zeta for the internal grid
Ny	initial number of points in eta for the internal grid
eps_u	the accuracy of u
verbose	If true convergence details are printed to std::cout

Hector() [3/3]

template<class IMatrix = dg::IHMatrix, class Matrix = dg::HMatrix, class container = dg::HVec>

dg::geo::Hector< IMatrix, Matrix, container >::Hector ( const CylindricalFunctorsLvl2 & psi, const CylindricalSymmTensorLvl1 & chi, double psi0, double psi1, double X0, double Y0, unsigned n = 13, unsigned Nx = 2, unsigned Ny = 10, double eps_u = 1e-10, bool verbose = false )

inline

Construct a curvilinear grid with monitor metric.

Parameters

psi	the flux function \( \psi(x,y)\) and its derivatives in Cartesian coordinates (x,y)
chi	the symmetric adaption tensor \(\chi(x,y)\) and its divergence in Cartesian coordinates (x,y)
psi0	first boundary
psi1	second boundary
X0	a point in the inside of the ring bounded by psi0 (shouldn't be the O-point)
Y0	a point in the inside of the ring bounded by psi0 (shouldn't be the O-point)
n	number of polynomials used for the internal grid
Nx	initial number of points in zeta for the internal grid
Ny	initial number of points in eta for the internal grid
eps_u	the accuracy of u
verbose	If true convergence details are printed to std::cout

Member Function Documentation

clone()

template<class IMatrix = dg::IHMatrix, class Matrix = dg::HMatrix, class container = dg::HVec>

virtual Hector * dg::geo::Hector< IMatrix, Matrix, container >::clone ( ) const

inlinefinaloverridevirtual

Abstract clone method that returns a copy on the heap.

Returns

a copy of *this on the heap

Implements dg::geo::aRealGenerator2d< real_type >.

internal_grid()

template<class IMatrix = dg::IHMatrix, class Matrix = dg::HMatrix, class container = dg::HVec>

const dg::geo::CurvilinearGrid2d & dg::geo::Hector< IMatrix, Matrix, container >::internal_grid ( ) const

inline

Return the internally used orthogonal grid.

Returns

orthogonal zeta, eta grid

isConformal()

template<class IMatrix = dg::IHMatrix, class Matrix = dg::HMatrix, class container = dg::HVec>

bool dg::geo::Hector< IMatrix, Matrix, container >::isConformal ( ) const

inline

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

• hector.h