LORENE
Mapping grid -> physical space (spherical coordinates)

These classes implement the mapping between the grid coordinates $(\xi, \theta', \phi')$ (described by the Mg3d class) and the physical coordinates $(r, \theta, \phi)$ [cf. More...

Topics

 Coord Arithmetics.
 ()

Classes

class  Lorene::Coord
 Active physical coordinates and mapping derivatives. More...
class  Lorene::Map_radial
 Base class for pure radial mappings. More...
class  Lorene::Map_af
 Affine radial mapping. More...
class  Lorene::Map_et
 Radial mapping of rather general form. More...
class  Lorene::Map_log
 Logarithmic radial mapping. More...

Variables

Base_vect_spher Lorene::bvect_spher
 Base class for coordinate mappings.

Detailed Description

These classes implement the mapping between the grid coordinates $(\xi, \theta', \phi')$ (described by the Mg3d class) and the physical coordinates $(r, \theta, \phi)$ [cf.

Bonazzola, Gourgoulhon & Marck, Phys. Rev. D 58 , 104020 (1998)].

The class Map and its derived classes determine the methods for partial derivatives with respect to the physical coordinates, as well as resolution of basic partial differential equations (e.g. Poisson equations).

Variable Documentation

◆ bvect_spher

Base_vect_spher Lorene::bvect_spher

Base class for coordinate mappings.

()

This class is the basic class for describing the mapping between the grid coordinates $(\xi, \theta', \phi')$ and the physical coordinates $(r, \theta, \phi)$ [cf. Bonazzola, Gourgoulhon & Marck, Phys. Rev. D 58, 104020 (1998)]. The class Map is an abstract one: it cannot be instanciated. Specific implementation of coordinate mappings will be performed by derived classes of Map.

The class Map and its derived classes determine the methods for partial derivatives with respect to the physical coordinates, as well as resolution of basic partial differential equations (e.g. Poisson equations).

The mapping is defined with respect to some ``absolute'' reference frame, whose Cartesian coordinates are denoted by (X,Y,Z). The coordinates (X, Y, Z) of center of the mapping (i.e. the point r =0) are given by the data members (ori_x,ori_y,ori_z). The Cartesian coordinate relative to the mapping (i.e. defined from $(r, \theta, \phi)$ by the usual formul\ae $x=r\sin\theta\cos\phi, \ldots$) are denoted by (x,y,z). The planes (x,y) and (X,Y) are supposed to coincide, so that the relative orientation of the mapping with respect to the absolute reference frame is described by only one angle (the data member rot_phi).

*/ class Map {

Data :

protected: / Pointer on the multi-grid Mgd3 on which this is defined
const Mg3d* mg ;

double ori_x ; ///< Absolute coordinate x of the origin double ori_y ; ///< Absolute coordinate y of the origin double ori_z ; ///< Absolute coordinate z of the origin double rot_phi ; ///< Angle between the x –axis and X –axis

/** Orthonormal vectorial basis $(\partial/\partial r,1/r\partial/\partial \theta, 1/(r\sin\theta)\partial/\partial \phi)$ associated with the coordinates $(r, \theta, \phi)$ of the mapping.

Definition at line 689 of file map.h.