Map Class Reference
[Mapping grid -> physical space (spherical coordinates)]

Base class for coordinate mappings. More...

#include <map.h>

Inheritance diagram for Map:
Map_radial Map_af Map_et Map_log

List of all members.

Public Member Functions

virtual ~Map ()
 Destructor.
virtual void sauve (FILE *) const
 Save in a file.
const Mg3d * get_mg () const
 Gives the Mg3d on which the mapping is defined.
double get_ori_x () const
 Returns the x coordinate of the origin.
double get_ori_y () const
 Returns the y coordinate of the origin.
double get_ori_z () const
 Returns the z coordinate of the origin.
double get_rot_phi () const
 Returns the angle between the x --axis and X --axis.
const Base_vect_spher & get_bvect_spher () const
 Returns the 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.
const Base_vect_cart & get_bvect_cart () const
 Returns the Cartesian basis $(\partial/\partial x,\partial/\partial y,\partial/\partial z)$ associated with the coordinates (x,y,z) of the mapping, i.e.
const Metric_flat & flat_met_spher () const
 Returns the flat metric associated with the spherical coordinates and with components expressed in the triad bvect_spher.
const Metric_flat & flat_met_cart () const
 Returns the flat metric associated with the Cartesian coordinates and with components expressed in the triad bvect_cart.
const Cmp & cmp_zero () const
 Returns the null Cmp defined on *this.
virtual const Map_af & mp_angu (int) const =0
 Returns the "angular" mapping for the outside of domain l_zone.
void convert_absolute (double xx, double yy, double zz, double &rr, double &theta, double &pphi) const
 Determines the coordinates $(r,\theta,\phi)$ corresponding to given absolute Cartesian coordinates (X,Y,Z).
virtual double val_r (int l, double xi, double theta, double pphi) const =0
 Returns the value of the radial coordinate r for a given $(\xi, \theta', \phi')$ in a given domain.
virtual void val_lx (double rr, double theta, double pphi, int &l, double &xi) const =0
 Computes the domain index l and the value of $\xi$ corresponding to a point given by its physical coordinates $(r, \theta, \phi)$.
virtual void val_lx (double rr, double theta, double pphi, const Param &par, int &l, double &xi) const =0
 Computes the domain index l and the value of $\xi$ corresponding to a point given by its physical coordinates $(r, \theta, \phi)$.
virtual bool operator== (const Map &) const =0
 Comparison operator (egality).
void set_ori (double xa0, double ya0, double za0)
 Sets a new origin.
void set_rot_phi (double phi0)
 Sets a new rotation angle.
virtual void homothetie (double lambda)=0
 Sets a new radial scale.
virtual void resize (int l, double lambda)=0
 Rescales the outer boundary of one domain.
virtual void operator= (const Map_af &)=0
 Assignment to an affine mapping.
virtual void adapt (const Cmp &ent, const Param &par, int nbr=0)=0
 Adaptation of the mapping to a given scalar field.
virtual void reevaluate (const Map *mp_prev, int nzet, Cmp &uu) const =0
 Recomputes the values of a Cmp at the collocation points after a change in the mapping.
virtual void reevaluate_symy (const Map *mp_prev, int nzet, Cmp &uu) const =0
 Recomputes the values of a Cmp at the collocation points after a change in the mapping.
virtual void reevaluate (const Map *mp_prev, int nzet, Scalar &uu) const =0
 Recomputes the values of a Scalar at the collocation points after a change in the mapping.
virtual void reevaluate_symy (const Map *mp_prev, int nzet, Scalar &uu) const =0
 Recomputes the values of a Scalar at the collocation points after a change in the mapping.
virtual void dsdxi (const Cmp &ci, Cmp &resu) const =0
 Computes $\partial/ \partial \xi$ of a Cmp .
virtual void dsdr (const Cmp &ci, Cmp &resu) const =0
 Computes $\partial/ \partial r$ of a Cmp .
virtual void srdsdt (const Cmp &ci, Cmp &resu) const =0
 Computes $1/r \partial/ \partial \theta$ of a Cmp .
virtual void srstdsdp (const Cmp &ci, Cmp &resu) const =0
 Computes $1/(r\sin\theta) \partial/ \partial \phi$ of a Cmp .
virtual void dsdxi (const Scalar &uu, Scalar &resu) const =0
 Computes $\partial/ \partial xi$ of a Scalar .
virtual void dsdr (const Scalar &uu, Scalar &resu) const =0
 Computes $\partial/ \partial r$ of a Scalar .
virtual void dsdradial (const Scalar &uu, Scalar &resu) const =0
 Computes $\partial/ \partial r$ of a Scalar if the description is affine and $\partial/ \partial \ln r$ if it is logarithmic.
virtual void srdsdt (const Scalar &uu, Scalar &resu) const =0
 Computes $1/r \partial/ \partial \theta$ of a Scalar .
virtual void srstdsdp (const Scalar &uu, Scalar &resu) const =0
 Computes $1/(r\sin\theta) \partial/ \partial \phi$ of a Scalar .
virtual void dsdt (const Scalar &uu, Scalar &resu) const =0
 Computes $\partial/ \partial \theta$ of a Scalar .
virtual void stdsdp (const Scalar &uu, Scalar &resu) const =0
 Computes $1/\sin\theta \partial/ \partial \varphi$ of a Scalar .
virtual void laplacien (const Scalar &uu, int zec_mult_r, Scalar &lap) const =0
 Computes the Laplacian of a scalar field.
virtual void laplacien (const Cmp &uu, int zec_mult_r, Cmp &lap) const =0
 Computes the Laplacian of a scalar field (Cmp version).
virtual void lapang (const Scalar &uu, Scalar &lap) const =0
 Computes the angular Laplacian of a scalar field.
virtual void primr (const Scalar &uu, Scalar &resu, bool null_infty) const =0
 Computes the radial primitive which vanishes for $r\to \infty$.
virtual void mult_r (Scalar &uu) const =0
 Multiplication by r of a Scalar , the dzpuis of uu is not changed.
virtual void mult_r (Cmp &ci) const =0
 Multiplication by r of a Cmp .
virtual void mult_r_zec (Scalar &) const =0
 Multiplication by r (in the compactified external domain only) of a Scalar.
virtual void mult_rsint (Scalar &) const =0
 Multiplication by $r\sin\theta$ of a Scalar.
virtual void div_rsint (Scalar &) const =0
 Division by $r\sin\theta$ of a Scalar.
virtual void div_r (Scalar &) const =0
 Division by r of a Scalar.
virtual void div_r_zec (Scalar &) const =0
 Division by r (in the compactified external domain only) of a Scalar.
virtual void mult_cost (Scalar &) const =0
 Multiplication by $\cos\theta$ of a Scalar.
virtual void div_cost (Scalar &) const =0
 Division by $\cos\theta$ of a Scalar.
virtual void mult_sint (Scalar &) const =0
 Multiplication by $\sin\theta$ of a Scalar.
virtual void div_sint (Scalar &) const =0
 Division by $\sin\theta$ of a Scalar.
virtual void div_tant (Scalar &) const =0
 Division by $\tan\theta$ of a Scalar.
virtual void comp_x_from_spherical (const Scalar &v_r, const Scalar &v_theta, const Scalar &v_phi, Scalar &v_x) const =0
 Computes the Cartesian x component (with respect to bvect_cart ) of a vector given by its spherical components with respect to bvect_spher .
virtual void comp_x_from_spherical (const Cmp &v_r, const Cmp &v_theta, const Cmp &v_phi, Cmp &v_x) const =0
 Cmp version
virtual void comp_y_from_spherical (const Scalar &v_r, const Scalar &v_theta, const Scalar &v_phi, Scalar &v_y) const =0
 Computes the Cartesian y component (with respect to bvect_cart ) of a vector given by its spherical components with respect to bvect_spher .
virtual void comp_y_from_spherical (const Cmp &v_r, const Cmp &v_theta, const Cmp &v_phi, Cmp &v_y) const =0
 Cmp version
virtual void comp_z_from_spherical (const Scalar &v_r, const Scalar &v_theta, Scalar &v_z) const =0
 Computes the Cartesian z component (with respect to bvect_cart ) of a vector given by its spherical components with respect to bvect_spher .
virtual void comp_z_from_spherical (const Cmp &v_r, const Cmp &v_theta, Cmp &v_z) const =0
 Cmp version
virtual void comp_r_from_cartesian (const Scalar &v_x, const Scalar &v_y, const Scalar &v_z, Scalar &v_r) const =0
 Computes the Spherical r component (with respect to bvect_spher ) of a vector given by its cartesian components with respect to bvect_cart .
virtual void comp_r_from_cartesian (const Cmp &v_x, const Cmp &v_y, const Cmp &v_z, Cmp &v_r) const =0
 Cmp version
virtual void comp_t_from_cartesian (const Scalar &v_x, const Scalar &v_y, const Scalar &v_z, Scalar &v_t) const =0
 Computes the Spherical $\theta$ component (with respect to bvect_spher ) of a vector given by its cartesian components with respect to bvect_cart .
virtual void comp_t_from_cartesian (const Cmp &v_x, const Cmp &v_y, const Cmp &v_z, Cmp &v_t) const =0
 Cmp version
virtual void comp_p_from_cartesian (const Scalar &v_x, const Scalar &v_y, Scalar &v_p) const =0
 Computes the Spherical $\phi$ component (with respect to bvect_spher ) of a vector given by its cartesian components with respect to bvect_cart .
virtual void comp_p_from_cartesian (const Cmp &v_x, const Cmp &v_y, Cmp &v_p) const =0
 Cmp version
virtual void dec_dzpuis (Scalar &) const =0
 Decreases by 1 the value of dzpuis of a Scalar and changes accordingly its values in the compactified external domain (CED).
virtual void dec2_dzpuis (Scalar &) const =0
 Decreases by 2 the value of dzpuis of a Scalar and changes accordingly its values in the compactified external domain (CED).
virtual void inc_dzpuis (Scalar &) const =0
 Increases by 1 the value of dzpuis of a Scalar and changes accordingly its values in the compactified external domain (CED).
virtual void inc2_dzpuis (Scalar &) const =0
 Increases by 2 the value of dzpuis of a Scalar and changes accordingly its values in the compactified external domain (CED).
virtual Tbl * integrale (const Cmp &) const =0
 Computes the integral over all space of a Cmp .
virtual void poisson (const Cmp &source, Param &par, Cmp &uu) const =0
 Computes the solution of a scalar Poisson equation.
virtual void poisson_tau (const Cmp &source, Param &par, Cmp &uu) const =0
 Computes the solution of a scalar Poisson equationwith a Tau method.
virtual void poisson_falloff (const Cmp &source, Param &par, Cmp &uu, int k_falloff) const =0
virtual void poisson_ylm (const Cmp &source, Param &par, Cmp &pot, int nylm, double *intvec) const =0
virtual void poisson_regular (const Cmp &source, int k_div, int nzet, double unsgam1, Param &par, Cmp &uu, Cmp &uu_regu, Cmp &uu_div, Tenseur &duu_div, Cmp &source_regu, Cmp &source_div) const =0
 Computes the solution of a scalar Poisson equation.
virtual void poisson_compact (const Cmp &source, const Cmp &aa, const Tenseur &bb, const Param &par, Cmp &psi) const =0
 Resolution of the elliptic equation $ a \Delta\psi + {\bf b} \cdot \nabla \psi = \sigma$ in the case where the stellar interior is covered by a single domain.
virtual void poisson_compact (int nzet, const Cmp &source, const Cmp &aa, const Tenseur &bb, const Param &par, Cmp &psi) const =0
 Resolution of the elliptic equation $ a \Delta\psi + {\bf b} \cdot \nabla \psi = \sigma$ in the case of a multidomain stellar interior.
virtual void poisson_angu (const Scalar &source, Param &par, Scalar &uu, double lambda=0) const =0
 Computes the solution of the generalized angular Poisson equation.
virtual Param * donne_para_poisson_vect (Param &para, int i) const =0
 Function intended to be used by Map::poisson_vect and Map::poisson_vect_oohara .
virtual void poisson_frontiere (const Cmp &source, const Valeur &limite, int raccord, int num_front, Cmp &pot, double=0., double=0.) const =0
 Computes the solution of a Poisson equation from the domain num_front+1 .
virtual void poisson_frontiere_double (const Cmp &source, const Valeur &lim_func, const Valeur &lim_der, int num_zone, Cmp &pot) const =0
virtual void poisson_interne (const Cmp &source, const Valeur &limite, Param &par, Cmp &pot) const =0
 Computes the solution of a Poisson equation in the shell, imposing a boundary condition at the surface of the star.
virtual void poisson2d (const Cmp &source_mat, const Cmp &source_quad, Param &par, Cmp &uu) const =0
 Computes the solution of a 2-D Poisson equation.
virtual void dalembert (Param &par, Scalar &fJp1, const Scalar &fJ, const Scalar &fJm1, const Scalar &source) const =0
 Performs one time-step integration of the d'Alembert scalar equation.

Public Attributes

Coord r
 r coordinate centered on the grid
Coord tet
 $\theta$ coordinate centered on the grid
Coord phi
 $\phi$ coordinate centered on the grid
Coord sint
 $\sin\theta$
Coord cost
 $\cos\theta$
Coord sinp
 $\sin\phi$
Coord cosp
 $\cos\phi$
Coord x
 x coordinate centered on the grid
Coord y
 y coordinate centered on the grid
Coord z
 z coordinate centered on the grid
Coord xa
 Absolute x coordinate.
Coord ya
 Absolute y coordinate.
Coord za
 Absolute z coordinate.

Protected Member Functions

 Map (const Mg3d &)
 Constructor from a multi-domain 3D grid.
 Map (const Map &)
 Copy constructor.
 Map (const Mg3d &, FILE *)
 Constructor from a file (see sauve(FILE* ) ).
virtual void reset_coord ()
 Resets all the member Coords.

Protected Attributes

const Mg3d * mg
 Pointer on the multi-grid Mgd3 on which this is defined.
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.
Base_vect_spher bvect_spher
 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.
Base_vect_cart bvect_cart
 Cartesian basis $(\partial/\partial x,\partial/\partial y,\partial/\partial z)$ associated with the coordinates (x,y,z) of the mapping, i.e.
Metric_flat * p_flat_met_spher
 Pointer onto the flat metric associated with the spherical coordinates and with components expressed in the triad bvect_spher.
Metric_flat * p_flat_met_cart
 Pointer onto the flat metric associated with the Cartesian coordinates and with components expressed in the triad bvect_cart.
Cmp * p_cmp_zero
 The null Cmp.
Map_af * p_mp_angu
 Pointer on the "angular" mapping.

Private Member Functions

virtual ostream & operator>> (ostream &) const =0
 Operator >>.

Friends

ostream & operator<< (ostream &, const Map &)
 Operator <<.

Detailed Description

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 $x=r\sin\theta\cos\phi, \ldots$) 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).

Definition at line 666 of file map.h.

Constructor & Destructor Documentation

Map::Map ( const Mg3d &  mgi  )  [explicit, protected]

Constructor from a multi-domain 3D grid.

Definition at line 135 of file map.C.

References p_cmp_zero, and Cmp::set_etat_zero().

Map::Map ( const Map &  mp  )  [protected]

Copy constructor.

Definition at line 153 of file map.C.

References p_cmp_zero, and Cmp::set_etat_zero().

Map::Map ( const Mg3d &  mgi,
FILE *  fd 
) [protected]

Constructor from a file (see sauve(FILE* ) ).

Definition at line 172 of file map.C.

References bvect_cart, bvect_spher, fread_be(), mg, ori_x, ori_y, ori_z, p_cmp_zero, rot_phi, Cmp::set_etat_zero(), Base_vect_spher::set_ori(), Base_vect_cart::set_rot_phi(), and Base_vect_spher::set_rot_phi().

Map::~Map (  )  [virtual]

Destructor.

Definition at line 209 of file map.C.

References p_cmp_zero, p_flat_met_cart, p_flat_met_spher, and p_mp_angu.

Member Function Documentation

virtual void Map::adapt ( const Cmp &  ent,
const Param &  par,
int  nbr = 0 
) [pure virtual]

Adaptation of the mapping to a given scalar field.

This is a virtual function: see the actual implementations in the derived classes for the meaning of the various parameters.

Implemented in Map_af, Map_et, and Map_log.

const Cmp& Map::cmp_zero (  )  const [inline]

Returns the null Cmp defined on *this.

To be used by the Tenseur class when necessary to return a null Cmp .

Definition at line 803 of file map.h.

References p_cmp_zero.

virtual void Map::comp_p_from_cartesian ( const Cmp &  v_x,
const Cmp &  v_y,
Cmp &  v_p 
) const [pure virtual]

Cmp version

Implemented in Map_radial.

virtual void Map::comp_p_from_cartesian ( const Scalar &  v_x,
const Scalar &  v_y,
Scalar &  v_p 
) const [pure virtual]

Computes the Spherical $\phi$ component (with respect to bvect_spher ) of a vector given by its cartesian components with respect to bvect_cart .

Parameters:
v_x [input] x-component of the vector
v_y [input] y-component of the vector
v_p [output] $\phi$-component of the vector

Implemented in Map_radial.

virtual void Map::comp_r_from_cartesian ( const Cmp &  v_x,
const Cmp &  v_y,
const Cmp &  v_z,
Cmp &  v_r 
) const [pure virtual]

Cmp version

Implemented in Map_radial.

virtual void Map::comp_r_from_cartesian ( const Scalar &  v_x,
const Scalar &  v_y,
const Scalar &  v_z,
Scalar &  v_r 
) const [pure virtual]

Computes the Spherical r component (with respect to bvect_spher ) of a vector given by its cartesian components with respect to bvect_cart .

Parameters:
v_x [input] x-component of the vector
v_y [input] y-component of the vector
v_z [input] z-component of the vector
v_r [output] r -component of the vector

Implemented in Map_radial.

virtual void Map::comp_t_from_cartesian ( const Cmp &  v_x,
const Cmp &  v_y,
const Cmp &  v_z,
Cmp &  v_t 
) const [pure virtual]

Cmp version

Implemented in Map_radial.

virtual void Map::comp_t_from_cartesian ( const Scalar &  v_x,
const Scalar &  v_y,
const Scalar &  v_z,
Scalar &  v_t 
) const [pure virtual]

Computes the Spherical $\theta$ component (with respect to bvect_spher ) of a vector given by its cartesian components with respect to bvect_cart .

Parameters:
v_x [input] x-component of the vector
v_y [input] y-component of the vector
v_z [input] z-component of the vector
v_t [output] $\theta$-component of the vector

Implemented in Map_radial.

virtual void Map::comp_x_from_spherical ( const Cmp &  v_r,
const Cmp &  v_theta,
const Cmp &  v_phi,
Cmp &  v_x 
) const [pure virtual]

Cmp version

Implemented in Map_radial.

virtual void Map::comp_x_from_spherical ( const Scalar &  v_r,
const Scalar &  v_theta,
const Scalar &  v_phi,
Scalar &  v_x 
) const [pure virtual]

Computes the Cartesian x component (with respect to bvect_cart ) of a vector given by its spherical components with respect to bvect_spher .

Parameters:
v_r [input] r -component of the vector
v_theta [input] $\theta$-component of the vector
v_phi [input] $\phi$-component of the vector
v_x [output] x-component of the vector

Implemented in Map_radial.

virtual void Map::comp_y_from_spherical ( const Cmp &  v_r,
const Cmp &  v_theta,
const Cmp &  v_phi,
Cmp &  v_y 
) const [pure virtual]

Cmp version

Implemented in Map_radial.

virtual void Map::comp_y_from_spherical ( const Scalar &  v_r,
const Scalar &  v_theta,
const Scalar &  v_phi,
Scalar &  v_y 
) const [pure virtual]

Computes the Cartesian y component (with respect to bvect_cart ) of a vector given by its spherical components with respect to bvect_spher .

Parameters:
v_r [input] r -component of the vector
v_theta [input] $\theta$-component of the vector
v_phi [input] $\phi$-component of the vector
v_y [output] y-component of the vector

Implemented in Map_radial.

virtual void Map::comp_z_from_spherical ( const Cmp &  v_r,
const Cmp &  v_theta,
Cmp &  v_z 
) const [pure virtual]

Cmp version

Implemented in Map_radial.

virtual void Map::comp_z_from_spherical ( const Scalar &  v_r,
const Scalar &  v_theta,
Scalar &  v_z 
) const [pure virtual]

Computes the Cartesian z component (with respect to bvect_cart ) of a vector given by its spherical components with respect to bvect_spher .

Parameters:
v_r [input] r -component of the vector
v_theta [input] $\theta$-component of the vector
v_z [output] z-component of the vector

Implemented in Map_radial.

void Map::convert_absolute ( double  xx,
double  yy,
double  zz,
double &  rr,
double &  theta,
double &  pphi 
) const

Determines the coordinates $(r,\theta,\phi)$ corresponding to given absolute Cartesian coordinates (X,Y,Z).

Parameters:
xx [input] value of the coordinate x (absolute frame)
yy [input] value of the coordinate y (absolute frame)
zz [input] value of the coordinate z (absolute frame)
rr [output] value of r
theta [output] value of $\theta$
pphi [output] value of $\phi$

Definition at line 298 of file map.C.

References ori_x, ori_y, ori_z, rot_phi, and sqrt().

virtual void Map::dalembert ( Param &  par,
Scalar &  fJp1,
const Scalar &  fJ,
const Scalar &  fJm1,
const Scalar &  source 
) const [pure virtual]

Performs one time-step integration of the d'Alembert scalar equation.

Parameters:
par [input/output] possible parameters to control the resolution of the wave equation. See the actual implementation in the derived class of Map for documentation. Note that, at least, param must contain the time step as first double parameter.
fJp1 [output] solution $f^{J+1}$ at time J+1 with boundary conditions of outgoing radiation (not exact!)
fJ [input] solution $f^J$ at time J
fJm1 [input] solution $f^{J-1}$ at time J-1
source [input] source $\sigma$ of the d'Alembert equation $\diamond u = \sigma$.

Implemented in Map_af, Map_et, and Map_log.

virtual void Map::dec2_dzpuis ( Scalar &   )  const [pure virtual]

Decreases by 2 the value of dzpuis of a Scalar and changes accordingly its values in the compactified external domain (CED).

Implemented in Map_radial.

virtual void Map::dec_dzpuis ( Scalar &   )  const [pure virtual]

Decreases by 1 the value of dzpuis of a Scalar and changes accordingly its values in the compactified external domain (CED).

Implemented in Map_radial.

virtual void Map::div_cost ( Scalar &   )  const [pure virtual]

Division by $\cos\theta$ of a Scalar.

Implemented in Map_radial.

virtual void Map::div_r ( Scalar &   )  const [pure virtual]

Division by r of a Scalar.

Implemented in Map_radial.

virtual void Map::div_r_zec ( Scalar &   )  const [pure virtual]

Division by r (in the compactified external domain only) of a Scalar.

Implemented in Map_radial.

virtual void Map::div_rsint ( Scalar &   )  const [pure virtual]

Division by $r\sin\theta$ of a Scalar.

Implemented in Map_radial.

virtual void Map::div_sint ( Scalar &   )  const [pure virtual]

Division by $\sin\theta$ of a Scalar.

Implemented in Map_radial.

virtual void Map::div_tant ( Scalar &   )  const [pure virtual]

Division by $\tan\theta$ of a Scalar.

Implemented in Map_radial.

virtual Param* Map::donne_para_poisson_vect ( Param &  para,
int  i 
) const [pure virtual]

Function intended to be used by Map::poisson_vect and Map::poisson_vect_oohara .

It constructs the sets of parameters used for each scalar Poisson equation from the one for the vectorial one.

Parameters:
para [input] : the Param used for the resolution of the vectorial Poisson equation : \ para.int() maximum number of iteration.\ para.double(0) relaxation parameter.\ para.double(1) required precision. \ para.tenseur_mod() source of the vectorial part at the previous step.\ para.cmp_mod() source of the scalar part at the previous step.
i [input] number of the scalar Poisson equation that is being solved (values from 0 to 2 for the componants of the vectorial part and 3 for the scalar one).
Returns:
the pointer on the parameter set used for solving the scalar Poisson equation labelled by i .

Implemented in Map_af, Map_et, and Map_log.

virtual void Map::dsdr ( const Scalar &  uu,
Scalar &  resu 
) const [pure virtual]

Computes $\partial/ \partial r$ of a Scalar .

Note that in the compactified external domain (CED), the dzpuis flag of the output is 2 if the input has dzpuis = 0, and is increased by 1 in other cases.

Parameters:
uu [input] field to consider
resu [output] derivative of uu

Implemented in Map_af, Map_et, and Map_log.

virtual void Map::dsdr ( const Cmp &  ci,
Cmp &  resu 
) const [pure virtual]

Computes $\partial/ \partial r$ of a Cmp .

Note that in the compactified external domain (CED), it computes $-\partial/ \partial u = r^2 \partial/ \partial r$.

Parameters:
ci [input] field to consider
resu [output] derivative of ci

Implemented in Map_af, Map_et, and Map_log.

virtual void Map::dsdradial ( const Scalar &  uu,
Scalar &  resu 
) const [pure virtual]

Computes $\partial/ \partial r$ of a Scalar if the description is affine and $\partial/ \partial \ln r$ if it is logarithmic.

Note that in the compactified external domain (CED), the dzpuis flag of the output is 2 if the input has dzpuis = 0, and is increased by 1 in other cases.

Parameters:
uu [input] field to consider
resu [output] derivative of uu

Implemented in Map_af, Map_et, and Map_log.

virtual void Map::dsdt ( const Scalar &  uu,
Scalar &  resu 
) const [pure virtual]

Computes $\partial/ \partial \theta$ of a Scalar .

Parameters:
uu [input] scalar field
resu [output] derivative of uu

Implemented in Map_af, Map_et, and Map_log.

virtual void Map::dsdxi ( const Scalar &  uu,
Scalar &  resu 
) const [pure virtual]

Computes $\partial/ \partial xi$ of a Scalar .

Note that in the compactified external domain (CED), the dzpuis flag of the output is 2 if the input has dzpuis = 0, and is increased by 1 in other cases.

Parameters:
uu [input] field to consider
resu [output] derivative of uu

Implemented in Map_af, Map_et, and Map_log.

virtual void Map::dsdxi ( const Cmp &  ci,
Cmp &  resu 
) const [pure virtual]

Computes $\partial/ \partial \xi$ of a Cmp .

Note that in the compactified external domain (CED), it computes $-\partial/ \partial u = \xi^2 \partial/ \partial \xi$.

Parameters:
ci [input] field to consider
resu [output] derivative of ci

Implemented in Map_af, Map_et, and Map_log.

const Metric_flat & Map::flat_met_cart (  )  const

Returns the flat metric associated with the Cartesian coordinates and with components expressed in the triad bvect_cart.

Definition at line 327 of file map.C.

References bvect_cart, and p_flat_met_cart.

const Metric_flat & Map::flat_met_spher (  )  const

Returns the flat metric associated with the spherical coordinates and with components expressed in the triad bvect_spher.

Definition at line 317 of file map.C.

References bvect_spher, and p_flat_met_spher.

const Base_vect_cart& Map::get_bvect_cart (  )  const [inline]

Returns the Cartesian basis $(\partial/\partial x,\partial/\partial y,\partial/\partial z)$ associated with the coordinates (x,y,z) of the mapping, i.e.

the Cartesian coordinates related to $(r, \theta, \phi)$ by means of usual formulae.

Definition at line 787 of file map.h.

References bvect_cart.

const Base_vect_spher& Map::get_bvect_spher (  )  const [inline]

Returns the 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 779 of file map.h.

References bvect_spher.

const Mg3d* Map::get_mg (  )  const [inline]

Gives the Mg3d on which the mapping is defined.

Definition at line 761 of file map.h.

References mg.

double Map::get_ori_x (  )  const [inline]

Returns the x coordinate of the origin.

Definition at line 764 of file map.h.

References ori_x.

double Map::get_ori_y (  )  const [inline]

Returns the y coordinate of the origin.

Definition at line 766 of file map.h.

References ori_y.

double Map::get_ori_z (  )  const [inline]

Returns the z coordinate of the origin.

Definition at line 768 of file map.h.

References ori_z.

double Map::get_rot_phi (  )  const [inline]

Returns the angle between the x --axis and X --axis.

Definition at line 771 of file map.h.

References rot_phi.

virtual void Map::homothetie ( double  lambda  )  [pure virtual]

Sets a new radial scale.

Parameters:
lambda [input] factor by which the value of r is to be multiplied

Implemented in Map_af, Map_et, and Map_log.

virtual void Map::inc2_dzpuis ( Scalar &   )  const [pure virtual]

Increases by 2 the value of dzpuis of a Scalar and changes accordingly its values in the compactified external domain (CED).

Implemented in Map_radial.

virtual void Map::inc_dzpuis ( Scalar &   )  const [pure virtual]

Increases by 1 the value of dzpuis of a Scalar and changes accordingly its values in the compactified external domain (CED).

Implemented in Map_radial.

virtual Tbl* Map::integrale ( const Cmp &   )  const [pure virtual]

Computes the integral over all space of a Cmp .

The computed quantity is $\int u \, r^2 \sin\theta \, dr\, d\theta \, d\phi$. The routine allocates a Tbl (size: mg->nzone ) to store the result (partial integral) in each domain and returns a pointer to it.

Implemented in Map_af, Map_et, and Map_log.

virtual void Map::lapang ( const Scalar &  uu,
Scalar &  lap 
) const [pure virtual]

Computes the angular Laplacian of a scalar field.

Parameters:
uu [input] Scalar field u (represented as a Scalar ) the Laplacian $\Delta u$ of which is to be computed
lap [output] Angular Laplacian of u (see documentation of Scalar

Implemented in Map_af, Map_et, and Map_log.

virtual void Map::laplacien ( const Cmp &  uu,
int  zec_mult_r,
Cmp &  lap 
) const [pure virtual]

Computes the Laplacian of a scalar field (Cmp version).

Implemented in Map_af, Map_et, and Map_log.

virtual void Map::laplacien ( const Scalar &  uu,
int  zec_mult_r,
Scalar &  lap 
) const [pure virtual]

Computes the Laplacian of a scalar field.

Parameters:
uu [input] Scalar field u (represented as a Scalar ) the Laplacian $\Delta u$ of which is to be computed
zec_mult_r [input] Determines the quantity computed in the compactified external domain (CED) : \ zec_mult_r = 0 : $\Delta u$ \ zec_mult_r = 2 : $r^2 \, \Delta u$ \ zec_mult_r = 4 (default) : $r^4 \, \Delta u$
lap [output] Laplacian of u

Implemented in Map_af, Map_et, and Map_log.

virtual const Map_af& Map::mp_angu ( int   )  const [pure virtual]

Returns the "angular" mapping for the outside of domain l_zone.

Valid only for the class Map_af.

Implemented in Map_af, Map_et, and Map_log.

virtual void Map::mult_cost ( Scalar &   )  const [pure virtual]

Multiplication by $\cos\theta$ of a Scalar.

Implemented in Map_radial.

virtual void Map::mult_r ( Cmp &  ci  )  const [pure virtual]

Multiplication by r of a Cmp .

In the CED, there is only a decrement of dzpuis

Implemented in Map_radial.

virtual void Map::mult_r ( Scalar &  uu  )  const [pure virtual]

Multiplication by r of a Scalar , the dzpuis of uu is not changed.

Implemented in Map_radial.

virtual void Map::mult_r_zec ( Scalar &   )  const [pure virtual]

Multiplication by r (in the compactified external domain only) of a Scalar.

Implemented in Map_radial.

virtual void Map::mult_rsint ( Scalar &   )  const [pure virtual]

Multiplication by $r\sin\theta$ of a Scalar.

Implemented in Map_radial.

virtual void Map::mult_sint ( Scalar &   )  const [pure virtual]

Multiplication by $\sin\theta$ of a Scalar.

Implemented in Map_radial.

virtual void Map::operator= ( const Map_af &   )  [pure virtual]

Assignment to an affine mapping.

Implemented in Map_radial, Map_et, and Map_log.

virtual bool Map::operator== ( const Map &   )  const [pure virtual]

Comparison operator (egality).

virtual ostream& Map::operator>> ( ostream &   )  const [private, pure virtual]

Operator >>.

Implemented in Map_af, Map_et, and Map_log.

virtual void Map::poisson ( const Cmp &  source,
Param &  par,
Cmp &  uu 
) const [pure virtual]

Computes the solution of a scalar Poisson equation.

Parameters:
source [input] source $\sigma$ of the Poisson equation $\Delta u = \sigma$.
par [input/output] possible parameters to control the resolution of the Poisson equation. See the actual implementation in the derived class of Map for documentation.
uu [input/output] solution u with the boundary condition u =0 at spatial infinity.

Implemented in Map_af, Map_et, and Map_log.

virtual void Map::poisson2d ( const Cmp &  source_mat,
const Cmp &  source_quad,
Param &  par,
Cmp &  uu 
) const [pure virtual]

Computes the solution of a 2-D Poisson equation.

The 2-D Poisson equation writes

\[ {\partial^2 u\over\partial r^2} + {1\over r} {\partial u \over \partial r} + {1\over r^2} {\partial^2 u\over\partial \theta^2} = \sigma \ . \]

Parameters:
source_mat [input] Compactly supported part of the source $\sigma$ of the 2-D Poisson equation (typically matter terms)
source_quad [input] Non-compactly supported part of the source $\sigma$ of the 2-D Poisson equation (typically quadratic terms)
par [input/output] possible parameters to control the resolution of the Poisson equation. See the actual implementation in the derived class of Map for documentation.
uu [input/output] solution u with the boundary condition u =0 at spatial infinity.

Implemented in Map_af, Map_et, and Map_log.

virtual void Map::poisson_angu ( const Scalar &  source,
Param &  par,
Scalar &  uu,
double  lambda = 0 
) const [pure virtual]

Computes the solution of the generalized angular Poisson equation.

The generalized angular Poisson equation is $\Delta_{\theta\varphi} u + \lambda u = \sigma$, where $\Delta_{\theta\varphi} u := \frac{\partial^2 u} {\partial \theta^2} + \frac{1}{\tan \theta} \frac{\partial u} {\partial \theta} +\frac{1}{\sin^2 \theta}\frac{\partial^2 u} {\partial \varphi^2}$.

Parameters:
source [input] source $\sigma$ of the equation $\Delta_{\theta\varphi} u + \lambda u = \sigma$.
par [input/output] possible parameters to control the resolution of the Poisson equation. See the actual implementation in the derived class of Map for documentation.
uu [input/output] solution u
lambda [input] coefficient $\lambda$ in the above equation (default value = 0)

Implemented in Map_af, Map_et, and Map_log.

virtual void Map::poisson_compact ( int  nzet,
const Cmp &  source,
const Cmp &  aa,
const Tenseur &  bb,
const Param &  par,
Cmp &  psi 
) const [pure virtual]

Resolution of the elliptic equation $ a \Delta\psi + {\bf b} \cdot \nabla \psi = \sigma$ in the case of a multidomain stellar interior.

Parameters:
nzet [input] number of domains covering the stellar interior
source [input] source $\sigma$ of the above equation
aa [input] factor a in the above equation
bb [input] vector b in the above equation
par [input/output] possible parameters to control the resolution of the equation. See the actual implementation in the derived class of Map for documentation.
psi [input/output] solution $\psi$ which satisfies $\psi(0)=0$.

Implemented in Map_radial.

virtual void Map::poisson_compact ( const Cmp &  source,
const Cmp &  aa,
const Tenseur &  bb,
const Param &  par,
Cmp &  psi 
) const [pure virtual]

Resolution of the elliptic equation $ a \Delta\psi + {\bf b} \cdot \nabla \psi = \sigma$ in the case where the stellar interior is covered by a single domain.

Parameters:
source [input] source $\sigma$ of the above equation
aa [input] factor a in the above equation
bb [input] vector b in the above equation
par [input/output] possible parameters to control the resolution of the equation. See the actual implementation in the derived class of Map for documentation.
psi [input/output] solution $\psi$ which satisfies $\psi(0)=0$.

Implemented in Map_radial.

virtual void Map::poisson_frontiere ( const Cmp &  source,
const Valeur &  limite,
int  raccord,
int  num_front,
Cmp &  pot,
double  = 0.,
double  = 0. 
) const [pure virtual]

Computes the solution of a Poisson equation from the domain num_front+1 .

imposing a boundary condition at the boundary between the domains num_front and num_front+1 .

Parameters:
source [input] : source of the equation.
limite [input] : limite[num_front] contains the angular function being the boudary condition.
raccord [input] : 1 for the Dirichlet problem and 2 for the Neumann one and 3 for Dirichlet-Neumann.
num_front [input] : index of the boudary at which the boundary condition has to be imposed.
pot [output] : result.
fact_dir [input] : Valeur by which we multiply the quantity we solve. (in the case of Dirichlet-Neumann boundary condition.)
fact_neu [input] : Valeur by which we multiply the radial derivative of the quantity we solve. (in the case of Dirichlet-Neumann boundary condition.)

Implemented in Map_af, Map_et, and Map_log.

virtual void Map::poisson_interne ( const Cmp &  source,
const Valeur &  limite,
Param &  par,
Cmp &  pot 
) const [pure virtual]

Computes the solution of a Poisson equation in the shell, imposing a boundary condition at the surface of the star.

Parameters:
source [input] : source of the equation.
limite [input] : limite[num_front] contains the angular function being the boudary condition.
par [input] : parameters of the computation.
pot [output] : result.

Implemented in Map_af, Map_et, and Map_log.

virtual void Map::poisson_regular ( const Cmp &  source,
int  k_div,
int  nzet,
double  unsgam1,
Param &  par,
Cmp &  uu,
Cmp &  uu_regu,
Cmp &  uu_div,
Tenseur &  duu_div,
Cmp &  source_regu,
Cmp &  source_div 
) const [pure virtual]

Computes the solution of a scalar Poisson equation.

The regularized source

Parameters:
source [input] source $\sigma$ of the Poisson equation $\Delta u = \sigma$.
k_div [input] regularization degree of the procedure
nzet [input] number of domains covering the star
unsgam1 [input] parameter $1/(\gamma-1)$ where $\gamma$ denotes the adiabatic index.
par [input/output] possible parameters to control the resolution of the Poisson equation. See the actual implementation in the derived class of Map for documentation.
uu [input/output] solution u with the boundary condition u =0 at spatial infinity.
uu_regu [output] solution of the regular part of the source.
uu_div [output] solution of the diverging part of the source.
duu_div [output] derivative of the diverging potential
source_regu [output] regularized source
source_div [output] diverging part of the source

Implemented in Map_af, Map_et, and Map_log.

virtual void Map::poisson_tau ( const Cmp &  source,
Param &  par,
Cmp &  uu 
) const [pure virtual]

Computes the solution of a scalar Poisson equationwith a Tau method.

Parameters:
source [input] source $\sigma$ of the Poisson equation $\Delta u = \sigma$.
par [input/output] possible parameters to control the resolution of the Poisson equation. See the actual implementation in the derived class of Map for documentation.
uu [input/output] solution u with the boundary condition u =0 at spatial infinity.

Implemented in Map_af, Map_et, and Map_log.

virtual void Map::primr ( const Scalar &  uu,
Scalar &  resu,
bool  null_infty 
) const [pure virtual]

Computes the radial primitive which vanishes for $r\to \infty$.

i.e. the function $ F(r,\theta,\varphi) = \int_r^\infty f(r',\theta,\varphi) \, dr' $

Parameters:
uu [input] function f (must have a dzpuis = 2)
resu [input] function F
null_infty if true (default), the primitive is null at infinity (or on the grid boundary). F is null at the center otherwise

Implemented in Map_af, Map_et, and Map_log.

virtual void Map::reevaluate ( const Map *  mp_prev,
int  nzet,
Scalar &  uu 
) const [pure virtual]

Recomputes the values of a Scalar at the collocation points after a change in the mapping.

Parameters:
mp_prev [input] Previous value of the mapping.
nzet [input] Number of domains where the computation must be done: the computation is performed for the domains of index $0\le {\tt l} \le {\tt nzet-1}$; uu is set to zero in the other domains.
uu [input/output] input : Scalar previously computed on the mapping *mp_prev ; ouput : values of (logically) the same Scalae at the grid points defined by *this.
virtual void Map::reevaluate ( const Map *  mp_prev,
int  nzet,
Cmp &  uu 
) const [pure virtual]

Recomputes the values of a Cmp at the collocation points after a change in the mapping.

Parameters:
mp_prev [input] Previous value of the mapping.
nzet [input] Number of domains where the computation must be done: the computation is performed for the domains of index $0\le {\tt l} \le {\tt nzet-1}$; uu is set to zero in the other domains.
uu [input/output] input : Cmp previously computed on the mapping *mp_prev ; ouput : values of (logically) the same Cmp at the grid points defined by *this.
virtual void Map::reevaluate_symy ( const Map *  mp_prev,
int  nzet,
Scalar &  uu 
) const [pure virtual]

Recomputes the values of a Scalar at the collocation points after a change in the mapping.

Case where the Scalar is symmetric with respect the plane y=0.

Parameters:
mp_prev [input] Previous value of the mapping.
nzet [input] Number of domains where the computation must be done: the computation is performed for the domains of index $0\le {\tt l} \le {\tt nzet-1}$; uu is set to zero in the other domains.
uu [input/output] input : Scalar previously computed on the mapping *mp_prev ; ouput : values of (logically) the same Scalar at the grid points defined by *this.
virtual void Map::reevaluate_symy ( const Map *  mp_prev,
int  nzet,
Cmp &  uu 
) const [pure virtual]

Recomputes the values of a Cmp at the collocation points after a change in the mapping.

Case where the Cmp is symmetric with respect the plane y=0.

Parameters:
mp_prev [input] Previous value of the mapping.
nzet [input] Number of domains where the computation must be done: the computation is performed for the domains of index $0\le {\tt l} \le {\tt nzet-1}$; uu is set to zero in the other domains.
uu [input/output] input : Cmp previously computed on the mapping *mp_prev ; ouput : values of (logically) the same Cmp at the grid points defined by *this.
void Map::reset_coord (  )  [protected, virtual]

Resets all the member Coords.

Reimplemented in Map_radial, and Map_et.

Definition at line 272 of file map.C.

References cosp, cost, Coord::del_t(), phi, r, sinp, sint, tet, x, xa, y, ya, z, and za.

virtual void Map::resize ( int  l,
double  lambda 
) [pure virtual]

Rescales the outer boundary of one domain.

The inner boundary is unchanged. The inner boundary of the next domain is changed to match the new outer boundary.

Parameters:
l [input] index of the domain
lambda [input] factor by which the value of $R(\theta, \varphi)$ defining the outer boundary of the domain is to be multiplied.

Implemented in Map_af, Map_et, and Map_log.

void Map::sauve ( FILE *  fd  )  const [virtual]

Save in a file.

Reimplemented in Map_radial, Map_af, Map_et, and Map_log.

Definition at line 220 of file map.C.

References fwrite_be(), mg, ori_x, ori_y, ori_z, rot_phi, and Mg3d::sauve().

void Map::set_ori ( double  xa0,
double  ya0,
double  za0 
)

Sets a new origin.

Definition at line 249 of file map.C.

References bvect_spher, ori_x, ori_y, ori_z, reset_coord(), and Base_vect_spher::set_ori().

void Map::set_rot_phi ( double  phi0  ) 

Sets a new rotation angle.

Definition at line 259 of file map.C.

References bvect_cart, bvect_spher, reset_coord(), rot_phi, Base_vect_cart::set_rot_phi(), and Base_vect_spher::set_rot_phi().

virtual void Map::srdsdt ( const Scalar &  uu,
Scalar &  resu 
) const [pure virtual]

Computes $1/r \partial/ \partial \theta$ of a Scalar .

Note that in the compactified external domain (CED), the dzpuis flag of the output is 2 if the input has dzpuis = 0, and is increased by 1 in other cases.

Parameters:
uu [input] field to consider
resu [output] derivative of uu

Implemented in Map_af, Map_et, and Map_log.

virtual void Map::srdsdt ( const Cmp &  ci,
Cmp &  resu 
) const [pure virtual]

Computes $1/r \partial/ \partial \theta$ of a Cmp .

Note that in the compactified external domain (CED), it computes $1/u \partial/ \partial \theta = r \partial/ \partial \theta$.

Parameters:
ci [input] field to consider
resu [output] derivative of ci

Implemented in Map_af, Map_et, and Map_log.

virtual void Map::srstdsdp ( const Scalar &  uu,
Scalar &  resu 
) const [pure virtual]

Computes $1/(r\sin\theta) \partial/ \partial \phi$ of a Scalar .

Note that in the compactified external domain (CED), the dzpuis flag of the output is 2 if the input has dzpuis = 0, and is increased by 1 in other cases.

Parameters:
uu [input] field to consider
resu [output] derivative of uu

Implemented in Map_af, Map_et, and Map_log.

virtual void Map::srstdsdp ( const Cmp &  ci,
Cmp &  resu 
) const [pure virtual]

Computes $1/(r\sin\theta) \partial/ \partial \phi$ of a Cmp .

Note that in the compactified external domain (CED), it computes $1/(u\sin\theta) \partial/ \partial \phi = r/\sin\theta \partial/ \partial \phi$.

Parameters:
ci [input] field to consider
resu [output] derivative of ci

Implemented in Map_af, Map_et, and Map_log.

virtual void Map::stdsdp ( const Scalar &  uu,
Scalar &  resu 
) const [pure virtual]

Computes $1/\sin\theta \partial/ \partial \varphi$ of a Scalar .

Parameters:
uu [input] scalar field
resu [output] derivative of uu

Implemented in Map_af, Map_et, and Map_log.

virtual void Map::val_lx ( double  rr,
double  theta,
double  pphi,
const Param &  par,
int &  l,
double &  xi 
) const [pure virtual]

Computes the domain index l and the value of $\xi$ corresponding to a point given by its physical coordinates $(r, \theta, \phi)$.

This version enables to pass some parameters to control the accuracy of the computation.

Parameters:
rr [input] value of r
theta [input] value of $\theta$
pphi [input] value of $\phi$
par [input/output] parameters to control the accuracy of the computation
l [output] value of the domain index
xi [output] value of $\xi$

Implemented in Map_af, Map_et, and Map_log.

virtual void Map::val_lx ( double  rr,
double  theta,
double  pphi,
int &  l,
double &  xi 
) const [pure virtual]

Computes the domain index l and the value of $\xi$ corresponding to a point given by its physical coordinates $(r, \theta, \phi)$.

Parameters:
rr [input] value of r
theta [input] value of $\theta$
pphi [input] value of $\phi$
l [output] value of the domain index
xi [output] value of $\xi$

Implemented in Map_af, Map_et, and Map_log.

virtual double Map::val_r ( int  l,
double  xi,
double  theta,
double  pphi 
) const [pure virtual]

Returns the value of the radial coordinate r for a given $(\xi, \theta', \phi')$ in a given domain.

Parameters:
l [input] index of the domain
xi [input] value of $\xi$
theta [input] value of $\theta'$
pphi [input] value of $\phi'$
Returns:
value of $r=R_l(\xi, \theta', \phi')$

Implemented in Map_af, Map_et, and Map_log.

Friends And Related Function Documentation

ostream& operator<< ( ostream &  ,
const Map &   
) [friend]

Operator <<.

Member Data Documentation

Base_vect_cart Map::bvect_cart [protected]

Cartesian basis $(\partial/\partial x,\partial/\partial y,\partial/\partial z)$ associated with the coordinates (x,y,z) of the mapping, i.e.

the Cartesian coordinates related to $(r, \theta, \phi)$ by means of usual formulae.

Definition at line 693 of file map.h.

Base_vect_spher Map::bvect_spher [protected]

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 685 of file map.h.

Coord Map::cosp

$\cos\phi$

Definition at line 720 of file map.h.

Coord Map::cost

$\cos\theta$

Definition at line 718 of file map.h.

const Mg3d* Map::mg [protected]

Pointer on the multi-grid Mgd3 on which this is defined.

Definition at line 672 of file map.h.

double Map::ori_x [protected]

Absolute coordinate x of the origin.

Definition at line 674 of file map.h.

double Map::ori_y [protected]

Absolute coordinate y of the origin.

Definition at line 675 of file map.h.

double Map::ori_z [protected]

Absolute coordinate z of the origin.

Definition at line 676 of file map.h.

Cmp* Map::p_cmp_zero [protected]

The null Cmp.

To be used by the Tenseur class when necessary to return a null Cmp .

Definition at line 709 of file map.h.

Metric_flat* Map::p_flat_met_cart [mutable, protected]

Pointer onto the flat metric associated with the Cartesian coordinates and with components expressed in the triad bvect_cart.

Definition at line 703 of file map.h.

Metric_flat* Map::p_flat_met_spher [mutable, protected]

Pointer onto the flat metric associated with the spherical coordinates and with components expressed in the triad bvect_spher.

Definition at line 698 of file map.h.

Map_af* Map::p_mp_angu [mutable, protected]

Pointer on the "angular" mapping.

Definition at line 711 of file map.h.

Coord Map::phi

$\phi$ coordinate centered on the grid

Definition at line 716 of file map.h.

Coord Map::r

r coordinate centered on the grid

Definition at line 714 of file map.h.

double Map::rot_phi [protected]

Angle between the x --axis and X --axis.

Definition at line 677 of file map.h.

Coord Map::sinp

$\sin\phi$

Definition at line 719 of file map.h.

Coord Map::sint

$\sin\theta$

Definition at line 717 of file map.h.

Coord Map::tet

$\theta$ coordinate centered on the grid

Definition at line 715 of file map.h.

Coord Map::x

x coordinate centered on the grid

Definition at line 722 of file map.h.

Coord Map::xa

Absolute x coordinate.

Definition at line 726 of file map.h.

Coord Map::y

y coordinate centered on the grid

Definition at line 723 of file map.h.

Coord Map::ya

Absolute y coordinate.

Definition at line 727 of file map.h.

Coord Map::z

z coordinate centered on the grid

Definition at line 724 of file map.h.

Coord Map::za

Absolute z coordinate.

Definition at line 728 of file map.h.

The documentation for this class was generated from the following files:
Generated on 7 Oct 2014 for LORENE by  doxygen 1.6.1