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

Radial mapping of rather general form. More...

#include <map.h>

Inheritance diagram for Map_et:

Public Member Functions
	Map_et (const Mg3d &mgrille, const double *r_limits)
	Standard Constructor.
	Map_et (const Mg3d &mgrille, const double *r_limits, const Tbl &tab)
	Constructor using the equation of the surface of the star.
	Map_et (const Map_et &)
	Copy constructor.
	Map_et (const Mg3d &, FILE *)
	Constructor from a file (see `sauve(FILE*)` ).
virtual	~Map_et ()
	Destructor.
virtual void	operator= (const Map_et &mp)
	Assignment to another `Map_et`.
virtual void	operator= (const Map_af &mpa)
	Assignment to an affine mapping.
void	set_ff (const Valeur &)
	Assigns a given value to the function $F(\theta',\phi')$ .
void	set_gg (const Valeur &)
	Assigns a given value to the function $G(\theta',\phi')$ .
virtual const Map_af &	mp_angu (int) const
	Returns the "angular" mapping for the outside of domain `l_zone`.
const double *	get_alpha () const
	Returns a pointer on the array `alpha` (values of $\alpha$ in each domain).
const double *	get_beta () const
	Returns a pointer on the array `beta` (values of $\beta$ in each domain).
const Valeur &	get_ff () const
	Returns a (constant) reference to the function $F(\theta',\phi')$ .
const Valeur &	get_gg () const
	Returns a (constant) reference to the function $G(\theta',\phi')$ .
virtual double	val_r (int l, double xi, double theta, double pphi) const
	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
	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
	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
	Comparison operator (egality).
virtual double	val_r_jk (int l, double xi, int j, int k) const
	Returns the value of the radial coordinate r for a given $\xi$ and a given collocation point in $(\theta', \phi')$ in a given domain.
virtual void	val_lx_jk (double rr, int j, int k, const Param &par, int &l, double &xi) const
	Computes the domain index l and the value of $\xi$ corresponding to a point of arbitrary r but collocation values of $(\theta, \phi)$ .
virtual void	sauve (FILE *) const
	Save in a file.
virtual void	homothetie (double lambda)
	Sets a new radial scale.
virtual void	resize (int l, double lambda)
	Rescales the outer boundary of one domain.
void	resize_extr (double lambda)
	Rescales the outer boundary of the outermost domain in the case of non-compactified external domain.
void	set_alpha (double alpha0, int l)
	Modifies the value of $\alpha$ in domain no. l.
void	set_beta (double beta0, int l)
	Modifies the value of $\beta$ in domain no. l.
virtual void	adapt (const Cmp &ent, const Param &par, int nbr_filtre=0)
	Adaptation of the mapping to a given scalar field.
virtual void	dsdxi (const Cmp &ci, Cmp &resu) const
	Computes $\partial/ \partial \xi$ of a `Cmp`.
virtual void	dsdr (const Cmp &ci, Cmp &resu) const
	Computes $\partial/ \partial r$ of a `Cmp`.
virtual void	srdsdt (const Cmp &ci, Cmp &resu) const
	Computes $1/r \partial/ \partial \theta$ of a `Cmp`.
virtual void	srstdsdp (const Cmp &ci, Cmp &resu) const
	Computes $1/(r\sin\theta) \partial/ \partial \phi$ of a `Cmp`.
virtual void	dsdxi (const Scalar &uu, Scalar &resu) const
	Computes $\partial/ \partial \xi$ of a `Scalar`.
virtual void	dsdr (const Scalar &uu, Scalar &resu) const
	Computes $\partial/ \partial r$ of a `Scalar`.
virtual void	dsdradial (const Scalar &uu, Scalar &resu) const
	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
	Computes $1/r \partial/ \partial \theta$ of a `Scalar`.
virtual void	srstdsdp (const Scalar &uu, Scalar &resu) const
	Computes $1/(r\sin\theta) \partial/ \partial \phi$ of a `Scalar`.
virtual void	dsdt (const Scalar &uu, Scalar &resu) const
	Computes $\partial/ \partial \theta$ of a `Scalar`.
virtual void	stdsdp (const Scalar &uu, Scalar &resu) const
	Computes $1/\sin\theta \partial/ \partial \varphi$ of a `Scalar`.
virtual void	laplacien (const Scalar &uu, int zec_mult_r, Scalar &lap) const
	Computes the Laplacian of a scalar field.
virtual void	laplacien (const Cmp &uu, int zec_mult_r, Cmp &lap) const
	Computes the Laplacian of a scalar field (`Cmp` version).
virtual void	lapang (const Scalar &uu, Scalar &lap) const
	Computes the angular Laplacian of a scalar field.
virtual void	primr (const Scalar &uu, Scalar &resu, bool null_infty) const
	Computes the radial primitive which vanishes for $r\to \infty$ .
virtual Tbl *	integrale (const Cmp &) const
	Computes the integral over all space of a `Cmp`.
virtual void	poisson (const Cmp &source, Param &par, Cmp &uu) const
	Computes the solution of a scalar Poisson equation.
virtual void	poisson_tau (const Cmp &source, Param &par, Cmp &uu) const
	Computes the solution of a scalar Poisson equation with a Tau method.
virtual void	poisson_falloff (const Cmp &source, Param &par, Cmp &uu, int k_falloff) const
virtual void	poisson_ylm (const Cmp &source, Param &par, Cmp &uu, int nylm, double *intvec) const
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
	Computes the solution of a scalar Poisson equation.
virtual void	poisson_angu (const Scalar &source, Param &par, Scalar &uu, double lambda=0) const
	Computes the solution of the generalized angular Poisson equation.
virtual Param *	donne_para_poisson_vect (Param &para, int i) const
	Internal function intended to be used by `Map::poisson_vect` and `Map::poisson_vect_oohara` .
virtual void	poisson_frontiere (const Cmp &, const Valeur &, int, int, Cmp &, double=0., double=0.) const
	Not yet implemented.
virtual void	poisson_frontiere_double (const Cmp &source, const Valeur &lim_func, const Valeur &lim_der, int num_zone, Cmp &pot) const
virtual void	poisson_interne (const Cmp &source, const Valeur &limite, Param &par, Cmp &pot) const
	Computes the solution of a Poisson equation in the shell .
virtual void	poisson2d (const Cmp &source_mat, const Cmp &source_quad, Param &par, Cmp &uu) const
	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
	Not yet implemented.
virtual bool	operator== (const Map &) const =0
	Comparison operator (egality).
virtual void	reevaluate (const Map *mp_prev, int nzet, Cmp &uu) const
	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
	Recomputes the values of a `Scalar` at the collocation points after a change in the mapping.
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 (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, Cmp &uu) const
	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, Scalar &uu) const
	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, 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, Scalar &uu) const =0
	Recomputes the values of a `Scalar` at the collocation points after a change in the mapping.
virtual void	mult_r (Scalar &uu) const
	Multiplication by r of a `Scalar`, the `dzpuis` of `uu` is not changed.
virtual void	mult_r (Cmp &ci) const
	Multiplication by r of a `Cmp`.
virtual void	mult_r_zec (Scalar &) const
	Multiplication by r (in the compactified external domain only) of a `Scalar`.
virtual void	mult_rsint (Scalar &) const
	Multiplication by $r\sin\theta$ of a `Scalar`.
virtual void	div_rsint (Scalar &) const
	Division by $r\sin\theta$ of a `Scalar`.
virtual void	div_r (Scalar &) const
	Division by r of a `Scalar`.
virtual void	div_r_zec (Scalar &) const
	Division by r (in the compactified external domain only) of a `Scalar`.
virtual void	mult_cost (Scalar &) const
	Multiplication by $\cos\theta$ of a `Scalar`.
virtual void	div_cost (Scalar &) const
	Division by $\cos\theta$ of a `Scalar`.
virtual void	mult_sint (Scalar &) const
	Multiplication by $\sin\theta$ of a `Scalar`.
virtual void	div_sint (Scalar &) const
	Division by $\sin\theta$ of a `Scalar`.
virtual void	div_tant (Scalar &) const
	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
	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
	`Cmp` version
virtual void	comp_y_from_spherical (const Scalar &v_r, const Scalar &v_theta, const Scalar &v_phi, Scalar &v_y) const
	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
	`Cmp` version
virtual void	comp_z_from_spherical (const Scalar &v_r, const Scalar &v_theta, Scalar &v_z) const
	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
	`Cmp` version
virtual void	comp_r_from_cartesian (const Scalar &v_x, const Scalar &v_y, const Scalar &v_z, Scalar &v_r) const
	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
	`Cmp` version
virtual void	comp_t_from_cartesian (const Scalar &v_x, const Scalar &v_y, const Scalar &v_z, Scalar &v_t) const
	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
	`Cmp` version
virtual void	comp_p_from_cartesian (const Scalar &v_x, const Scalar &v_y, Scalar &v_p) const
	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
	`Cmp` version
virtual void	dec_dzpuis (Scalar &) const
	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
	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
	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
	Increases by 2 the value of `dzpuis` of a `Scalar` and changes accordingly its values in the compactified external domain (CED).
virtual void	poisson_compact (const Cmp &source, const Cmp &aa, const Tenseur &bb, const Param &par, Cmp &psi) const
	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
	Resolution of the elliptic equation $a \Delta\psi + {\bf b} \cdot \nabla \psi = \sigma$ in the case of a multidomain stellar interior.
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`.
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).
void	set_ori (double xa0, double ya0, double za0)
	Sets a new origin.
void	set_rot_phi (double phi0)
	Sets a new rotation angle.
Public Attributes
Coord	rsxdxdr
	$1/(\partial R/\partial \xi) R/\xi$ in the nucleus; \ $1/(\partial R/\partial \xi) R/(\xi + \beta/\alpha)$ in the shells; \ $1/(\partial U/\partial \xi) U/(\xi-1)$ in the outermost compactified domain.
Coord	rsx2drdx
	$[ R/ (\alpha \xi + \beta) ]^2 (\partial R/\partial \xi) / \alpha$ in the nucleus and the shells; \ $\partial U/\partial \xi / \alpha$ in the outermost compactified domain.
Coord	xsr
	$\xi/R$ in the nucleus; \ 1/R in the non-compactified shells; \ $(\xi-1)/U$ in the compactified outer domain.
Coord	dxdr
	$1/(\partial R/\partial\xi) = \partial \xi /\partial r$ in the nucleus and in the non-compactified shells; \ $-1/(\partial U/\partial\xi) = - \partial \xi /\partial u$ in the compactified outer domain.
Coord	drdt
	$\partial R/\partial\theta'$ in the nucleus and in the non-compactified shells; \ $-\partial U/\partial\theta'$ in the compactified external domain (CED).
Coord	stdrdp
	${1\over\sin\theta} \partial R/\partial\varphi'$ in the nucleus and in the non-compactified shells; \ $-{1\over\sin\theta}\partial U/\partial\varphi'$ in the compactified external domain (CED).
Coord	srdrdt
	$1/R \times (\partial R/\partial\theta')$ in the nucleus and in the non-compactified shells; \ $-1/U \times (\partial U/\partial\theta)$ in the compactified outer domain.
Coord	srstdrdp
	$1/(R\sin\theta) \times (\partial R/\partial\varphi')$ in the nucleus and in the non-compactified shells; \ $-1/(U\sin\theta) \times (\partial U/\partial\varphi')$ in the compactified outer domain.
Coord	sr2drdt
	$1/R^2 \times (\partial R/\partial\theta')$ in the nucleus and in the non-compactified shells; \ $-1/U^2 \times (\partial U/\partial\theta')$ in the compactified outer domain.
Coord	sr2stdrdp
	$1/(R^2\sin\theta) \times (\partial R/\partial\varphi')$ in the nucleus and in the non-compactified shells; \ $-1/(U^2\sin\theta) \times (\partial U/\partial\varphi')$ in the compactified outer domain.
Coord	d2rdx2
	$\partial^2 R/\partial\xi^2$ in the nucleus and in the non-compactified shells; \ $-\partial^2 U/\partial\xi^2$ in the compactified outer domain.
Coord	lapr_tp
	$1/R^2 \times [ 1/\sin(\theta)\times \partial /\partial\theta' (\sin\theta \partial R /\partial\theta') + 1/\sin^2\theta \partial^2 R /\partial{\varphi'}^2]$ in the nucleus and in the non-compactified shells; \ $- 1/U^2 \times [ 1/\sin(\theta)\times \partial /\partial\theta' (\sin\theta \partial U /\partial\theta') + 1/\sin^2\theta \partial^2 U /\partial{\varphi'}^2]$ in the compactified outer domain.
Coord	d2rdtdx
	$\partial^2 R/\partial\xi\partial\theta'$ in the nucleus and in the non-compactified shells; \ $-\partial^2 U/\partial\xi\partial\theta'$ in the compactified outer domain.
Coord	sstd2rdpdx
	$1/\sin\theta \times \partial^2 R/\partial\xi\partial\varphi'$ in the nucleus and in the non-compactified shells; \ $-1/\sin\theta \times \partial^2 U/\partial\xi\partial\varphi'$ in the compactified outer domain.
Coord	sr2d2rdt2
	$1/R^2 \partial^2 R/\partial{\theta'}^2$ in the nucleus and in the non-compactified shells; \ $-1/U^2 \partial^2 U/\partial{\theta'}^2$ in the compactified outer domain.
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
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
void	set_coord ()
	Assignement of the building functions to the member `Coords`.
void	fait_poly ()
	Construction of the polynomials $A(\xi)$ and $B(\xi)$ .
virtual ostream &	operator>> (ostream &) const
	Operator >>.
Private Attributes
double *	alpha
	Array (size: `mg->nzone` ) of the values of $\alpha$ in each domain.
double *	beta
	Array (size: `mg->nzone` ) of the values of $\beta$ in each domain.
Tbl **	aa
	Array (size: `mg->nzone` ) of `Tbl` which stores the values of $A(\xi)$ in each domain.
Tbl **	daa
	Array (size: `mg->nzone` ) of `Tbl` which stores the values of $A'(\xi)$ in each domain.
Tbl **	ddaa
	Array (size: `mg->nzone` ) of `Tbl` which stores the values of $A''(\xi)$ in each domain.
Tbl	aasx
	Values at the `nr` collocation points of $A(\xi)/\xi$ in the nucleus.
Tbl	aasx2
	Values at the `nr` collocation points of $A(\xi)/\xi^2$ in the nucleus.
Tbl	zaasx
	Values at the `nr` collocation points of $A(\xi)/(\xi-1)$ in the outermost compactified domain.
Tbl	zaasx2
	Values at the `nr` collocation points of $A(\xi)/(\xi-1)^2$ in the outermost compactified domain.
Tbl **	bb
	Array (size: `mg->nzone` ) of `Tbl` which stores the values of $B(\xi)$ in each domain.
Tbl **	dbb
	Array (size: `mg->nzone` ) of `Tbl` which stores the values of $B'(\xi)$ in each domain.
Tbl **	ddbb
	Array (size: `mg->nzone` ) of `Tbl` which stores the values of $B''(\xi)$ in each domain.
Tbl	bbsx
	Values at the `nr` collocation points of $B(\xi)/\xi$ in the nucleus.
Tbl	bbsx2
	Values at the `nr` collocation points of $B(\xi)/\xi^2$ in the nucleus.
Valeur	ff
	Values of the function $F(\theta', \phi')$ at the `nt*np` angular collocation points in each domain.
Valeur	gg
	Values of the function $G(\theta', \phi')$ at the `nt*np` angular collocation points in each domain.
Friends
Mtbl *	map_et_fait_r (const Map *)
Mtbl *	map_et_fait_tet (const Map *)
Mtbl *	map_et_fait_phi (const Map *)
Mtbl *	map_et_fait_sint (const Map *)
Mtbl *	map_et_fait_cost (const Map *)
Mtbl *	map_et_fait_sinp (const Map *)
Mtbl *	map_et_fait_cosp (const Map *)
Mtbl *	map_et_fait_x (const Map *)
Mtbl *	map_et_fait_y (const Map *)
Mtbl *	map_et_fait_z (const Map *)
Mtbl *	map_et_fait_xa (const Map *)
Mtbl *	map_et_fait_ya (const Map *)
Mtbl *	map_et_fait_za (const Map *)
Mtbl *	map_et_fait_xsr (const Map *)
Mtbl *	map_et_fait_dxdr (const Map *)
Mtbl *	map_et_fait_drdt (const Map *)
Mtbl *	map_et_fait_stdrdp (const Map *)
Mtbl *	map_et_fait_srdrdt (const Map *)
Mtbl *	map_et_fait_srstdrdp (const Map *)
Mtbl *	map_et_fait_sr2drdt (const Map *)
Mtbl *	map_et_fait_sr2stdrdp (const Map *)
Mtbl *	map_et_fait_d2rdx2 (const Map *)
Mtbl *	map_et_fait_lapr_tp (const Map *)
Mtbl *	map_et_fait_d2rdtdx (const Map *)
Mtbl *	map_et_fait_sstd2rdpdx (const Map *)
Mtbl *	map_et_fait_sr2d2rdt2 (const Map *)
Mtbl *	map_et_fait_rsxdxdr (const Map *)
Mtbl *	map_et_fait_rsx2drdx (const Map *)
ostream &	operator<< (ostream &, const Map &)
	Operator <<.

Detailed Description

Radial mapping of rather general form.

()

This mapping relates the grid coordinates $(\xi, \theta', \phi')$ and the physical coordinates $(r, \theta, \phi)$ in the following manner [see Bonazzola, Gourgoulhon & Marck, Phys. Rev. D 58 , 104020 (1998) for details]: $\theta=\theta'$ , $\phi=\phi'$ and

$r = \alpha [\xi + A(\xi) F(\theta', \phi') + B(\xi) G(\theta', \phi')] + \beta$ in non-compactified domains,
$u={1\over r} = \alpha [\xi + A(\xi) F(\theta', \phi')] + \beta$ in the (usually outermost) compactified domain, where $\alpha$ and $\beta$ are constant in each domain, $A(\xi)$ and $B(\xi)$ are constant polynomials defined by
$A(\xi) = 3 \xi^4 - 2 \xi^6$ and $B(\xi) = (5\xi^3 - 3\xi^5)/2$ in the nucleus (innermost domain which contains r =0);
$A(\xi) = (\xi^3 - 3\xi + 2)/4$ and $B(\xi) = (-\xi^3 + 3\xi +2)/4$ in the other domains. The functions $F(\theta', \phi')$ and $G(\theta', \phi')$ depend on the domain under consideration and define the boundaries of this domain.

Definition at line 2748 of file map.h.

Constructor & Destructor Documentation

Map_et::Map_et	(	const Mg3d &	mgrille,
		const double *	r_limits
	)

Standard Constructor.

Parameters:

mgrille [input] Multi-domain grid on which the mapping is defined

r_limits

[input] Array (size: number of domains + 1) of the value of r at the boundaries of the various domains :

r_limits[l] : inner boundary of the domain no. l
r_limits[l+1] : outer boundary of the domain no. l

Definition at line 145 of file map_et.C.

References alpha, beta, fait_poly(), ff, Mg3d::get_nzone(), Mg3d::get_type_r(), gg, Map::mg, set_coord(), Valeur::set_etat_zero(), and Valeur::std_base_scal().

Map_et::Map_et	(	const Mg3d &	mgrille,
		const double *	r_limits,
		const Tbl &	tab
	)

Constructor using the equation of the surface of the star.

Parameters:

mgrille [input] Multi-domain grid on which the mapping is defined It must contains at least one shell.

r_limits

[input] Array (size: number of domains + 1) of the value of r at the boundaries of the various domains :

r_limits[l] : inner boundary of the domain no. l
r_limits[l+1] : outer boundary of the domain no. l The first value is not used.

tab [input] equation of the surface between the nucleus and the first shell in the form : ${\rm tab}(k,j) = r(\phi_k,\theta_j)$ , where $\phi_k$ and $\theta_j$ are the values of the angular colocation points.

Definition at line 219 of file map_et.C.

References alpha, Valeur::annule(), Valeur::annule_hard(), beta, fait_poly(), ff, Base_val::get_base_p(), Tbl::get_dim(), Tbl::get_ndim(), Mg3d::get_np(), Mg3d::get_nt(), Mg3d::get_nzone(), gg, max(), min(), P_COSSIN, Valeur::set(), Tbl::set(), set_coord(), Valeur::set_etat_c_qcq(), Tbl::set_etat_qcq(), Valeur::std_base_scal(), and Mg3d::std_base_scal().

Map_et::Map_et ( const Map_et & mpi )

Copy constructor.

Definition at line 384 of file map_et.C.

References alpha, beta, fait_poly(), Mg3d::get_nzone(), Map::mg, and set_coord().

Map_et::Map_et	(	const Mg3d &	mgi,
		FILE *	fich
	)

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

Definition at line 445 of file map_et.C.

References alpha, beta, fait_poly(), fread_be(), Mg3d::get_nzone(), Map::mg, and set_coord().

Map_et::~Map_et ( ) [virtual]

Destructor.

Definition at line 482 of file map_et.C.

References aa, alpha, bb, beta, daa, dbb, ddaa, ddbb, Mg3d::get_nzone(), and Map::mg.

Member Function Documentation

void Map_et::adapt	(	const Cmp &	ent,
		const Param &	par,
		int	nbr_filtre = `0`
	)			`[virtual]`

Adaptation of the mapping to a given scalar field.

Computes the functions $F(\theta',\phi')$ and $G(\theta',\phi')$ as well as the factors $\alpha$ and $\beta$ , so that the boundaries of some domains coincide with isosurfaces of the scalar field ent .

Parameters:

	ent	[input] scalar field, the isosurfaces of which are used to determine the mapping
	par	[input/output] parameters of the computation: \ `par.get_int(0)` : maximum number of iterations to locate zeros by the secant method \ `par.get_int(1)` : number of domains where the adjustment to the isosurfaces of `ent` is to be performed \ `par.get_int(2)` : number of domains `nz_search` where the isosurfaces will be searched : the routine scans the `nz_search` innermost domains, starting from the domain of index `nz_search-1` . NB: the field `ent` must be continuous over these domains \ `par.get_int(3)` : 1 = performs the full computation, 0 = performs only the rescaling by the factor `par.get_double_mod(0)` \ `par.get_int(4)` : theta index of the collocation point $(\theta_, \phi_)$ [using the notations of Bonazzola, Gourgoulhon & Marck, Phys. Rev. D 58 , 104020 (1998)] defining an isosurface of `ent` \ `par.get_int(5)` : phi index of the collocation point $(\theta_, \phi_)$ [using the notations of Bonazzola, Gourgoulhon & Marck, Phys. Rev. D 58 , 104020 (1998)] defining an isosurface of `ent` \ `par.get_int_mod(0)` [output] : number of iterations actually used in the secant method \ `par.get_double(0)` : required absolute precision in the determination of zeros by the secant method \ `par.get_double(1)` : factor by which the values of $\lambda$ and $\mu$ [using the notations of Bonazzola, Gourgoulhon & Marck, Phys. Rev. D 58 , 104020 (1998)] will be multiplied : 1 = regular mapping, 0 = contracting mapping \ `par.get_double(2)` : factor by which all the radial distances will be multiplied \ `par.get_tbl(0)` : array of values of the field `ent` to define the isosurfaces.
	nbr\_filtre	[input] Number of the last coefficients in $\varphi$ set to zero.

Implements Map.

Definition at line 104 of file map_et_adapt.C.

References alpha, beta, Valeur::c, Valeur::c_cf, Valeur::coef(), ff, Param::get_double(), Mtbl::get_etat(), Valeur::get_etat(), Itbl::get_etat(), Tbl::get_etat(), Param::get_int(), Param::get_int_mod(), Valeur::get_mg(), Cmp::get_mp(), Tbl::get_ndim(), Mg3d::get_np(), Mg3d::get_nt(), Mg3d::get_nzone(), Tbl::get_taille(), Param::get_tbl(), Mg3d::get_type_r(), gg, homothetie(), max(), Map::mg, min(), MSQ_P, P_COSSIN, P_COSSIN_P, reset_coord(), Mtbl_cf::set(), Valeur::set_etat_cf_qcq(), Tbl::set_etat_qcq(), Tbl::set_etat_zero(), Valeur::std_base_scal(), Mtbl_cf::t, Mtbl::t, Itbl::t, Tbl::t, Cmp::va, and val_r_jk().

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

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 Map::p_cmp_zero.

void Map_radial::comp_p_from_cartesian	(	const Cmp &	v_x,
		const Cmp &	v_y,
		Cmp &	v_p
	)			const `[virtual, inherited]`

Cmp version

Implements Map.

Definition at line 172 of file map_radial_comp_rtp.C.

References Map_radial::comp_p_from_cartesian().

void Map_radial::comp_p_from_cartesian	(	const Scalar &	v_x,
		const Scalar &	v_y,
		Scalar &	v_p
	)			const `[virtual, inherited]`

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

Implements Map.

Definition at line 179 of file map_radial_comp_rtp.C.

References Scalar::check_dzpuis(), Scalar::dz_nonzero(), Scalar::get_dzpuis(), Scalar::get_etat(), Tensor::get_mp(), Scalar::get_spectral_va(), Valeur::mult_cp(), and Scalar::set_dzpuis().

void Map_radial::comp_r_from_cartesian	(	const Cmp &	v_x,
		const Cmp &	v_y,
		const Cmp &	v_z,
		Cmp &	v_r
	)			const `[virtual, inherited]`

Cmp version

Implements Map.

Definition at line 61 of file map_radial_comp_rtp.C.

References Map_radial::comp_r_from_cartesian().

void Map_radial::comp_r_from_cartesian	(	const Scalar &	v_x,
		const Scalar &	v_y,
		const Scalar &	v_z,
		Scalar &	v_r
	)			const `[virtual, inherited]`

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

Implements Map.

Definition at line 68 of file map_radial_comp_rtp.C.

References Scalar::check_dzpuis(), Scalar::dz_nonzero(), Scalar::get_dzpuis(), Scalar::get_etat(), Tensor::get_mp(), Scalar::get_spectral_va(), Valeur::mult_cp(), Valeur::mult_ct(), Valeur::mult_sp(), Valeur::mult_st(), and Scalar::set_dzpuis().

void Map_radial::comp_t_from_cartesian	(	const Cmp &	v_x,
		const Cmp &	v_y,
		const Cmp &	v_z,
		Cmp &	v_t
	)			const `[virtual, inherited]`

Cmp version

Implements Map.

Definition at line 117 of file map_radial_comp_rtp.C.

References Map_radial::comp_t_from_cartesian().

void Map_radial::comp_t_from_cartesian	(	const Scalar &	v_x,
		const Scalar &	v_y,
		const Scalar &	v_z,
		Scalar &	v_t
	)			const `[virtual, inherited]`

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

Implements Map.

Definition at line 124 of file map_radial_comp_rtp.C.

References Scalar::check_dzpuis(), Scalar::dz_nonzero(), Scalar::get_dzpuis(), Scalar::get_etat(), Tensor::get_mp(), Scalar::get_spectral_va(), Valeur::mult_cp(), Valeur::mult_ct(), Valeur::mult_sp(), Valeur::mult_st(), and Scalar::set_dzpuis().

void Map_radial::comp_x_from_spherical	(	const Cmp &	v_r,
		const Cmp &	v_theta,
		const Cmp &	v_phi,
		Cmp &	v_x
	)			const `[virtual, inherited]`

Cmp version

Implements Map.

Definition at line 64 of file map_radial_comp_xyz.C.

References Map_radial::comp_x_from_spherical().

void Map_radial::comp_x_from_spherical	(	const Scalar &	v_r,
		const Scalar &	v_theta,
		const Scalar &	v_phi,
		Scalar &	v_x
	)			const `[virtual, inherited]`

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

Implements Map.

Definition at line 72 of file map_radial_comp_xyz.C.

References Scalar::check_dzpuis(), Scalar::dz_nonzero(), Scalar::get_dzpuis(), Scalar::get_etat(), Tensor::get_mp(), Scalar::get_spectral_va(), Valeur::mult_cp(), Valeur::mult_ct(), Valeur::mult_sp(), Valeur::mult_st(), and Scalar::set_dzpuis().

void Map_radial::comp_y_from_spherical	(	const Cmp &	v_r,
		const Cmp &	v_theta,
		const Cmp &	v_phi,
		Cmp &	v_y
	)			const `[virtual, inherited]`

Cmp version

Implements Map.

Definition at line 122 of file map_radial_comp_xyz.C.

References Map_radial::comp_y_from_spherical().

void Map_radial::comp_y_from_spherical	(	const Scalar &	v_r,
		const Scalar &	v_theta,
		const Scalar &	v_phi,
		Scalar &	v_y
	)			const `[virtual, inherited]`

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

Implements Map.

Definition at line 131 of file map_radial_comp_xyz.C.

References Scalar::check_dzpuis(), Scalar::dz_nonzero(), Scalar::get_dzpuis(), Scalar::get_etat(), Tensor::get_mp(), Scalar::get_spectral_va(), Valeur::mult_cp(), Valeur::mult_ct(), Valeur::mult_sp(), Valeur::mult_st(), and Scalar::set_dzpuis().

void Map_radial::comp_z_from_spherical	(	const Cmp &	v_r,
		const Cmp &	v_theta,
		Cmp &	v_z
	)			const `[virtual, inherited]`

Cmp version

Implements Map.

Definition at line 180 of file map_radial_comp_xyz.C.

References Map_radial::comp_z_from_spherical().

void Map_radial::comp_z_from_spherical	(	const Scalar &	v_r,
		const Scalar &	v_theta,
		Scalar &	v_z
	)			const `[virtual, inherited]`

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

Implements Map.

Definition at line 188 of file map_radial_comp_xyz.C.

References Scalar::check_dzpuis(), Scalar::dz_nonzero(), Scalar::get_dzpuis(), Scalar::get_etat(), Tensor::get_mp(), Scalar::get_spectral_va(), Valeur::mult_st(), and Scalar::set_dzpuis().

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

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 Map::ori_x, Map::ori_y, Map::ori_z, Map::rot_phi, and sqrt().

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

Not yet implemented.

Implements Map.

Definition at line 65 of file map_et_dalembert.C.

References Scalar::get_etat(), Map::get_mg(), Tensor::get_mp(), and Map::mg.

void Map_radial::dec2_dzpuis ( Scalar & ci ) const [virtual, inherited]

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

Implements Map.

Definition at line 744 of file map_radial_r_manip.C.

References Valeur::annule(), Scalar::get_dzpuis(), Scalar::get_etat(), Valeur::get_mg(), Mg3d::get_nzone(), Mg3d::get_type_r(), Map::mg, Scalar::set_dzpuis(), Scalar::set_etat_qcq(), Scalar::set_spectral_va(), and Map_radial::xsr.

void Map_radial::dec_dzpuis ( Scalar & ci ) const [virtual, inherited]

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

Implements Map.

Definition at line 639 of file map_radial_r_manip.C.

References Valeur::annule(), Scalar::get_dzpuis(), Scalar::get_etat(), Valeur::get_mg(), Mg3d::get_nzone(), Mg3d::get_type_r(), Map::mg, Scalar::set_dzpuis(), Scalar::set_etat_qcq(), Scalar::set_spectral_va(), and Map_radial::xsr.

void Map_radial::div_cost ( Scalar & ci ) const [virtual, inherited]

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

Implements Map.

Definition at line 81 of file map_radial_th_manip.C.

References Scalar::get_etat(), Valeur::get_mg(), Map::mg, Valeur::scost(), Scalar::set_etat_qcq(), and Scalar::set_spectral_va().

void Map_radial::div_r ( Scalar & ci ) const [virtual, inherited]

Division by r of a Scalar.

Implements Map.

Definition at line 510 of file map_radial_r_manip.C.

References Scalar::annule(), Tensor::annule_domain(), Valeur::base, Scalar::get_etat(), Valeur::get_mg(), Mg3d::get_nzone(), Mg3d::get_type_r(), Map::mg, Valeur::mult_x(), Scalar::set_etat_qcq(), Scalar::set_spectral_va(), Valeur::sx(), and Map_radial::xsr.

void Map_radial::div_r_zec ( Scalar & uu ) const [virtual, inherited]

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

Implements Map.

Definition at line 581 of file map_radial_r_manip.C.

References Valeur::annule(), Valeur::base, Scalar::get_etat(), Valeur::get_mg(), Mg3d::get_nzone(), Scalar::get_spectral_va(), Mg3d::get_type_r(), Map::mg, Valeur::mult_xm1_zec(), Scalar::set_etat_qcq(), Scalar::set_spectral_va(), and Map_radial::xsr.

void Map_radial::div_rsint ( Scalar & ci ) const [virtual, inherited]

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

Implements Map.

Definition at line 430 of file map_radial_r_manip.C.

References Scalar::annule(), Tensor::annule_domain(), Valeur::base, Scalar::get_etat(), Valeur::get_mg(), Mg3d::get_nzone(), Mg3d::get_type_r(), Map::mg, Valeur::mult_x(), Scalar::set_etat_qcq(), Scalar::set_spectral_va(), Valeur::ssint(), Valeur::sx(), and Map_radial::xsr.

void Map_radial::div_sint ( Scalar & ci ) const [virtual, inherited]

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

Implements Map.

Definition at line 129 of file map_radial_th_manip.C.

References Scalar::get_etat(), Valeur::get_mg(), Map::mg, Scalar::set_etat_qcq(), Scalar::set_spectral_va(), and Valeur::ssint().

void Map_radial::div_tant ( Scalar & ci ) const [virtual, inherited]

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

Implements Map.

Definition at line 154 of file map_radial_th_manip.C.

References Scalar::get_etat(), Valeur::get_mg(), Map::mg, Valeur::mult_ct(), Scalar::set_etat_qcq(), Scalar::set_spectral_va(), and Valeur::ssint().

Param * Map_et::donne_para_poisson_vect	(	Param &	para,
		int	i
	)			const `[virtual]`

Internal 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 .

Implements Map.

Definition at line 71 of file map_poisson_vect.C.

References Param::add_cmp_mod(), Param::add_double(), Param::add_int(), Param::add_int_mod(), Param::get_cmp_mod(), Param::get_double(), Param::get_int(), Param::get_int_mod(), Param::get_tenseur_mod(), and Tenseur::set().

void Map_et::dsdr	(	const Scalar &	uu,
		Scalar &	resu
	)			const `[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`

Implements Map.

Definition at line 211 of file map_et_deriv.C.

References Tensor::annule_domain(), Valeur::coef(), Scalar::dsdx(), Map_radial::dxdr, Valeur::get_base(), Scalar::get_dzpuis(), Scalar::get_etat(), Map::get_mg(), Tensor::get_mp(), Mg3d::get_nzone(), Scalar::get_spectral_va(), Mg3d::get_type_r(), Map::mg, Coord::set(), Scalar::set_dzpuis(), Scalar::set_etat_zero(), Scalar::set_spectral_base(), Scalar::set_spectral_va(), and Map_radial::xsr.

void Map_et::dsdr	(	const Cmp &	ci,
		Cmp &	resu
	)			const `[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`

Implements Map.

Definition at line 183 of file map_et_deriv.C.

References Cmp::check_dzpuis(), Map_radial::dxdr, Cmp::get_etat(), Map::get_mg(), Cmp::get_mp(), Mg3d::get_nzone(), Mg3d::get_type_r(), Map::mg, Cmp::set_dzpuis(), Cmp::set_etat_zero(), and Cmp::va.

void Map_et::dsdradial	(	const Scalar &	uu,
		Scalar &	resu
	)			const `[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`

Implements Map.

Definition at line 270 of file map_et_deriv.C.

References Tensor::annule_domain(), Valeur::coef(), Scalar::dsdx(), Map_radial::dxdr, Valeur::get_base(), Scalar::get_dzpuis(), Scalar::get_etat(), Map::get_mg(), Tensor::get_mp(), Mg3d::get_nzone(), Scalar::get_spectral_va(), Mg3d::get_type_r(), Map::mg, Coord::set(), Scalar::set_dzpuis(), Scalar::set_etat_zero(), Scalar::set_spectral_base(), Scalar::set_spectral_va(), and Map_radial::xsr.

void Map_et::dsdt	(	const Scalar &	uu,
		Scalar &	resu
	)			const `[virtual]`

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

Parameters:

	uu	[input] scalar field
	resu	[output] derivative of `uu`

Implements Map.

Definition at line 625 of file map_et_deriv.C.

References Map_radial::drdt, Valeur::dsdt(), Valeur::dsdx(), Map_radial::dxdr, Valeur::get_base(), Scalar::get_etat(), Map::get_mg(), Tensor::get_mp(), Scalar::get_spectral_va(), Map::mg, Valeur::set_base(), and Scalar::set_etat_zero().

void Map_et::dsdxi	(	const Scalar &	uu,
		Scalar &	resu
	)			const `[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`

Implements Map.

Definition at line 119 of file map_et_deriv.C.

References Tensor::annule_domain(), Valeur::coef(), Scalar::dsdx(), Valeur::get_base(), Scalar::get_dzpuis(), Scalar::get_etat(), Map::get_mg(), Tensor::get_mp(), Mg3d::get_nzone(), Scalar::get_spectral_va(), Mg3d::get_type_r(), Map::mg, Coord::set(), Valeur::set_base(), Scalar::set_dzpuis(), Scalar::set_etat_zero(), Scalar::set_spectral_base(), Scalar::set_spectral_va(), and Map_radial::xsr.

void Map_et::dsdxi	(	const Cmp &	ci,
		Cmp &	resu
	)			const `[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`

Implements Map.

Definition at line 91 of file map_et_deriv.C.

References Cmp::check_dzpuis(), Cmp::dsdx(), Cmp::get_etat(), Map::get_mg(), Cmp::get_mp(), Mg3d::get_nzone(), Mg3d::get_type_r(), Map::mg, Cmp::set_dzpuis(), Cmp::set_etat_zero(), and Cmp::va.

void Map_et::fait_poly ( ) [private]

Construction of the polynomials $A(\xi)$ and $B(\xi)$ .

Definition at line 641 of file map_et.C.

References aa, aasx, aasx2, bb, bbsx, bbsx2, daa, dbb, ddaa, ddbb, Mg3d::get_grille3d(), Mg3d::get_nr(), Mg3d::get_nzone(), Mg3d::get_type_r(), Map::mg, Tbl::set(), Tbl::set_etat_qcq(), Tbl::set_etat_zero(), Map::x, zaasx, and zaasx2.

const Metric_flat & Map::flat_met_cart ( ) const [inherited]

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 Map::bvect_cart, and Map::p_flat_met_cart.

const Metric_flat & Map::flat_met_spher ( ) const [inherited]

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 Map::bvect_spher, and Map::p_flat_met_spher.

const double * Map_et::get_alpha ( ) const

Returns a pointer on the array alpha (values of $\alpha$ in each domain).

Definition at line 1022 of file map_et.C.

References alpha.

const double * Map_et::get_beta ( ) const

Returns a pointer on the array beta (values of $\beta$ in each domain).

Definition at line 1026 of file map_et.C.

References beta.

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

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 Map::bvect_cart.

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

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 Map::bvect_spher.

const Valeur & Map_et::get_ff ( ) const

Returns a (constant) reference to the function $F(\theta',\phi')$ .

Definition at line 1030 of file map_et.C.

References ff.

const Valeur & Map_et::get_gg ( ) const

Returns a (constant) reference to the function $G(\theta',\phi')$ .

Definition at line 1034 of file map_et.C.

References gg.

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

Gives the Mg3d on which the mapping is defined.

Definition at line 761 of file map.h.

References Map::mg.

double Map::get_ori_x ( ) const [inline, inherited]

Returns the x coordinate of the origin.

Definition at line 764 of file map.h.

References Map::ori_x.

double Map::get_ori_y ( ) const [inline, inherited]

Returns the y coordinate of the origin.

Definition at line 766 of file map.h.

References Map::ori_y.

double Map::get_ori_z ( ) const [inline, inherited]

Returns the z coordinate of the origin.

Definition at line 768 of file map.h.

References Map::ori_z.

double Map::get_rot_phi ( ) const [inline, inherited]

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

Definition at line 771 of file map.h.

References Map::rot_phi.

void Map_et::homothetie ( double lambda ) [virtual]

Sets a new radial scale.

Parameters:

lambda

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

Implements Map.

Definition at line 901 of file map_et.C.

References alpha, beta, Mg3d::get_nzone(), Mg3d::get_type_r(), Map::mg, and reset_coord().

void Map_radial::inc2_dzpuis ( Scalar & ci ) const [virtual, inherited]

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

Implements Map.

Definition at line 795 of file map_radial_r_manip.C.

References Valeur::annule(), Scalar::get_dzpuis(), Scalar::get_etat(), Valeur::get_mg(), Mg3d::get_nzone(), Mg3d::get_type_r(), Map::mg, Scalar::set_dzpuis(), Scalar::set_etat_qcq(), Scalar::set_spectral_va(), and Map_radial::xsr.

void Map_radial::inc_dzpuis ( Scalar & ci ) const [virtual, inherited]

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

Implements Map.

Definition at line 692 of file map_radial_r_manip.C.

References Valeur::annule(), Scalar::get_dzpuis(), Scalar::get_etat(), Valeur::get_mg(), Mg3d::get_nzone(), Mg3d::get_type_r(), Map::mg, Scalar::set_dzpuis(), Scalar::set_etat_qcq(), Scalar::set_spectral_va(), and Map_radial::xsr.

Tbl * Map_et::integrale ( const Cmp & ci ) const [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.

Implements Map.

Definition at line 70 of file map_et_integ.C.

References Tbl::annule_hard(), Cmp::get_dzpuis(), Cmp::get_etat(), Mg3d::get_nzone(), Map::mg, rsx2drdx, Cmp::set_dzpuis(), and Cmp::va.

void Map_et::lapang	(	const Scalar &	uu,
		Scalar &	lap
	)			const `[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`

Implements Map.

Definition at line 279 of file map_et_lap.C.

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

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

Implements Map.

Definition at line 176 of file map_et_lap.C.

References Valeur::annule(), Valeur::base, Cmp::check_dzpuis(), Map_radial::d2rdtdx, Map_radial::d2rdx2, Valeur::dsdt(), Map_radial::dxdr, Cmp::get_etat(), Map::get_mg(), Cmp::get_mp(), Mg3d::get_nzone(), Mg3d::get_type_r(), Valeur::lapang(), Map_radial::lapr_tp, Map::mg, Valeur::set_base(), Cmp::set_dzpuis(), Cmp::set_etat_qcq(), Cmp::set_etat_zero(), Map_radial::sr2drdt, Map_radial::sr2stdrdp, Map_radial::srdrdt, Map_radial::srstdrdp, Map_radial::sstd2rdpdx, Valeur::stdsdp(), Valeur::sx(), Cmp::va, Map_radial::xsr, and Valeur::ylm().

void Map_et::laplacien	(	const Scalar &	uu,
		int	zec_mult_r,
		Scalar &	lap
	)			const `[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

Implements Map.

Definition at line 71 of file map_et_lap.C.

References Valeur::annule(), Valeur::base, Scalar::check_dzpuis(), Map_radial::d2rdtdx, Map_radial::d2rdx2, Valeur::d2sdx2(), Valeur::dsdt(), Valeur::dsdx(), Map_radial::dxdr, Scalar::get_etat(), Map::get_mg(), Tensor::get_mp(), Mg3d::get_nzone(), Scalar::get_spectral_va(), Mg3d::get_type_r(), Valeur::lapang(), Map_radial::lapr_tp, Map::mg, Valeur::set_base(), Scalar::set_dzpuis(), Scalar::set_etat_qcq(), Scalar::set_etat_zero(), Scalar::set_spectral_va(), Map_radial::sr2drdt, Map_radial::sr2stdrdp, Map_radial::srdrdt, Map_radial::srstdrdp, Map_radial::sstd2rdpdx, Valeur::stdsdp(), Valeur::sx(), Map_radial::xsr, and Valeur::ylm().

const Map_af & Map_et::mp_angu ( int ) const [virtual]

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

Valid only for the class Map_af.

Implements Map.

Definition at line 1041 of file map_et.C.

References c_est_pas_fait(), and Map::p_mp_angu.

void Map_radial::mult_cost ( Scalar & ci ) const [virtual, inherited]

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

Implements Map.

Definition at line 57 of file map_radial_th_manip.C.

References Scalar::get_etat(), Valeur::get_mg(), Map::mg, Valeur::mult_ct(), Scalar::set_etat_qcq(), and Scalar::set_spectral_va().

void Map_radial::mult_r ( Cmp & ci ) const [virtual, inherited]

Multiplication by r of a Cmp.

In the CED, there is only a decrement of dzpuis

Implements Map.

Definition at line 215 of file map_radial_r_manip.C.

References Cmp::annule(), Valeur::base, Cmp::get_dzpuis(), Cmp::get_etat(), Valeur::get_mg(), Mg3d::get_nzone(), Mg3d::get_type_r(), Map::mg, Valeur::mult_x(), Cmp::set_dzpuis(), Cmp::va, and Map_radial::xsr.

void Map_radial::mult_r ( Scalar & uu ) const [virtual, inherited]

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

Implements Map.

Definition at line 140 of file map_radial_r_manip.C.

References Scalar::annule(), Tensor::annule_domain(), Valeur::base, Scalar::get_etat(), Valeur::get_mg(), Mg3d::get_nzone(), Mg3d::get_type_r(), Map::mg, Valeur::mult_x(), Scalar::set_etat_qcq(), Scalar::set_spectral_va(), Valeur::sxm1_zec(), and Map_radial::xsr.

void Map_radial::mult_r_zec ( Scalar & ci ) const [virtual, inherited]

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

Implements Map.

Definition at line 292 of file map_radial_r_manip.C.

References Valeur::annule(), Valeur::base, Scalar::get_etat(), Valeur::get_mg(), Mg3d::get_nzone(), Mg3d::get_type_r(), Map::mg, Scalar::set_etat_qcq(), Scalar::set_spectral_va(), Valeur::sxm1_zec(), and Map_radial::xsr.

void Map_radial::mult_rsint ( Scalar & ci ) const [virtual, inherited]

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

Implements Map.

Definition at line 351 of file map_radial_r_manip.C.

References Scalar::annule(), Tensor::annule_domain(), Valeur::base, Scalar::get_etat(), Valeur::get_mg(), Mg3d::get_nzone(), Mg3d::get_type_r(), Map::mg, Valeur::mult_st(), Valeur::mult_x(), Scalar::set_etat_qcq(), Scalar::set_spectral_va(), Valeur::sxm1_zec(), and Map_radial::xsr.

void Map_radial::mult_sint ( Scalar & ci ) const [virtual, inherited]

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

Implements Map.

Definition at line 105 of file map_radial_th_manip.C.

References Scalar::get_etat(), Valeur::get_mg(), Map::mg, Valeur::mult_st(), Scalar::set_etat_qcq(), and Scalar::set_spectral_va().

void Map_et::operator= ( const Map_af & mpa ) [virtual]

Assignment to an affine mapping.

Implements Map_radial.

Definition at line 535 of file map_et.C.

References alpha, beta, ff, Map_af::get_alpha(), Map_af::get_beta(), Map::get_mg(), Mg3d::get_nzone(), Map::get_ori_x(), Map::get_ori_y(), Map::get_ori_z(), Map::get_rot_phi(), gg, Map::mg, reset_coord(), Map::set_ori(), and Map::set_rot_phi().

void Map_et::operator= ( const Map_et & mp ) [virtual]

Assignment to another Map_et.

Definition at line 509 of file map_et.C.

References alpha, beta, ff, get_alpha(), get_beta(), Map::get_mg(), Mg3d::get_nzone(), Map::get_ori_x(), Map::get_ori_y(), Map::get_ori_z(), Map::get_rot_phi(), gg, Map::mg, reset_coord(), Map::set_ori(), and Map::set_rot_phi().

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

Comparison operator (egality).

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

Comparison operator (egality).

Implements Map_radial.

Definition at line 980 of file map_et.C.

References alpha, beta, Map::bvect_cart, Map::bvect_spher, diffrelmax(), ff, Map::get_bvect_cart(), Map::get_bvect_spher(), Map::get_mg(), Mg3d::get_nzone(), Map::get_ori_x(), Map::get_ori_y(), Map::get_ori_z(), gg, max(), Map::mg, Map::ori_x, Map::ori_y, and Map::ori_z.

ostream & Map_et::operator>> ( ostream & ost ) const [private, virtual]

Operator >>.

Implements Map.

Definition at line 794 of file map_et.C.

References Valeur::affiche_seuil(), alpha, beta, ff, Mg3d::get_np(), Mg3d::get_nr(), Mg3d::get_nt(), Mg3d::get_nzone(), Mg3d::get_type_p(), Mg3d::get_type_t(), gg, Map::mg, Map::r, and val_r().

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

Computes the solution of a scalar Poisson equation.

Following the method explained in Sect. III.C of Bonazzola, Gourgoulhon & Marck, Phys. Rev. D 58 , 104020 (1998), the Poisson equation $\Delta u = \sigma$ is re-written as $a \tilde\Delta u = \sigma + R(u)$ , where $\tilde\Delta$ is the Laplacian in an affine mapping and R(u) contains the terms generated by the deviation of the mapping *this from spherical symmetry. This equation is solved by iterations. At each step J the equation effectively solved is $\tilde\Delta u^{J+1} = s^J$ where

$s^J = 1/a_l^{\rm max} \{ {\tt source} + R(u^J) + (a_l^{\rm max}-a) [ \lambda s^{J-1} + (1-\lambda) s^{J-2} ] \} \ ,$

with $a_l^{\rm max} := \max(a)$ in domain no. l and $\lambda$ is a relaxation parameter.

Parameters:

	source	[input] source $\sigma$ of the Poisson equation
	par	[input/output] parameters for the iterative method: \ `par.get_int(0)` : [input] maximum number of iterations \ `par.get_double(0)` : [input] relaxation parameter $\lambda$ \ `par.get_double(1)` : [input] required precision: the iterative method is stopped as soon as the relative difference between and $u^{J-1}$ is greater than `par.get_double(1)` \ `par.get_cmp_mod(0)` : [input/output] input : `Cmp` containing $s^{J-1}$ (cf. the above equation) to start the iteration (if nothing is known a priori, this `Cmp` must be set to zero); output: value of $s^{J-1}$ , to used in a next call to the routine \ `par.get_int_mod(0)` : [output] number of iterations actually used to get the solution.
	uu	[input/output] input : previously computed value of u to start the iteration (term R(u) ) (if nothing is known a priori, `uu` must be set to zero); output: solution u with the boundary condition u =0 at spatial infinity.

Implements Map.

Definition at line 97 of file map_et_poisson.C.

References alpha, Valeur::annule(), Valeur::base, Cmp::check_dzpuis(), Map_radial::d2rdtdx, Map_radial::d2rdx2, Cmp::dec2_dzpuis(), Cmp::dec_dzpuis(), diffrel(), Valeur::dsdt(), Map_radial::dxdr, Param::get_cmp_mod(), Param::get_double(), Cmp::get_dzpuis(), Cmp::get_etat(), Param::get_int(), Param::get_int_mod(), Cmp::get_mp(), Mg3d::get_nzone(), Mg3d::get_type_r(), Valeur::lapang(), Map_radial::lapr_tp, max(), Map::mg, Map_af::poisson(), rsxdxdr, Valeur::set_base(), Cmp::set_dzpuis(), Cmp::set_etat_qcq(), Mtbl::set_etat_qcq(), Map_radial::sr2drdt, Map_radial::sr2stdrdp, Map_radial::srdrdt, Map_radial::srstdrdp, Map_radial::sstd2rdpdx, Valeur::stdsdp(), Valeur::sx(), Mtbl::t, Cmp::va, Map_radial::xsr, and Valeur::ylm().

void Map_et::poisson2d	(	const Cmp &	source_mat,
		const Cmp &	source_quad,
		Param &	par,
		Cmp &	uu
	)			const `[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] Parameters to control the resolution : \ `par.get_double_mod(0)` : [output] constant `lambda` such that the source of the equation effectively solved is `source_mat` + lambda * source_quad , in order to fulfill the virial identity GRV2. \ If the theta basis is `T_SIN_I` , the following arguments are required: \ `par.get_int(0)` : [input] maximum number of iterations \ `par.get_double(0)` : [input] relaxation parameter \ `par.get_double(1)` : [input] required precision: the iterative method is stopped as soon as the relative difference between and $u^{J-1}$ is greater than `par.get_double(1)` \ `par.get_cmp_mod(0)` : [input/output] input : `Cmp` containing $s^{J-1}$ to start the iteration (if nothing is known a priori, this `Cmp` must be set to zero); output: value of $s^{J-1}$ , to used in a next call to the routine \ `par.get_int_mod(0)` : [output] number of iterations actually used to get the solution.
	uu	[input/output] solution u with the boundary condition u =0 at spatial infinity.

Implements Map.

Definition at line 75 of file map_et_poisson2d.C.

References alpha, Mtbl::annule(), Valeur::base, Cmp::check_dzpuis(), Map_radial::d2rdtdx, Map_radial::d2rdx2, Valeur::d2sdt2(), diffrel(), Valeur::dsdt(), Map_radial::dxdr, Param::get_cmp_mod(), Param::get_double(), Param::get_double_mod(), Cmp::get_dzpuis(), Cmp::get_etat(), Param::get_int(), Param::get_int_mod(), Map::get_mg(), Cmp::get_mp(), Mg3d::get_nzone(), Mg3d::get_type_r(), Cmp::import(), max(), Map::mg, Map_af::poisson2d(), rsxdxdr, Map_af::set_alpha(), Valeur::set_base(), Map_af::set_beta(), Cmp::set_dzpuis(), Cmp::set_etat_qcq(), Mtbl::set_etat_qcq(), Map_radial::sr2d2rdt2, Map_radial::sr2drdt, Map_radial::srdrdt, Valeur::sx(), Mtbl::t, T_COS_P, T_SIN_I, Cmp::va, val_r(), and Map_radial::xsr.

void Map_et::poisson_angu	(	const Scalar &	source,
		Param &	par,
		Scalar &	uu,
		double	lambda = `0`
	)			const `[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)

Implements Map.

Definition at line 588 of file map_et_poisson.C.

References Valeur::base, Map_radial::d2rdtdx, Map_radial::d2rdx2, diffrel(), Valeur::dsdt(), Valeur::dsdx(), Map_radial::dxdr, Scalar::filtre_r(), Param::get_cmp_mod(), Param::get_double(), Scalar::get_dzpuis(), Scalar::get_etat(), Param::get_int(), Param::get_int_mod(), Tensor::get_mp(), Mg3d::get_nr(), Mg3d::get_nzone(), Scalar::get_spectral_va(), Map_radial::lapr_tp, max(), Map::mg, Scalar::mult_r(), Map_af::poisson_angu(), Valeur::set_base(), Scalar::set_dzpuis(), Scalar::set_spectral_va(), Map_radial::sr2drdt, Map_radial::sr2stdrdp, Map_radial::srdrdt, Map_radial::srstdrdp, Map_radial::sstd2rdpdx, and Valeur::stdsdp().

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

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 $\psi(0)=0$ .

Implements Map.

Definition at line 449 of file map_radial_poisson_cpt.C.

References Cmp::annule(), Mtbl::annule_hard(), Tbl::annule_hard(), Map::bvect_spher, Valeur::c_cf, Valeur::coef(), diffrel(), Map_af::dsdr(), Cmp::dsdr(), Param::get_double(), Tenseur::get_etat(), Cmp::get_etat(), Mg3d::get_grille3d(), Param::get_int(), Param::get_int_mod(), Tenseur::get_mp(), Cmp::get_mp(), Mg3d::get_np(), Mg3d::get_nr(), Mg3d::get_nt(), Mg3d::get_nzone(), Tenseur::get_triad(), Cmp::laplacien(), Map_af::laplacien(), max(), Map::mg, min(), Map_radial::poisson_compact(), Mtbl::set(), Tbl::set(), Cmp::set_etat_qcq(), Cmp::set_etat_zero(), Cmp::srdsdt(), Cmp::srstdsdp(), Valeur::std_base_scal(), Tbl::t, Cmp::va, Grille3d::x, Valeur::ylm(), and Valeur::ylm_i().

void Map_radial::poisson_compact	(	const Cmp &	source,
		const Cmp &	aa,
		const Tenseur &	bb,
		const Param &	par,
		Cmp &	psi
	)			const `[virtual, inherited]`

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] parameters of the iterative method of resolution : \ `par.get_int(0)` : [input] maximum number of iterations \ `par.get_double(0)` : [input] required precision: the iterative method is stopped as soon as the relative difference between $\psi^J$ and $\psi^{J-1}$ is greater than `par.get_double(0)` \ `par.get_double(1)` : [input] relaxation parameter $\lambda$ \ `par.get_int_mod(0)` : [output] number of iterations actually used to get the solution.
	psi	[input/output]: input : previously computed value of $\psi$ to start the iteration (if nothing is known a priori, `psi` must be set to zero); output: solution $\psi$ which satisfies $\psi(0)=0$ .

Implements Map.

Definition at line 151 of file map_radial_poisson_cpt.C.

References Cmp::annule(), Map::bvect_spher, Valeur::c_cf, Valeur::coef(), Valeur::d2sdx2(), diffrel(), Cmp::dsdr(), Valeur::dsdx(), Map_radial::dxdr, Param::get_double(), Tenseur::get_etat(), Cmp::get_etat(), Param::get_int(), Param::get_int_mod(), Tenseur::get_mp(), Cmp::get_mp(), Mg3d::get_nr(), Mg3d::get_nzone(), Tenseur::get_triad(), Valeur::lapang(), Cmp::laplacien(), max(), Map::mg, min(), Valeur::mult_x(), Cmp::set_etat_qcq(), Cmp::set_etat_zero(), Cmp::srdsdt(), Cmp::srstdsdp(), Valeur::std_base_scal(), Valeur::sx(), Cmp::va, Valeur::ylm(), and Valeur::ylm_i().

void Map_et::poisson_frontiere	(	const Cmp &	,
		const Valeur &	,
		int	,
		int	,
		Cmp &	,
		double	= `0.`,
		double	= `0.`
	)			const `[virtual]`

Not yet implemented.

Implements Map.

Definition at line 120 of file cmp_pde_frontiere.C.

void Map_et::poisson_interne	(	const Cmp &	source,
		const Valeur &	limite,
		Param &	par,
		Cmp &	pot
	)			const `[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.

Implements Map.

Definition at line 270 of file cmp_pde_frontiere.C.

References alpha, Valeur::base, Map_radial::d2rdtdx, Map_radial::d2rdx2, diffrel(), Valeur::dsdt(), Map_radial::dxdr, Param::get_cmp_mod(), Param::get_double(), Cmp::get_etat(), Param::get_int(), Param::get_int_mod(), Cmp::get_mp(), Mg3d::get_nzone(), Valeur::lapang(), Map_radial::lapr_tp, max(), Map::mg, Map_af::poisson_interne(), rsxdxdr, Valeur::set_base(), Cmp::set_etat_qcq(), Mtbl::set_etat_qcq(), Map_radial::sr2drdt, Map_radial::sr2stdrdp, Map_radial::srdrdt, Map_radial::srstdrdp, Map_radial::sstd2rdpdx, Valeur::stdsdp(), Valeur::sx(), Mtbl::t, Cmp::va, Map_radial::xsr, and Valeur::ylm().

void Map_et::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 `[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] parameters for the iterative method: \ `par.get_int(0)` : [input] maximum number of iterations \ `par.get_double(0)` : [input] relaxation parameter $\lambda$ \ `par.get_double(1)` : [input] required precision: the iterative method is stopped as soon as the relative difference between and $u^{J-1}$ is greater than `par.get_double(1)` \ `par.get_cmp_mod(0)` : [input/output] input : `Cmp` containing $s^{J-1}$ (cf. the above equation) to start the iteration (if nothing is known a priori, this `Cmp` must be set to zero); output: value of $s^{J-1}$ , to used in a next call to the routine \ `par.get_int_mod(0)` : [output] number of iterations actually used to get the solution.
	uu	[input/output] input : previously computed value of u to start the iteration (term R(u) ) (if nothing is known a priori, `uu` must be set to zero); 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

Implements Map.

Definition at line 80 of file map_et_poisson_regu.C.

References alpha, Valeur::annule(), Valeur::base, Cmp::check_dzpuis(), Map_radial::d2rdtdx, Map_radial::d2rdx2, Cmp::dec2_dzpuis(), Cmp::dec_dzpuis(), diffrel(), Valeur::dsdt(), Map_radial::dxdr, Map::get_bvect_spher(), Param::get_cmp_mod(), Param::get_double(), Cmp::get_dzpuis(), Cmp::get_etat(), Param::get_int(), Param::get_int_mod(), Cmp::get_mp(), Mg3d::get_nzone(), Mg3d::get_type_r(), Valeur::lapang(), Map_radial::lapr_tp, max(), Map::mg, Map_af::poisson_regular(), rsxdxdr, Tenseur::set(), Valeur::set_base(), Cmp::set_dzpuis(), Cmp::set_etat_qcq(), Mtbl::set_etat_qcq(), Tenseur::set_triad(), Map_radial::sr2drdt, Map_radial::sr2stdrdp, Map_radial::srdrdt, Map_radial::srstdrdp, Map_radial::sstd2rdpdx, Valeur::stdsdp(), Valeur::sx(), Mtbl::t, Cmp::va, Map_radial::xsr, and Valeur::ylm().

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

Computes the solution of a scalar Poisson equation with a Tau method.

Following the method explained in Sect. III.C of Bonazzola, Gourgoulhon & Marck, Phys. Rev. D 58 , 104020 (1998), the Poisson equation $\Delta u = \sigma$ is re-written as $a \tilde\Delta u = \sigma + R(u)$ , where $\tilde\Delta$ is the Laplacian in an affine mapping and R(u) contains the terms generated by the deviation of the mapping *this from spherical symmetry. This equation is solved by iterations. At each step J the equation effectively solved is $\tilde\Delta u^{J+1} = s^J$ where

$s^J = 1/a_l^{\rm max} \{ {\tt source} + R(u^J) + (a_l^{\rm max}-a) [ \lambda s^{J-1} + (1-\lambda) s^{J-2} ] \} \ ,$

with $a_l^{\rm max} := \max(a)$ in domain no. l and $\lambda$ is a relaxation parameter.

Parameters:

	source	[input] source $\sigma$ of the Poisson equation
	par	[input/output] parameters for the iterative method: \ `par.get_int(0)` : [input] maximum number of iterations \ `par.get_double(0)` : [input] relaxation parameter $\lambda$ \ `par.get_double(1)` : [input] required precision: the iterative method is stopped as soon as the relative difference between and $u^{J-1}$ is greater than `par.get_double(1)` \ `par.get_cmp_mod(0)` : [input/output] input : `Cmp` containing $s^{J-1}$ (cf. the above equation) to start the iteration (if nothing is known a priori, this `Cmp` must be set to zero); output: value of $s^{J-1}$ , to used in a next call to the routine \ `par.get_int_mod(0)` : [output] number of iterations actually used to get the solution.
	uu	[input/output] input : previously computed value of u to start the iteration (term R(u) ) (if nothing is known a priori, `uu` must be set to zero); output: solution u with the boundary condition u =0 at spatial infinity.

Implements Map.

Definition at line 346 of file map_et_poisson.C.

References alpha, Valeur::annule(), Valeur::base, Cmp::check_dzpuis(), Map_radial::d2rdtdx, Map_radial::d2rdx2, Cmp::dec2_dzpuis(), Cmp::dec_dzpuis(), diffrel(), Valeur::dsdt(), Map_radial::dxdr, Param::get_cmp_mod(), Param::get_double(), Cmp::get_dzpuis(), Cmp::get_etat(), Param::get_int(), Param::get_int_mod(), Cmp::get_mp(), Mg3d::get_nzone(), Mg3d::get_type_r(), Valeur::lapang(), Map_radial::lapr_tp, max(), Map::mg, Map_af::poisson_tau(), rsxdxdr, Valeur::set_base(), Cmp::set_dzpuis(), Cmp::set_etat_qcq(), Mtbl::set_etat_qcq(), Map_radial::sr2drdt, Map_radial::sr2stdrdp, Map_radial::srdrdt, Map_radial::srstdrdp, Map_radial::sstd2rdpdx, Valeur::stdsdp(), Valeur::sx(), Mtbl::t, Cmp::va, Map_radial::xsr, and Valeur::ylm().

void Map_et::primr	(	const Scalar &	uu,
		Scalar &	resu,
		bool	null_infty
	)			const `[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

Implements Map.

Definition at line 106 of file map_et_integ.C.

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

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, inherited]`

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`.

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

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 `Scalar` at the grid points defined by `this`.

Definition at line 169 of file map_radial_reevaluate.C.

References Param::add_double(), Param::add_int(), Param::add_int_mod(), Scalar::annule(), Coord::c, Valeur::c, Valeur::c_cf, Valeur::coef(), Coord::fait(), Scalar::get_dzpuis(), Scalar::get_etat(), Tensor::get_mp(), Mg3d::get_np(), Mg3d::get_nr(), Mg3d::get_nt(), Mg3d::get_nzone(), Map::mg, Map::r, Valeur::set_etat_c_qcq(), Tbl::set_etat_qcq(), Mtbl::set_etat_qcq(), Scalar::set_spectral_va(), Mtbl::t, Map_radial::val_lx_jk(), and Mtbl_cf::val_point_jk().

void Map_radial::reevaluate	(	const Map *	mp_prev,
		int	nzet,
		Cmp &	uu
	)			const `[virtual, inherited]`

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`.

Definition at line 54 of file map_radial_reevaluate.C.

References Param::add_double(), Param::add_int(), Param::add_int_mod(), Cmp::annule(), Coord::c, Coord::fait(), Cmp::get_dzpuis(), Cmp::get_etat(), Cmp::get_mp(), Mg3d::get_np(), Mg3d::get_nr(), Mg3d::get_nt(), Mg3d::get_nzone(), Map::mg, Map::r, Tbl::set_etat_qcq(), Mtbl::set_etat_qcq(), Mtbl::t, Cmp::va, Map_radial::val_lx_jk(), and Mtbl_cf::val_point_jk().

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

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, inherited]`

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_radial::reevaluate_symy	(	const Map *	mp_prev,
		int	nzet,
		Scalar &	uu
	)			const `[virtual, inherited]`

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

Case where the Scalar is symmetric with respect to 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`.

Definition at line 189 of file map_radial_reeval_symy.C.

References Param::add_double(), Param::add_int(), Param::add_int_mod(), Scalar::annule(), Coord::c, Valeur::c, Valeur::c_cf, Valeur::coef(), Coord::fait(), Scalar::get_dzpuis(), Scalar::get_etat(), Tensor::get_mp(), Mg3d::get_np(), Mg3d::get_nr(), Mg3d::get_nt(), Mg3d::get_nzone(), Mg3d::get_type_p(), Map::mg, Map::r, Valeur::set_etat_c_qcq(), Tbl::set_etat_qcq(), Mtbl::set_etat_qcq(), Scalar::set_spectral_va(), Mtbl::t, Map_radial::val_lx_jk(), and Mtbl_cf::val_point_jk_symy().

void Map_radial::reevaluate_symy	(	const Map *	mp_prev,
		int	nzet,
		Cmp &	uu
	)			const `[virtual, inherited]`

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

Case where the Cmp is symmetric with respect to 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`.

Definition at line 55 of file map_radial_reeval_symy.C.

References Param::add_double(), Param::add_int(), Param::add_int_mod(), Cmp::annule(), Coord::c, Coord::fait(), Cmp::get_dzpuis(), Cmp::get_etat(), Cmp::get_mp(), Mg3d::get_np(), Mg3d::get_nr(), Mg3d::get_nt(), Mg3d::get_nzone(), Mg3d::get_type_p(), Map::mg, Map::r, Tbl::set_etat_qcq(), Mtbl::set_etat_qcq(), Mtbl::t, Cmp::va, Map_radial::val_lx_jk(), and Mtbl_cf::val_point_jk_symy().

void Map_et::reset_coord ( ) [protected, virtual]

Resets all the member Coords.

Reimplemented from Map_radial.

Definition at line 624 of file map_et.C.

References Coord::del_t(), rsx2drdx, and rsxdxdr.

void Map_et::resize	(	int	l,
		double	lambda
	)			`[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.

Implements Map.

Definition at line 924 of file map_et.C.

References alpha, beta, ff, Mg3d::get_type_r(), gg, Map::mg, reset_coord(), and Valeur::set().

void Map_et::resize_extr ( double lambda )

Rescales the outer boundary of the outermost domain in the case of non-compactified external domain.

The inner boundary is unchanged.

Parameters:

lambda

[input] factor by which the value of the radius of the outermost domain is to be multiplied.

Definition at line 51 of file map_et_resize_extr.C.

References alpha, beta, Mg3d::get_nzone(), Mg3d::get_type_r(), Map::mg, and reset_coord().

void Map_et::sauve ( FILE * fich ) const [virtual]

Save in a file.

Reimplemented from Map_radial.

Definition at line 775 of file map_et.C.

References alpha, beta, ff, fwrite_be(), Mg3d::get_nzone(), gg, Map::mg, and Valeur::sauve().

void Map_et::set_alpha	(	double	alpha0,
		int	l
	)

Modifies the value of $\alpha$ in domain no. l.

Definition at line 420 of file map_et.C.

References alpha, and reset_coord().

void Map_et::set_beta	(	double	beta0,
		int	l
	)

Modifies the value of $\beta$ in domain no. l.

Definition at line 431 of file map_et.C.

References beta, and reset_coord().

void Map_et::set_coord ( ) [private]

Assignement of the building functions to the member Coords.

Definition at line 580 of file map_et.C.

References Map::cosp, Map::cost, Map_radial::d2rdtdx, Map_radial::d2rdx2, Map_radial::drdt, Map_radial::dxdr, Map_radial::lapr_tp, Map::phi, Map::r, rsx2drdx, rsxdxdr, Coord::set(), Map::sinp, Map::sint, Map_radial::sr2d2rdt2, Map_radial::sr2drdt, Map_radial::sr2stdrdp, Map_radial::srdrdt, Map_radial::srstdrdp, Map_radial::sstd2rdpdx, Map_radial::stdrdp, Map::tet, Map::x, Map::xa, Map_radial::xsr, Map::y, Map::ya, Map::z, and Map::za.

void Map_et::set_ff ( const Valeur & ffi )

Assigns a given value to the function $F(\theta',\phi')$ .

Definition at line 558 of file map_et.C.

References ff, and reset_coord().

void Map_et::set_gg ( const Valeur & ggi )

Assigns a given value to the function $G(\theta',\phi')$ .

Definition at line 566 of file map_et.C.

References gg, and reset_coord().

void Map::set_ori	(	double	xa0,
		double	ya0,
		double	za0
	)			`[inherited]`

Sets a new origin.

Definition at line 249 of file map.C.

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

void Map::set_rot_phi ( double phi0 ) [inherited]

Sets a new rotation angle.

Definition at line 259 of file map.C.

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

void Map_et::srdsdt	(	const Scalar &	uu,
		Scalar &	resu
	)			const `[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`

Implements Map.

Definition at line 387 of file map_et_deriv.C.

References Valeur::annule(), Valeur::base, Valeur::coef(), Valeur::dsdt(), Valeur::dsdx(), Map_radial::dxdr, Scalar::get_dzpuis(), Scalar::get_etat(), Map::get_mg(), Tensor::get_mp(), Mg3d::get_nzone(), Scalar::get_spectral_va(), Mg3d::get_type_r(), Map::mg, Valeur::mult_x(), Scalar::set_dzpuis(), Scalar::set_etat_zero(), Map_radial::srdrdt, Valeur::sx(), and Map_radial::xsr.

void Map_et::srdsdt	(	const Cmp &	ci,
		Cmp &	resu
	)			const `[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`

Implements Map.

Definition at line 333 of file map_et_deriv.C.

References Valeur::base, Cmp::check_dzpuis(), Valeur::dsdt(), Valeur::dsdx(), Map_radial::dxdr, Cmp::get_etat(), Map::get_mg(), Cmp::get_mp(), Mg3d::get_nzone(), Mg3d::get_type_r(), Map::mg, Cmp::set_dzpuis(), Cmp::set_etat_zero(), Map_radial::srdrdt, Valeur::sx(), Cmp::va, and Map_radial::xsr.

void Map_et::srstdsdp	(	const Scalar &	uu,
		Scalar &	resu
	)			const `[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`

Implements Map.

Definition at line 536 of file map_et_deriv.C.

References Valeur::annule(), Valeur::base, Valeur::coef(), Valeur::dsdp(), Valeur::dsdx(), Map_radial::dxdr, Scalar::get_dzpuis(), Scalar::get_etat(), Map::get_mg(), Tensor::get_mp(), Mg3d::get_nzone(), Scalar::get_spectral_va(), Mg3d::get_type_r(), Map::mg, Valeur::mult_x(), Scalar::set_dzpuis(), Scalar::set_etat_zero(), Map_radial::srstdrdp, Valeur::ssint(), Valeur::sx(), and Map_radial::xsr.

void Map_et::srstdsdp	(	const Cmp &	ci,
		Cmp &	resu
	)			const `[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`

Implements Map.

Definition at line 481 of file map_et_deriv.C.

References Valeur::base, Cmp::check_dzpuis(), Valeur::dsdp(), Valeur::dsdx(), Map_radial::dxdr, Cmp::get_etat(), Map::get_mg(), Cmp::get_mp(), Mg3d::get_nzone(), Mg3d::get_type_r(), Map::mg, Cmp::set_dzpuis(), Cmp::set_etat_zero(), Map_radial::srstdrdp, Valeur::ssint(), Valeur::sx(), Cmp::va, and Map_radial::xsr.

void Map_et::stdsdp	(	const Scalar &	uu,
		Scalar &	resu
	)			const `[virtual]`

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

Parameters:

	uu	[input] scalar field
	resu	[output] derivative of `uu`

Implements Map.

Definition at line 670 of file map_et_deriv.C.

References Valeur::dsdx(), Map_radial::dxdr, Valeur::get_base(), Scalar::get_etat(), Map::get_mg(), Tensor::get_mp(), Scalar::get_spectral_va(), Map::mg, Valeur::set_base(), Scalar::set_etat_zero(), Map_radial::stdrdp, and Valeur::stdsdp().

void Map_et::val_lx	(	double	rr,
		double	theta,
		double	pphi,
		const Param &	par,
		int &	l,
		double &	xi
	)			const `[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: \ `par.get_int(0)` : [input] maximum number of iterations in the secant method to locate $\xi$ \ `par.get_int_mod(0)` : [output] effective number of iterations used \ `par.get_double(0)` : [input] absolute precision in the secant method to locate $\xi$
	l	[output] value of the domain index
	xi	[output] value of $\xi$

Implements Map.

Definition at line 165 of file map_et_radius.C.

References Param::add_double(), alpha, beta, Valeur::c, ff, Param::get_double(), Tbl::get_etat(), Valeur::get_etat(), Param::get_int(), Param::get_int_mod(), Mg3d::get_nzone(), Mg3d::get_type_r(), gg, Map::mg, Mtbl::t, Valeur::val_point(), and zerosec().

void Map_et::val_lx	(	double	rr,
		double	theta,
		double	pphi,
		int &	l,
		double &	xi
	)			const `[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 $\xi$

Implements Map.

Definition at line 142 of file map_et_radius.C.

References Param::add_double(), Param::add_int(), and Param::add_int_mod().

void Map_et::val_lx_jk	(	double	rr,
		int	j,
		int	k,
		const Param &	par,
		int &	l,
		double &	xi
	)			const `[virtual]`

Computes the domain index l and the value of $\xi$ corresponding to a point of arbitrary r but collocation values of $(\theta, \phi)$ .

Parameters:

	rr	[input] value of r
	j	[input] index of the collocation point in $\theta$
	k	[input] index of the collocation point in $\phi$
	par	[input/output] parameters to control the accuracy of the computation: \ `par.get_int(0)` : [input] maximum number of iterations in the secant method to locate $\xi$ \ `par.get_int_mod(0)` : [output] effective number of iterations used \ `par.get_double(0)` : [input] absolute precision in the secant method to locate $\xi$
	l	[output] value of the domain index
	xi	[output] value of $\xi$

Implements Map_radial.

Definition at line 414 of file map_et_radius.C.

References Param::add_double(), alpha, beta, Valeur::c, ff, Param::get_double(), Tbl::get_etat(), Valeur::get_etat(), Param::get_int(), Param::get_int_mod(), Mg3d::get_nzone(), Mg3d::get_type_r(), gg, Map::mg, Mtbl::t, and zerosec().

double Map_et::val_r	(	int	l,
		double	xi,
		double	theta,
		double	pphi
	)			const `[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 $r=R_l(\xi, \theta', \phi')$

Implements Map.

Definition at line 88 of file map_et_radius.C.

References alpha, beta, ff, Mg3d::get_type_r(), gg, Map::mg, and Valeur::val_point().

double Map_et::val_r_jk	(	int	l,
		double	xi,
		int	j,
		int	k
	)			const `[virtual]`

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

Parameters:

	l	[input] index of the domain
	xi	[input] value of $\xi$
	j	[input] index of the collocation point in $\theta'$
	k	[input] index of the collocation point in $\phi'$

Returns:: value of $r=R_l(\xi, {\theta'}_j, {\phi'}_k)$

Implements Map_radial.

Definition at line 363 of file map_et_radius.C.

References alpha, beta, ff, Mg3d::get_type_r(), gg, and Map::mg.

Friends And Related Function Documentation

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

Operator <<.

Member Data Documentation

Tbl** Map_et::aa [private]

Array (size: mg->nzone ) of Tbl which stores the values of $A(\xi)$ in each domain.

Definition at line 2761 of file map.h.

Tbl Map_et::aasx [private]

Values at the nr collocation points of $A(\xi)/\xi$ in the nucleus.

Definition at line 2774 of file map.h.

Tbl Map_et::aasx2 [private]

Values at the nr collocation points of $A(\xi)/\xi^2$ in the nucleus.

Definition at line 2777 of file map.h.

double* Map_et::alpha [private]

Array (size: mg->nzone ) of the values of $\alpha$ in each domain.

Definition at line 2754 of file map.h.

Tbl** Map_et::bb [private]

Array (size: mg->nzone ) of Tbl which stores the values of $B(\xi)$ in each domain.

Definition at line 2792 of file map.h.

Tbl Map_et::bbsx [private]

Values at the nr collocation points of $B(\xi)/\xi$ in the nucleus.

Definition at line 2805 of file map.h.

Tbl Map_et::bbsx2 [private]

Values at the nr collocation points of $B(\xi)/\xi^2$ in the nucleus.

Definition at line 2808 of file map.h.

double* Map_et::beta [private]

Array (size: mg->nzone ) of the values of $\beta$ in each domain.

Definition at line 2756 of file map.h.

Base_vect_cart Map::bvect_cart [protected, inherited]

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, inherited]

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 [inherited]

$\cos\phi$

Definition at line 720 of file map.h.

Coord Map::cost [inherited]

$\cos\theta$

Definition at line 718 of file map.h.

Coord Map_radial::d2rdtdx [inherited]

$\partial^2 R/\partial\xi\partial\theta'$ in the nucleus and in the non-compactified shells; \ $-\partial^2 U/\partial\xi\partial\theta'$ in the compactified outer domain.

Definition at line 1636 of file map.h.

Coord Map_radial::d2rdx2 [inherited]

$\partial^2 R/\partial\xi^2$ in the nucleus and in the non-compactified shells; \ $-\partial^2 U/\partial\xi^2$ in the compactified outer domain.

Definition at line 1615 of file map.h.

Tbl** Map_et::daa [private]

Array (size: mg->nzone ) of Tbl which stores the values of $A'(\xi)$ in each domain.

Definition at line 2766 of file map.h.

Tbl** Map_et::dbb [private]

Array (size: mg->nzone ) of Tbl which stores the values of $B'(\xi)$ in each domain.

Definition at line 2797 of file map.h.

Tbl** Map_et::ddaa [private]

Array (size: mg->nzone ) of Tbl which stores the values of $A''(\xi)$ in each domain.

Definition at line 2771 of file map.h.

Tbl** Map_et::ddbb [private]

Array (size: mg->nzone ) of Tbl which stores the values of $B''(\xi)$ in each domain.

Definition at line 2802 of file map.h.

Coord Map_radial::drdt [inherited]

$\partial R/\partial\theta'$ in the nucleus and in the non-compactified shells; \ $-\partial U/\partial\theta'$ in the compactified external domain (CED).

Definition at line 1564 of file map.h.

Coord Map_radial::dxdr [inherited]

$1/(\partial R/\partial\xi) = \partial \xi /\partial r$ in the nucleus and in the non-compactified shells; \ $-1/(\partial U/\partial\xi) = - \partial \xi /\partial u$ in the compactified outer domain.

Definition at line 1556 of file map.h.

Valeur Map_et::ff [private]

Values of the function $F(\theta', \phi')$ at the nt*np angular collocation points in each domain.

The Valeur ff is defined on the multi-grid mg->g_angu (cf. class Mg3d ).

Definition at line 2815 of file map.h.

Valeur Map_et::gg [private]

Values of the function $G(\theta', \phi')$ at the nt*np angular collocation points in each domain.

The Valeur gg is defined on the multi-grid mg->g_angu (cf. class Mg3d ).

Definition at line 2822 of file map.h.

Coord Map_radial::lapr_tp [inherited]

$1/R^2 \times [ 1/\sin(\theta)\times \partial /\partial\theta' (\sin\theta \partial R /\partial\theta') + 1/\sin^2\theta \partial^2 R /\partial{\varphi'}^2]$ in the nucleus and in the non-compactified shells; \ $- 1/U^2 \times [ 1/\sin(\theta)\times \partial /\partial\theta' (\sin\theta \partial U /\partial\theta') + 1/\sin^2\theta \partial^2 U /\partial{\varphi'}^2]$ in the compactified outer domain.

Definition at line 1627 of file map.h.

const Mg3d* Map::mg [protected, inherited]

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

Definition at line 672 of file map.h.

double Map::ori_x [protected, inherited]

Absolute coordinate x of the origin.

Definition at line 674 of file map.h.

double Map::ori_y [protected, inherited]

Absolute coordinate y of the origin.

Definition at line 675 of file map.h.

double Map::ori_z [protected, inherited]

Absolute coordinate z of the origin.

Definition at line 676 of file map.h.

Cmp* Map::p_cmp_zero [protected, inherited]

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, inherited]

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, inherited]

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, inherited]

Pointer on the "angular" mapping.

Definition at line 711 of file map.h.

Coord Map::phi [inherited]

$\phi$ coordinate centered on the grid

Definition at line 716 of file map.h.

Coord Map::r [inherited]

r coordinate centered on the grid

Definition at line 714 of file map.h.

double Map::rot_phi [protected, inherited]

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

Definition at line 677 of file map.h.

Coord Map_et::rsx2drdx

$[ R/ (\alpha \xi + \beta) ]^2 (\partial R/\partial \xi) / \alpha$ in the nucleus and the shells; \ $\partial U/\partial \xi / \alpha$ in the outermost compactified domain.

Definition at line 2837 of file map.h.

Coord Map_et::rsxdxdr

$1/(\partial R/\partial \xi) R/\xi$ in the nucleus; \ $1/(\partial R/\partial \xi) R/(\xi + \beta/\alpha)$ in the shells; \ $1/(\partial U/\partial \xi) U/(\xi-1)$ in the outermost compactified domain.

Definition at line 2830 of file map.h.

Coord Map::sinp [inherited]

$\sin\phi$

Definition at line 719 of file map.h.

Coord Map::sint [inherited]

$\sin\theta$

Definition at line 717 of file map.h.

Coord Map_radial::sr2d2rdt2 [inherited]

$1/R^2 \partial^2 R/\partial{\theta'}^2$ in the nucleus and in the non-compactified shells; \ $-1/U^2 \partial^2 U/\partial{\theta'}^2$ in the compactified outer domain.

Definition at line 1653 of file map.h.

Coord Map_radial::sr2drdt [inherited]

$1/R^2 \times (\partial R/\partial\theta')$ in the nucleus and in the non-compactified shells; \ $-1/U^2 \times (\partial U/\partial\theta')$ in the compactified outer domain.

Definition at line 1596 of file map.h.

Coord Map_radial::sr2stdrdp [inherited]

$1/(R^2\sin\theta) \times (\partial R/\partial\varphi')$ in the nucleus and in the non-compactified shells; \ $-1/(U^2\sin\theta) \times (\partial U/\partial\varphi')$ in the compactified outer domain.

Definition at line 1604 of file map.h.

Coord Map_radial::srdrdt [inherited]

$1/R \times (\partial R/\partial\theta')$ in the nucleus and in the non-compactified shells; \ $-1/U \times (\partial U/\partial\theta)$ in the compactified outer domain.

Definition at line 1580 of file map.h.

Coord Map_radial::srstdrdp [inherited]

$1/(R\sin\theta) \times (\partial R/\partial\varphi')$ in the nucleus and in the non-compactified shells; \ $-1/(U\sin\theta) \times (\partial U/\partial\varphi')$ in the compactified outer domain.

Definition at line 1588 of file map.h.

Coord Map_radial::sstd2rdpdx [inherited]

$1/\sin\theta \times \partial^2 R/\partial\xi\partial\varphi'$ in the nucleus and in the non-compactified shells; \ $-1/\sin\theta \times \partial^2 U/\partial\xi\partial\varphi'$ in the compactified outer domain.

Definition at line 1644 of file map.h.

Coord Map_radial::stdrdp [inherited]

${1\over\sin\theta} \partial R/\partial\varphi'$ in the nucleus and in the non-compactified shells; \ $-{1\over\sin\theta}\partial U/\partial\varphi'$ in the compactified external domain (CED).

Definition at line 1572 of file map.h.

Coord Map::tet [inherited]

$\theta$ coordinate centered on the grid

Definition at line 715 of file map.h.

Coord Map::x [inherited]

x coordinate centered on the grid

Definition at line 722 of file map.h.

Coord Map::xa [inherited]

Absolute x coordinate.

Definition at line 726 of file map.h.

Coord Map_radial::xsr [inherited]

$\xi/R$ in the nucleus; \ 1/R in the non-compactified shells; \ $(\xi-1)/U$ in the compactified outer domain.

Definition at line 1545 of file map.h.

Coord Map::y [inherited]

y coordinate centered on the grid

Definition at line 723 of file map.h.

Coord Map::ya [inherited]

Absolute y coordinate.

Definition at line 727 of file map.h.

Coord Map::z [inherited]

z coordinate centered on the grid

Definition at line 724 of file map.h.

Coord Map::za [inherited]

Absolute z coordinate.

Definition at line 728 of file map.h.

Tbl Map_et::zaasx [private]

Values at the nr collocation points of $A(\xi)/(\xi-1)$ in the outermost compactified domain.

Definition at line 2782 of file map.h.

Tbl Map_et::zaasx2 [private]

Values at the nr collocation points of $A(\xi)/(\xi-1)^2$ in the outermost compactified domain.

Definition at line 2787 of file map.h.

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

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

Public Member Functions

Public Attributes

Protected Member Functions

Protected Attributes

Private Member Functions

Private Attributes

Friends

Detailed Description

Constructor & Destructor Documentation

Member Function Documentation

Friends And Related Function Documentation

Member Data Documentation

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