Affine radial mapping. More...

#include <map.h>

Inheritance diagram for Lorene::Map_af:

Public Member Functions
	Map_af (const Mg3d &mgrille, const double *r_limits)
	Standard Constructor. More...

	Map_af (const Mg3d &mgrille, const Tbl &r_limits)
	Standard Constructor with Tbl. More...

	Map_af (const Map_af &)
	Copy constructor. More...

	Map_af (const Mg3d &, const string &)
	Constructor from a formatted file. More...

	Map_af (const Mg3d &, FILE *)
	Constructor from a file (see `sauve(FILE*)` ) More...

	Map_af (const Map &)
	Constructor from a general mapping. More...

virtual	~Map_af ()
	Destructor. More...

virtual void	operator= (const Map_af &)
	Assignment to another affine mapping. More...

const double *	get_alpha () const
	Returns the pointer on the array `alpha`. More...

const double *	get_beta () const
	Returns the pointer on the array `beta`. More...

virtual const Map_af &	mp_angu (int) const
	Returns the "angular" mapping for the outside of domain `l_zone`. More...

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. More...

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 $(r, \theta, \phi)$ . More...

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 $(r, \theta, \phi)$ . More...

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. More...

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 $(\theta, \phi)$ . More...

virtual bool	operator== (const Map &) const
	Comparison operator (egality) More...

virtual void	sauve (FILE *) const
	Save in a file. More...

virtual void	homothetie (double lambda)
	Sets a new radial scale. More...

virtual void	resize (int l, double lambda)
	Rescales the outer boundary of one domain. More...

void	homothetie_interne (double lambda)
	Sets a new radial scale at the bondary between the nucleus and the first shell. More...

virtual void	adapt (const Cmp &ent, const Param &par, int nbr=0)
	Adaptation of the mapping to a given scalar field. More...

void	set_alpha (double alpha0, int l)
	Modifies the value of $\alpha$ in domain no. l. More...

void	set_beta (double beta0, int l)
	Modifies the value of $\beta$ in domain no. l. More...

virtual void	dsdxi (const Cmp &ci, Cmp &resu) const
	Computes $\partial/ \partial \xi$ of a `Cmp`. More...

virtual void	dsdr (const Cmp &ci, Cmp &resu) const
	Computes $\partial/ \partial r$ of a `Cmp`. More...

virtual void	srdsdt (const Cmp &ci, Cmp &resu) const
	Computes $1/r \partial/ \partial \theta$ of a `Cmp`. More...

virtual void	srstdsdp (const Cmp &ci, Cmp &resu) const
	Computes $1/(r\sin\theta) \partial/ \partial \phi$ of a `Cmp`. More...

virtual void	dsdr (const Scalar &uu, Scalar &resu) const
	Computes $\partial/ \partial r$ of a `Scalar`. More...

virtual void	dsdxi (const Scalar &uu, Scalar &resu) const
	Computes $\partial/ \partial \xi$ of a `Scalar`. More...

virtual void	dsdradial (const Scalar &, Scalar &) const
	Computes $\partial/ \partial r$ of a `Scalar`. More...

virtual void	srdsdt (const Scalar &uu, Scalar &resu) const
	Computes $1/r \partial/ \partial \theta$ of a `Scalar`. More...

virtual void	srstdsdp (const Scalar &uu, Scalar &resu) const
	Computes $1/(r\sin\theta) \partial/ \partial \phi$ of a `Scalar`. More...

virtual void	dsdt (const Scalar &uu, Scalar &resu) const
	Computes $\partial/ \partial \theta$ of a `Scalar`. More...

virtual void	stdsdp (const Scalar &uu, Scalar &resu) const
	Computes $1/\sin\theta \partial/ \partial \varphi$ of a `Scalar`. More...

virtual void	laplacien (const Scalar &uu, int zec_mult_r, Scalar &lap) const
	Computes the Laplacian of a scalar field. More...

virtual void	laplacien (const Cmp &uu, int zec_mult_r, Cmp &lap) const
	Computes the Laplacian of a scalar field (`Cmp` version). More...

virtual void	lapang (const Scalar &uu, Scalar &lap) const
	Computes the angular Laplacian of a scalar field. More...

virtual void	primr (const Scalar &uu, Scalar &resu, bool null_infty) const
	Computes the radial primitive which vanishes for $r\to \infty$ . More...

virtual Tbl *	integrale (const Cmp &) const
	Computes the integral over all space of a `Cmp`. More...

virtual void	poisson (const Cmp &source, Param &par, Cmp &uu) const
	Computes the solution of a scalar Poisson equation. More...

virtual void	poisson_tau (const Cmp &source, Param &par, Cmp &uu) const
	Computes the solution of a scalar Poisson equation using a Tau method. More...

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 &pot, 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. More...

virtual void	poisson_angu (const Scalar &source, Param &par, Scalar &uu, double lambda=0) const
	Computes the solution of the generalized angular Poisson equation. More...

virtual void	poisson_angu (const Cmp &source, Param &par, Cmp &uu, double lambda=0) const

virtual Param *	donne_para_poisson_vect (Param &par, int i) const
	Internal function intended to be used by `Map::poisson_vect` and `Map::poisson_vect_oohara` . More...

virtual void	poisson_frontiere (const Cmp &, const Valeur &, int, int, Cmp &, double=0., double=0.) const
	Solver of the Poisson equation with boundary condition for the affine mapping case. More...

virtual void	poisson_frontiere_double (const Cmp &source, const Valeur &lim_func, const Valeur &lim_der, int num_zone, Cmp &pot) const
	Solver of the Poisson equation with boundary condition for the affine mapping case, cases with boundary conditions of both Dirichlet and Neumann type (no condition imposed at infinity). More...

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, imposing a boundary condition at the surface of the star. More...

double	integrale_surface (const Cmp &ci, double rayon) const
	Performs the surface integration of `ci` on the sphere of radius `rayon` . More...

double	integrale_surface (const Scalar &ci, double rayon) const
	Performs the surface integration of `ci` on the sphere of radius `rayon` . More...

double	integrale_surface_falloff (const Cmp &ci) const

double	integrale_surface_infini (const Cmp &ci) const
	Performs the surface integration of `ci` at infinity. More...

double	integrale_surface_infini (const Scalar &ci) const
	Performs the surface integration of `ci` at infinity. More...

void	sol_elliptic (Param_elliptic &params, const Scalar &so, Scalar &uu) const
	General elliptic solver. More...

void	sol_elliptic_boundary (Param_elliptic &params, const Scalar &so, Scalar &uu, const Mtbl_cf &bound, double fact_dir, double fact_neu) const
	General elliptic solver including inner boundary conditions. More...

void	sol_elliptic_boundary (Param_elliptic &params, const Scalar &so, Scalar &uu, const Scalar &bound, double fact_dir, double fact_neu) const
	General elliptic solver including inner boundary conditions, with boundary given as a Scalar on mono-domain angular grid. More...

void	sol_elliptic_no_zec (Param_elliptic &params, const Scalar &so, Scalar &uu, double val) const
	General elliptic solver. More...

void	sol_elliptic_only_zec (Param_elliptic &params, const Scalar &so, Scalar &uu, double val) const
	General elliptic solver. More...

void	sol_elliptic_sin_zec (Param_elliptic &params, const Scalar &so, Scalar &uu, double coefs, double ) const
	General elliptic solver. More...

void	sol_elliptic_fixe_der_zero (double val, Param_elliptic &params, const Scalar &so, Scalar &uu) const
	General elliptic solver fixing the derivative at the origin and relaxing the continuity of the first derivative at the boundary between the nucleus and the first shell. More...

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. More...

void	sol_elliptic_2d (Param_elliptic &, const Scalar &, Scalar &) const
	General elliptic solver in a 2D case. More...

void	sol_elliptic_pseudo_1d (Param_elliptic &, const Scalar &, Scalar &) const
	General elliptic solver in a pseudo 1d case. More...

virtual void	dalembert (Param &par, Scalar &fJp1, const Scalar &fJ, const Scalar &fJm1, const Scalar &source) const
	Performs one time-step integration of the d'Alembert scalar equation. More...

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. More...

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. More...

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. More...

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. More...

virtual void	mult_r (Scalar &uu) const
	Multiplication by r of a `Scalar`, the `dzpuis` of `uu` is not changed. More...

virtual void	mult_r (Cmp &ci) const
	Multiplication by r of a `Cmp`. More...

virtual void	mult_r_zec (Scalar &) const
	Multiplication by r (in the compactified external domain only) of a `Scalar`. More...

virtual void	mult_rsint (Scalar &) const
	Multiplication by $r\sin\theta$ of a `Scalar`. More...

virtual void	div_rsint (Scalar &) const
	Division by $r\sin\theta$ of a `Scalar`. More...

virtual void	div_r (Scalar &) const
	Division by r of a `Scalar`. More...

virtual void	div_r_zec (Scalar &) const
	Division by r (in the compactified external domain only) of a `Scalar`. More...

virtual void	mult_cost (Scalar &) const
	Multiplication by $\cos\theta$ of a `Scalar`. More...

virtual void	div_cost (Scalar &) const
	Division by $\cos\theta$ of a `Scalar`. More...

virtual void	mult_sint (Scalar &) const
	Multiplication by $\sin\theta$ of a `Scalar`. More...

virtual void	div_sint (Scalar &) const
	Division by $\sin\theta$ of a `Scalar`. More...

virtual void	div_tant (Scalar &) const
	Division by $\tan\theta$ of a `Scalar`. More...

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`. More...

virtual void	comp_x_from_spherical (const Cmp &v_r, const Cmp &v_theta, const Cmp &v_phi, Cmp &v_x) const
	`Cmp` version More...

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` . More...

virtual void	comp_y_from_spherical (const Cmp &v_r, const Cmp &v_theta, const Cmp &v_phi, Cmp &v_y) const
	`Cmp` version More...

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` . More...

virtual void	comp_z_from_spherical (const Cmp &v_r, const Cmp &v_theta, Cmp &v_z) const
	`Cmp` version More...

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` . More...

virtual void	comp_r_from_cartesian (const Cmp &v_x, const Cmp &v_y, const Cmp &v_z, Cmp &v_r) const
	`Cmp` version More...

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` . More...

virtual void	comp_t_from_cartesian (const Cmp &v_x, const Cmp &v_y, const Cmp &v_z, Cmp &v_t) const
	`Cmp` version More...

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` . More...

virtual void	comp_p_from_cartesian (const Cmp &v_x, const Cmp &v_y, Cmp &v_p) const
	`Cmp` version More...

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). More...

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). More...

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). More...

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). More...

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. More...

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. More...

const Mg3d *	get_mg () const
	Gives the `Mg3d` on which the mapping is defined. More...

double	get_ori_x () const
	Returns the x coordinate of the origin. More...

double	get_ori_y () const
	Returns the y coordinate of the origin. More...

double	get_ori_z () const
	Returns the z coordinate of the origin. More...

double	get_rot_phi () const
	Returns the angle between the x –axis and X –axis. More...

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. More...

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. More...

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`. More...

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`. More...

const Cmp &	cmp_zero () const
	Returns the null `Cmp` defined on `*this`. More...

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). More...

void	set_ori (double xa0, double ya0, double za0)
	Sets a new origin. More...

void	set_rot_phi (double phi0)
	Sets a new rotation angle. More...

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

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. More...

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). More...

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). More...

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. More...

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. More...

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. More...

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. More...

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. More...

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. More...

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. More...

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. More...

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. More...

Coord	r
	r coordinate centered on the grid More...

Coord	tet
	$\theta$ coordinate centered on the grid More...

Coord	phi
	$\phi$ coordinate centered on the grid More...

Coord	sint
	$\sin\theta$ More...

Coord	cost
	$\cos\theta$ More...

Coord	sinp
	$\sin\phi$ More...

Coord	cosp
	$\cos\phi$ More...

Coord	x
	x coordinate centered on the grid More...

Coord	y
	y coordinate centered on the grid More...

Coord	z
	z coordinate centered on the grid More...

Coord	xa
	Absolute x coordinate. More...

Coord	ya
	Absolute y coordinate. More...

Coord	za
	Absolute z coordinate. More...

Protected Member Functions
virtual void	reset_coord ()
	Resets all the member `Coords`. More...

Protected Attributes
const Mg3d *	mg
	Pointer on the multi-grid `Mgd3` on which `this` is defined. More...

double	ori_x
	Absolute coordinate x of the origin. More...

double	ori_y
	Absolute coordinate y of the origin. More...

double	ori_z
	Absolute coordinate z of the origin. More...

double	rot_phi
	Angle between the x –axis and X –axis. More...

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. More...

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. More...

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`. More...

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`. More...

Cmp *	p_cmp_zero
	The null Cmp. More...

Map_af *	p_mp_angu
	Pointer on the "angular" mapping. More...

Private Member Functions
void	set_coord ()
	Assignment of the building functions to the member `Coords`. More...

virtual ostream &	operator>> (ostream &) const
	Operator >> More...

Private Attributes
double *	alpha
	Array (size: `mg->nzone` ) of the values of $\alpha$ in each domain. More...

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

Friends
Mtbl *	map_af_fait_r (const Map *)

Mtbl *	map_af_fait_tet (const Map *)

Mtbl *	map_af_fait_phi (const Map *)

Mtbl *	map_af_fait_sint (const Map *)

Mtbl *	map_af_fait_cost (const Map *)

Mtbl *	map_af_fait_sinp (const Map *)

Mtbl *	map_af_fait_cosp (const Map *)

Mtbl *	map_af_fait_x (const Map *)

Mtbl *	map_af_fait_y (const Map *)

Mtbl *	map_af_fait_z (const Map *)

Mtbl *	map_af_fait_xa (const Map *)

Mtbl *	map_af_fait_ya (const Map *)

Mtbl *	map_af_fait_za (const Map *)

Mtbl *	map_af_fait_xsr (const Map *)

Mtbl *	map_af_fait_dxdr (const Map *)

Mtbl *	map_af_fait_drdt (const Map *)

Mtbl *	map_af_fait_stdrdp (const Map *)

Mtbl *	map_af_fait_srdrdt (const Map *)

Mtbl *	map_af_fait_srstdrdp (const Map *)

Mtbl *	map_af_fait_sr2drdt (const Map *)

Mtbl *	map_af_fait_sr2stdrdp (const Map *)

Mtbl *	map_af_fait_d2rdx2 (const Map *)

Mtbl *	map_af_fait_lapr_tp (const Map *)

Mtbl *	map_af_fait_d2rdtdx (const Map *)

Mtbl *	map_af_fait_sstd2rdpdx (const Map *)

Mtbl *	map_af_fait_sr2d2rdt2 (const Map *)

Detailed Description

Affine radial mapping.

()

The affine radial mapping is the simplest one between the grid coordinates $(\xi, \theta', \phi')$ and the physical coordinates $(r, \theta, \phi)$ . It is defined by $\theta=\theta'$ , $\phi=\phi'$ and

$r=\alpha \xi + \beta$ , in non-compactified domains,
$u={1\over r} = \alpha \xi + \beta$ in the (usually outermost) compactified domain, where $\alpha$ and $\beta$ are constant in each domain.

Definition at line 2042 of file map.h.

Constructor & Destructor Documentation

◆ Map_af() [1/6]

Lorene::Map_af::Map_af	(	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 213 of file map_af.C.

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

◆ Map_af() [2/6]

Lorene::Map_af::Map_af	(	const Mg3d &	mgrille,
		const Tbl &	r_limits
	)

Standard Constructor with Tbl.

Parameters

mgrille	[input] Multi-domain grid on which the mapping is defined
r_limits	[input] Array (size: number of domains) 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` except in the last domain The last boundary is set to inifnity if the grid contains a compactified domain.

Definition at line 258 of file map_af.C.

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

◆ Map_af() [3/6]

Lorene::Map_af::Map_af ( const Map_af & mp )

Copy constructor.

Definition at line 304 of file map_af.C.

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

◆ Map_af() [4/6]

Lorene::Map_af::Map_af	(	const Mg3d &	mgrille,
		const string &	filename
	)

Constructor from a formatted file.

Definition at line 323 of file map_af.C.

References Lorene::Mg3d::get_nzone(), Lorene::Mg3d::get_type_r(), Lorene::Map::mg, Lorene::search_file(), Lorene::Tbl::set(), and Lorene::Tbl::set_etat_qcq().

◆ Map_af() [5/6]

Lorene::Map_af::Map_af	(	const Mg3d &	mgi,
		FILE *	fd
	)

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

Definition at line 428 of file map_af.C.

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

◆ Map_af() [6/6]

Lorene::Map_af::Map_af ( const Map & mpi )

explicit

Constructor from a general mapping.

If the input mapping belongs to the class Map_af , this constructor does the same job as the copy constructor Map_af(const Map_af& ) .

If the input mapping belongs to the class Map_et , this constructor sets in each domain, the values of $\alpha$ and $\beta$ to those of the Map_et .

Definition at line 444 of file map_af.C.

References alpha, beta, get_alpha(), Lorene::Map_et::get_alpha(), get_beta(), Lorene::Map_et::get_beta(), Lorene::Mg3d::get_nzone(), Lorene::Map::get_ori_x(), Lorene::Map::get_ori_y(), Lorene::Map::get_ori_z(), Lorene::Map::get_rot_phi(), Lorene::Map::mg, set_coord(), Lorene::Map::set_ori(), and Lorene::Map::set_rot_phi().

◆ ~Map_af()

Lorene::Map_af::~Map_af ( )

virtual

Destructor.

Definition at line 495 of file map_af.C.

References alpha, and beta.

Member Function Documentation

◆ adapt()

void Lorene::Map_af::adapt	(	const Cmp &	ent,
		const Param &	par,
		int	nbr = `0`
	)

virtual

Adaptation of the mapping to a given scalar field.

Implements Lorene::Map.

Definition at line 800 of file map_af.C.

References Lorene::c_est_pas_fait().

◆ cmp_zero()

const Cmp& Lorene::Map::cmp_zero ( ) const

inlineinherited

Returns the null Cmp defined on *this.

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

Definition at line 819 of file map.h.

References Lorene::Map::p_cmp_zero.

◆ comp_p_from_cartesian() [1/2]

void Lorene::Map_radial::comp_p_from_cartesian	(	const Scalar &	v_x,
		const Scalar &	v_y,
		Scalar &	v_p
	)		const

virtualinherited

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 Lorene::Map.

Definition at line 186 of file map_radial_comp_rtp.C.

References Lorene::Scalar::get_etat().

◆ comp_p_from_cartesian() [2/2]

void Lorene::Map_radial::comp_p_from_cartesian	(	const Cmp &	v_x,
		const Cmp &	v_y,
		Cmp &	v_p
	)		const

virtualinherited

Cmp version

Implements Lorene::Map.

Definition at line 179 of file map_radial_comp_rtp.C.

References Lorene::Map_radial::comp_p_from_cartesian().

◆ comp_r_from_cartesian() [1/2]

void Lorene::Map_radial::comp_r_from_cartesian	(	const Scalar &	v_x,
		const Scalar &	v_y,
		const Scalar &	v_z,
		Scalar &	v_r
	)		const

virtualinherited

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 Lorene::Map.

Definition at line 75 of file map_radial_comp_rtp.C.

References Lorene::Scalar::get_etat().

◆ comp_r_from_cartesian() [2/2]

void Lorene::Map_radial::comp_r_from_cartesian	(	const Cmp &	v_x,
		const Cmp &	v_y,
		const Cmp &	v_z,
		Cmp &	v_r
	)		const

virtualinherited

Cmp version

Implements Lorene::Map.

Definition at line 68 of file map_radial_comp_rtp.C.

References Lorene::Map_radial::comp_r_from_cartesian().

◆ comp_t_from_cartesian() [1/2]

void Lorene::Map_radial::comp_t_from_cartesian	(	const Scalar &	v_x,
		const Scalar &	v_y,
		const Scalar &	v_z,
		Scalar &	v_t
	)		const

virtualinherited

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 Lorene::Map.

Definition at line 131 of file map_radial_comp_rtp.C.

References Lorene::Scalar::get_etat().

◆ comp_t_from_cartesian() [2/2]

void Lorene::Map_radial::comp_t_from_cartesian	(	const Cmp &	v_x,
		const Cmp &	v_y,
		const Cmp &	v_z,
		Cmp &	v_t
	)		const

virtualinherited

Cmp version

Implements Lorene::Map.

Definition at line 124 of file map_radial_comp_rtp.C.

References Lorene::Map_radial::comp_t_from_cartesian().

◆ comp_x_from_spherical() [1/2]

void Lorene::Map_radial::comp_x_from_spherical	(	const Scalar &	v_r,
		const Scalar &	v_theta,
		const Scalar &	v_phi,
		Scalar &	v_x
	)		const

virtualinherited

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 Lorene::Map.

Definition at line 79 of file map_radial_comp_xyz.C.

References Lorene::Scalar::get_etat().

◆ comp_x_from_spherical() [2/2]

void Lorene::Map_radial::comp_x_from_spherical	(	const Cmp &	v_r,
		const Cmp &	v_theta,
		const Cmp &	v_phi,
		Cmp &	v_x
	)		const

virtualinherited

Cmp version

Implements Lorene::Map.

Definition at line 71 of file map_radial_comp_xyz.C.

References Lorene::Map_radial::comp_x_from_spherical().

◆ comp_y_from_spherical() [1/2]

void Lorene::Map_radial::comp_y_from_spherical	(	const Scalar &	v_r,
		const Scalar &	v_theta,
		const Scalar &	v_phi,
		Scalar &	v_y
	)		const

virtualinherited

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 Lorene::Map.

Definition at line 138 of file map_radial_comp_xyz.C.

References Lorene::Scalar::get_etat().

◆ comp_y_from_spherical() [2/2]

void Lorene::Map_radial::comp_y_from_spherical	(	const Cmp &	v_r,
		const Cmp &	v_theta,
		const Cmp &	v_phi,
		Cmp &	v_y
	)		const

virtualinherited

Cmp version

Implements Lorene::Map.

Definition at line 129 of file map_radial_comp_xyz.C.

References Lorene::Map_radial::comp_y_from_spherical().

◆ comp_z_from_spherical() [1/2]

void Lorene::Map_radial::comp_z_from_spherical	(	const Scalar &	v_r,
		const Scalar &	v_theta,
		Scalar &	v_z
	)		const

virtualinherited

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 Lorene::Map.

Definition at line 195 of file map_radial_comp_xyz.C.

References Lorene::Scalar::get_etat().

◆ comp_z_from_spherical() [2/2]

void Lorene::Map_radial::comp_z_from_spherical	(	const Cmp &	v_r,
		const Cmp &	v_theta,
		Cmp &	v_z
	)		const

virtualinherited

Cmp version

Implements Lorene::Map.

Definition at line 187 of file map_radial_comp_xyz.C.

References Lorene::Map_radial::comp_z_from_spherical().

◆ convert_absolute()

void Lorene::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 305 of file map.C.

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

◆ dalembert()

void Lorene::Map_af::dalembert	(	Param &	par,
		Scalar &	fJp1,
		const Scalar &	fJ,
		const Scalar &	fJm1,
		const Scalar &	source
	)		const

virtual

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

Parameters

par	[input/output] possible parameters to control the resolution of the d'Alembert equation: \ `par.get_double(0)` : [input] the time step dt ,\ `par.get_int(0)` : [input] the type of boundary conditions set at the outer boundary (0 : reflexion, 1 : Sommerfeld outgoing wave, valid only for l=0 components, 2 : Bayliss & Turkel outgoing wave, valid for l=0, 1, 2 components)\ `par.get_int_mod(0)` : [input/output] set to 0 at first call, is used as a working flag after (must not be modified after first call)\ `par.get_int(1)` : [input] (optional) if present, a shift of -1 is done in the multipolar spectrum in terms of $\ell$ . The value of this variable gives the minimal value of (the shifted) $\ell$ for which the wave equation is solved.\ `par.get_tensor_mod(0)` : [input] (optional) if the wave equation is on a curved space-time, this is the potential in front of the Laplace operator. It has to be updated at every time-step (for a potential depending on time).\ Note: there are many other working objects attached to this `Param` , so one should not modify it.
fJp1	[output] solution $f^{J+1}$ at time J+1 with boundary conditions defined by `par.get_int(0)`
fJ	[input] solution at time J
fJm1	[input] solution $f^{J-1}$ at time J-1
source	[input] source $\sigma$ of the d'Alembert equation $\diamond u = \sigma$ .

!!

Implements Lorene::Map.

Definition at line 125 of file map_af_dalembert.C.

References Lorene::Scalar::get_etat().

◆ dec2_dzpuis()

void Lorene::Map_radial::dec2_dzpuis ( Scalar & ci ) const

virtualinherited

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

Implements Lorene::Map.

Definition at line 751 of file map_radial_r_manip.C.

References Lorene::Scalar::get_etat().

◆ dec_dzpuis()

void Lorene::Map_radial::dec_dzpuis ( Scalar & ci ) const

virtualinherited

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

Implements Lorene::Map.

Definition at line 646 of file map_radial_r_manip.C.

References Lorene::Scalar::get_etat().

◆ div_cost()

void Lorene::Map_radial::div_cost ( Scalar & ci ) const

virtualinherited

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

Implements Lorene::Map.

Definition at line 88 of file map_radial_th_manip.C.

References Lorene::Scalar::get_etat().

◆ div_r()

void Lorene::Map_radial::div_r ( Scalar & ci ) const

virtualinherited

Division by r of a Scalar.

Implements Lorene::Map.

Definition at line 517 of file map_radial_r_manip.C.

References Lorene::Scalar::get_etat().

◆ div_r_zec()

void Lorene::Map_radial::div_r_zec ( Scalar & uu ) const

virtualinherited

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

Implements Lorene::Map.

Definition at line 588 of file map_radial_r_manip.C.

References Lorene::Scalar::get_etat().

◆ div_rsint()

void Lorene::Map_radial::div_rsint ( Scalar & ci ) const

virtualinherited

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

Implements Lorene::Map.

Definition at line 437 of file map_radial_r_manip.C.

References Lorene::Scalar::get_etat().

◆ div_sint()

void Lorene::Map_radial::div_sint ( Scalar & ci ) const

virtualinherited

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

Implements Lorene::Map.

Definition at line 136 of file map_radial_th_manip.C.

References Lorene::Scalar::get_etat().

◆ div_tant()

void Lorene::Map_radial::div_tant ( Scalar & ci ) const

virtualinherited

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

Implements Lorene::Map.

Definition at line 161 of file map_radial_th_manip.C.

References Lorene::Scalar::get_etat().

◆ donne_para_poisson_vect()

Param * Lorene::Map_af::donne_para_poisson_vect	(	Param &	par,
		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.

In the case of a Map_af the result is not used and the function only returns & par .

Implements Lorene::Map.

Definition at line 73 of file map_poisson_vect.C.

◆ dsdr() [1/2]

void Lorene::Map_af::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 Lorene::Map.

Definition at line 282 of file map_af_deriv.C.

References Lorene::Cmp::get_etat().

◆ dsdr() [2/2]

void Lorene::Map_af::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 Lorene::Map.

Definition at line 366 of file map_af_deriv.C.

References Lorene::Scalar::get_etat().

◆ dsdradial()

void Lorene::Map_af::dsdradial	(	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 Lorene::Map.

Definition at line 420 of file map_af_deriv.C.

References Lorene::Scalar::get_etat().

◆ dsdt()

void Lorene::Map_af::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 Lorene::Map.

Definition at line 800 of file map_af_deriv.C.

References Lorene::Scalar::get_etat().

◆ dsdxi() [1/2]

void Lorene::Map_af::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 Lorene::Map.

Definition at line 139 of file map_af_deriv.C.

References Lorene::Cmp::get_etat().

◆ dsdxi() [2/2]

void Lorene::Map_af::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 Lorene::Map.

Definition at line 223 of file map_af_deriv.C.

References Lorene::Scalar::get_etat().

◆ flat_met_cart()

const Metric_flat & Lorene::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 334 of file map.C.

References Lorene::Map::bvect_cart, and Lorene::Map::p_flat_met_cart.

◆ flat_met_spher()

const Metric_flat & Lorene::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 324 of file map.C.

References Lorene::Map::bvect_spher, and Lorene::Map::p_flat_met_spher.

◆ get_alpha()

const double * Lorene::Map_af::get_alpha ( ) const

Returns the pointer on the array alpha.

Definition at line 604 of file map_af.C.

References alpha.

◆ get_beta()

const double * Lorene::Map_af::get_beta ( ) const

Returns the pointer on the array beta.

Definition at line 608 of file map_af.C.

References beta.

◆ get_bvect_cart()

const Base_vect_cart& Lorene::Map::get_bvect_cart ( ) const

inlineinherited

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 803 of file map.h.

References Lorene::Map::bvect_cart.

◆ get_bvect_spher()

const Base_vect_spher& Lorene::Map::get_bvect_spher ( ) const

inlineinherited

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 795 of file map.h.

References Lorene::Map::bvect_spher.

◆ get_mg()

const Mg3d* Lorene::Map::get_mg ( ) const

inlineinherited

Gives the Mg3d on which the mapping is defined.

Definition at line 777 of file map.h.

References Lorene::Map::mg.

◆ get_ori_x()

double Lorene::Map::get_ori_x ( ) const

inlineinherited

Returns the x coordinate of the origin.

Definition at line 780 of file map.h.

References Lorene::Map::ori_x.

◆ get_ori_y()

double Lorene::Map::get_ori_y ( ) const

inlineinherited

Returns the y coordinate of the origin.

Definition at line 782 of file map.h.

References Lorene::Map::ori_y.

◆ get_ori_z()

double Lorene::Map::get_ori_z ( ) const

inlineinherited

Returns the z coordinate of the origin.

Definition at line 784 of file map.h.

References Lorene::Map::ori_z.

◆ get_rot_phi()

double Lorene::Map::get_rot_phi ( ) const

inlineinherited

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

Definition at line 787 of file map.h.

References Lorene::Map::rot_phi.

◆ homothetie()

void Lorene::Map_af::homothetie ( double lambda )

virtual

Sets a new radial scale.

Parameters

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

Implements Lorene::Map.

Definition at line 664 of file map_af.C.

References Lorene::Mg3d::get_nzone(), Lorene::Mg3d::get_type_r(), and Lorene::Map::mg.

◆ homothetie_interne()

void Lorene::Map_af::homothetie_interne ( double lambda )

Sets a new radial scale at the bondary between the nucleus and the first shell.

Parameters

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

Definition at line 741 of file map_af.C.

References alpha, beta, and Lorene::Map_radial::reset_coord().

◆ inc2_dzpuis()

void Lorene::Map_radial::inc2_dzpuis ( Scalar & ci ) const

virtualinherited

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

Implements Lorene::Map.

Definition at line 802 of file map_radial_r_manip.C.

References Lorene::Scalar::get_etat().

◆ inc_dzpuis()

void Lorene::Map_radial::inc_dzpuis ( Scalar & ci ) const

virtualinherited

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

Implements Lorene::Map.

Definition at line 699 of file map_radial_r_manip.C.

References Lorene::Scalar::get_etat().

◆ integrale()

Tbl * Lorene::Map_af::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 Lorene::Map.

Definition at line 84 of file map_af_integ.C.

References Lorene::Cmp::get_etat().

◆ integrale_surface() [1/2]

double Lorene::Map_af::integrale_surface	(	const Cmp &	ci,
		double	rayon
	)		const

Performs the surface integration of ci on the sphere of radius rayon .

Definition at line 99 of file map_af_integ_surf.C.

References Lorene::Cmp::get_etat().

◆ integrale_surface() [2/2]

double Lorene::Map_af::integrale_surface	(	const Scalar &	ci,
		double	rayon
	)		const

Performs the surface integration of ci on the sphere of radius rayon .

Definition at line 295 of file map_af_integ_surf.C.

References Lorene::Scalar::get_etat().

◆ integrale_surface_infini() [1/2]

double Lorene::Map_af::integrale_surface_infini ( const Cmp & ci ) const

Performs the surface integration of ci at infinity.

ci must have dzpuis =2.

Definition at line 214 of file map_af_integ_surf.C.

References Lorene::Cmp::get_etat().

◆ integrale_surface_infini() [2/2]

double Lorene::Map_af::integrale_surface_infini ( const Scalar & ci ) const

Performs the surface integration of ci at infinity.

ci must have dzpuis =2.

Definition at line 412 of file map_af_integ_surf.C.

References Lorene::Scalar::get_etat().

◆ lapang()

void Lorene::Map_af::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 Lorene::Map.

Definition at line 552 of file map_af_lap.C.

References Lorene::Scalar::get_etat().

◆ laplacien() [1/2]

void Lorene::Map_af::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 Lorene::Map.

Definition at line 182 of file map_af_lap.C.

References Lorene::Scalar::get_etat().

◆ laplacien() [2/2]

void Lorene::Map_af::laplacien	(	const Cmp &	uu,
		int	zec_mult_r,
		Cmp &	lap
	)		const

virtual

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

Implements Lorene::Map.

Definition at line 370 of file map_af_lap.C.

References Lorene::Cmp::get_etat().

◆ mp_angu()

const Map_af & Lorene::Map_af::mp_angu ( int l_zone ) const

virtual

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

Valid only for the class Map_af.

Implements Lorene::Map.

Definition at line 783 of file map_af.C.

References Lorene::Mg3d::get_angu_1dom(), Lorene::Map::get_mg(), Map_af(), Lorene::Map::p_mp_angu, Lorene::Tbl::set(), Lorene::Tbl::set_etat_qcq(), and val_r_jk().

◆ mult_cost()

void Lorene::Map_radial::mult_cost ( Scalar & ci ) const

virtualinherited

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

Implements Lorene::Map.

Definition at line 64 of file map_radial_th_manip.C.

References Lorene::Scalar::get_etat().

◆ mult_r() [1/2]

void Lorene::Map_radial::mult_r ( Scalar & uu ) const

virtualinherited

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

Implements Lorene::Map.

Definition at line 147 of file map_radial_r_manip.C.

References Lorene::Scalar::get_etat().

◆ mult_r() [2/2]

void Lorene::Map_radial::mult_r ( Cmp & ci ) const

virtualinherited

Multiplication by r of a Cmp.

In the CED, there is only a decrement of dzpuis

Implements Lorene::Map.

Definition at line 222 of file map_radial_r_manip.C.

References Lorene::Cmp::get_etat().

◆ mult_r_zec()

void Lorene::Map_radial::mult_r_zec ( Scalar & ci ) const

virtualinherited

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

Implements Lorene::Map.

Definition at line 299 of file map_radial_r_manip.C.

References Lorene::Scalar::get_etat().

◆ mult_rsint()

void Lorene::Map_radial::mult_rsint ( Scalar & ci ) const

virtualinherited

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

Implements Lorene::Map.

Definition at line 358 of file map_radial_r_manip.C.

References Lorene::Scalar::get_etat().

◆ mult_sint()

void Lorene::Map_radial::mult_sint ( Scalar & ci ) const

virtualinherited

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

Implements Lorene::Map.

Definition at line 112 of file map_radial_th_manip.C.

References Lorene::Scalar::get_etat().

◆ operator=()

void Lorene::Map_af::operator= ( const Map_af & mpi )

virtual

Assignment to another affine mapping.

Implements Lorene::Map_radial.

Definition at line 507 of file map_af.C.

References alpha, beta, Lorene::Mg3d::get_nzone(), Lorene::Map::mg, Lorene::Map::ori_x, Lorene::Map::ori_y, Lorene::Map::ori_z, Lorene::Map_radial::reset_coord(), Lorene::Map::rot_phi, Lorene::Map::set_ori(), and Lorene::Map::set_rot_phi().

◆ operator==()

bool Lorene::Map_af::operator== ( const Map & mpi ) const

virtual

Comparison operator (egality)

Implements Lorene::Map_radial.

Definition at line 566 of file map_af.C.

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

◆ operator>>()

ostream & Lorene::Map_af::operator>> ( ostream & ost ) const

privatevirtual

Operator >>

Implements Lorene::Map.

Definition at line 630 of file map_af.C.

References alpha, beta, Lorene::Mg3d::get_nr(), Lorene::Mg3d::get_nzone(), Lorene::Map::mg, Lorene::Map::r, and val_r().

◆ poisson()

void Lorene::Map_af::poisson	(	const Cmp &	source,
		Param &	par,
		Cmp &	uu
	)		const

virtual

Computes the solution of a scalar Poisson equation.

Parameters

source	[input] source $\sigma$ of the Poisson equation $\Delta u = \sigma$ .
par	[] not used by this `Map_af` version.
uu	[output] solution u with the boundary condition u =0 at spatial infinity.

Implements Lorene::Map.

Definition at line 103 of file map_af_poisson.C.

References Lorene::Cmp::get_etat().

◆ poisson2d()

void Lorene::Map_af::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	[output] Parameter which contains the constant $\lambda$ used to fulfill the virial identity GRV2 : \ `par.get_double_mod(0)` : [output] constant `lambda` such that the source of the equation effectively solved is `source_mat` + `lambda` * `source_quad` .
uu	[input/output] solution u with the boundary condition u =0 at spatial infinity.

Implements Lorene::Map.

Definition at line 84 of file map_af_poisson2d.C.

References Lorene::Cmp::get_etat().

◆ poisson_angu()

void Lorene::Map_af::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 Lorene::Map.

Definition at line 64 of file map_af_poisson_angu.C.

References Lorene::Scalar::get_etat().

◆ poisson_compact() [1/2]

void Lorene::Map_radial::poisson_compact	(	const Cmp &	source,
		const Cmp &	aa,
		const Tenseur &	bb,
		const Param &	par,
		Cmp &	psi
	)		const

virtualinherited

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 Lorene::Map.

Definition at line 158 of file map_radial_poisson_cpt.C.

References Lorene::Cmp::get_etat().

◆ poisson_compact() [2/2]

void Lorene::Map_radial::poisson_compact	(	int	nzet,
		const Cmp &	source,
		const Cmp &	aa,
		const Tenseur &	bb,
		const Param &	par,
		Cmp &	psi
	)		const

virtualinherited

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 Lorene::Map.

Definition at line 456 of file map_radial_poisson_cpt.C.

References Lorene::Cmp::get_etat(), and Lorene::Map_radial::poisson_compact().

◆ poisson_frontiere()

void Lorene::Map_af::poisson_frontiere	(	const Cmp &	source,
		const Valeur &	limite,
		int	type_raccord,
		int	num_front,
		Cmp &	pot,
		double	fact_dir = `0.`,
		double	fact_neu = `0.`
	)		const

virtual

Solver of the Poisson equation with boundary condition for the affine mapping case.

Implements Lorene::Map.

Definition at line 138 of file cmp_pde_frontiere.C.

References Lorene::Cmp::get_etat().

◆ poisson_frontiere_double()

void Lorene::Map_af::poisson_frontiere_double	(	const Cmp &	source,
		const Valeur &	lim_func,
		const Valeur &	lim_der,
		int	num_zone,
		Cmp &	pot
	)		const

virtual

Solver of the Poisson equation with boundary condition for the affine mapping case, cases with boundary conditions of both Dirichlet and Neumann type (no condition imposed at infinity).

Implements Lorene::Map.

Definition at line 211 of file cmp_pde_frontiere.C.

References Lorene::Cmp::get_etat().

◆ poisson_interne()

void Lorene::Map_af::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 Lorene::Map.

Definition at line 477 of file cmp_pde_frontiere.C.

References Lorene::Cmp::get_etat().

◆ poisson_regular()

void Lorene::Map_af::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 $\sigma_{\rm regu} = \sigma - \sigma_{\rm div}$ is constructed and solved.

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	[] not used by this `Map_af` version.
uu	[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 Lorene::Map.

Definition at line 112 of file map_af_poisson_regu.C.

References Lorene::Cmp::get_etat().

◆ poisson_tau()

void Lorene::Map_af::poisson_tau	(	const Cmp &	source,
		Param &	par,
		Cmp &	uu
	)		const

virtual

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

Parameters

source	[input] source $\sigma$ of the Poisson equation $\Delta u = \sigma$ .
par	[] not used by this `Map_af` version.
uu	[output] solution u with the boundary condition u =0 at spatial infinity.

Implements Lorene::Map.

Definition at line 168 of file map_af_poisson.C.

References Lorene::Cmp::get_etat().

◆ primr()

void Lorene::Map_af::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 Lorene::Map.

Definition at line 86 of file map_af_primr.C.

References Lorene::Scalar::get_etat(), MAX_BASE, R_CHEB, R_CHEBI, R_CHEBP, R_CHEBPIM_I, R_CHEBPIM_P, R_CHEBU, R_JACO02, R_LEG, R_LEGI, R_LEGP, and TRA_R.

◆ reevaluate() [1/2]

void Lorene::Map_radial::reevaluate	(	const Map *	mp_prev,
		int	nzet,
		Cmp &	uu
	)		const

virtualinherited

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`.

Implements Lorene::Map.

Definition at line 64 of file map_radial_reevaluate.C.

References Lorene::Cmp::get_dzpuis(), Lorene::Cmp::get_etat(), Lorene::Cmp::get_mp(), Lorene::Mg3d::get_nzone(), and Lorene::Map::mg.

◆ reevaluate() [2/2]

void Lorene::Map_radial::reevaluate	(	const Map *	mp_prev,
		int	nzet,
		Scalar &	uu
	)		const

virtualinherited

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`.

Implements Lorene::Map.

Definition at line 179 of file map_radial_reevaluate.C.

References Lorene::Scalar::get_dzpuis(), Lorene::Scalar::get_etat(), Lorene::Tensor::get_mp(), Lorene::Mg3d::get_nzone(), and Lorene::Map::mg.

◆ reevaluate_symy() [1/2]

void Lorene::Map_radial::reevaluate_symy	(	const Map *	mp_prev,
		int	nzet,
		Cmp &	uu
	)		const

virtualinherited

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`.

Implements Lorene::Map.

Definition at line 65 of file map_radial_reeval_symy.C.

References Lorene::Cmp::get_dzpuis(), Lorene::Cmp::get_etat(), Lorene::Cmp::get_mp(), Lorene::Mg3d::get_nzone(), and Lorene::Map::mg.

◆ reevaluate_symy() [2/2]

void Lorene::Map_radial::reevaluate_symy	(	const Map *	mp_prev,
		int	nzet,
		Scalar &	uu
	)		const

virtualinherited

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`.

Implements Lorene::Map.

Definition at line 199 of file map_radial_reeval_symy.C.

References Lorene::Scalar::get_dzpuis(), Lorene::Scalar::get_etat(), Lorene::Tensor::get_mp(), Lorene::Mg3d::get_nzone(), and Lorene::Map::mg.

◆ reset_coord()

void Lorene::Map_radial::reset_coord ( )

protectedvirtualinherited

Resets all the member Coords.

Reimplemented from Lorene::Map.

Reimplemented in Lorene::Map_et.

Definition at line 129 of file map_radial.C.

References Lorene::Map_radial::d2rdtdx, Lorene::Map_radial::d2rdx2, Lorene::Coord::del_t(), Lorene::Map_radial::drdt, Lorene::Map_radial::dxdr, Lorene::Map_radial::lapr_tp, Lorene::Map::reset_coord(), Lorene::Map_radial::sr2d2rdt2, Lorene::Map_radial::sr2drdt, Lorene::Map_radial::sr2stdrdp, Lorene::Map_radial::srdrdt, Lorene::Map_radial::srstdrdp, Lorene::Map_radial::sstd2rdpdx, Lorene::Map_radial::stdrdp, and Lorene::Map_radial::xsr.

◆ resize()

void Lorene::Map_af::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 Lorene::Map.

Definition at line 687 of file map_af.C.

References Lorene::Mg3d::get_type_r(), and Lorene::Map::mg.

◆ sauve()

void Lorene::Map_af::sauve ( FILE * fd ) const

virtual

Save in a file.

Reimplemented from Lorene::Map_radial.

Definition at line 616 of file map_af.C.

References alpha, beta, Lorene::fwrite_be(), Lorene::Mg3d::get_nzone(), Lorene::Map::mg, and Lorene::Map_radial::sauve().

◆ set_alpha()

void Lorene::Map_af::set_alpha	(	double	alpha0,
		int	l
	)

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

Definition at line 757 of file map_af.C.

References alpha, and Lorene::Map_radial::reset_coord().

◆ set_beta()

void Lorene::Map_af::set_beta	(	double	beta0,
		int	l
	)

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

Definition at line 768 of file map_af.C.

References beta, and Lorene::Map_radial::reset_coord().

◆ set_coord()

void Lorene::Map_af::set_coord ( )

private

Assignment of the building functions to the member Coords.

Definition at line 530 of file map_af.C.

◆ set_ori()

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

inherited

Sets a new origin.

Definition at line 256 of file map.C.

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

◆ set_rot_phi()

void Lorene::Map::set_rot_phi ( double phi0 )

inherited

Sets a new rotation angle.

Definition at line 266 of file map.C.

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

◆ sol_elliptic()

void Lorene::Map_af::sol_elliptic	(	Param_elliptic &	params,
		const Scalar &	so,
		Scalar &	uu
	)		const

General elliptic solver.

The field is zero at infinity.

Parameters

params	[input] : the operators and variables to be uses.
so	[input] : the source.
uu	[output] : the solution.

Definition at line 103 of file map_af_elliptic.C.

References Lorene::Scalar::get_etat().

◆ sol_elliptic_2d()

void Lorene::Map_af::sol_elliptic_2d	(	Param_elliptic &	ope_var,
		const Scalar &	source,
		Scalar &	pot
	)		const

General elliptic solver in a 2D case.

The field is zero at infinity.

Parameters

params	[input] : the operators and variables to be uses.
so	[input] : the source.
uu	[output] : the solution.

Definition at line 61 of file map_af_elliptic_2d.C.

References Lorene::Scalar::get_etat().

◆ sol_elliptic_boundary() [1/2]

void Lorene::Map_af::sol_elliptic_boundary	(	Param_elliptic &	params,
		const Scalar &	so,
		Scalar &	uu,
		const Mtbl_cf &	bound,
		double	fact_dir,
		double	fact_neu
	)		const

General elliptic solver including inner boundary conditions.

The field is zero at infinity.

Parameters

params	[input] : the operators and variables to be uses.
so	[input] : the source.
uu	[output] : the solution.
bound	[input] : the boundary condition
fact_dir	: 1 Dirchlet condition, 0 Neumann condition
fact_neu	: 0 Dirchlet condition, 1 Neumann condition

Definition at line 162 of file map_af_elliptic.C.

References Lorene::Scalar::get_etat().

◆ sol_elliptic_boundary() [2/2]

void Lorene::Map_af::sol_elliptic_boundary	(	Param_elliptic &	params,
		const Scalar &	so,
		Scalar &	uu,
		const Scalar &	bound,
		double	fact_dir,
		double	fact_neu
	)		const

General elliptic solver including inner boundary conditions, with boundary given as a Scalar on mono-domain angular grid.

Definition at line 225 of file map_af_elliptic.C.

References Lorene::Scalar::get_etat().

◆ sol_elliptic_fixe_der_zero()

void Lorene::Map_af::sol_elliptic_fixe_der_zero	(	double	val,
		Param_elliptic &	params,
		const Scalar &	so,
		Scalar &	uu
	)		const

General elliptic solver fixing the derivative at the origin and relaxing the continuity of the first derivative at the boundary between the nucleus and the first shell.

Parameters

val	[input] : valeur of the derivative.
params	[input] : the operators and variables to be uses.
so	[input] : the source.
uu	[output] : the solution.

Definition at line 486 of file map_af_elliptic.C.

References Lorene::Scalar::get_etat().

◆ sol_elliptic_no_zec()

void Lorene::Map_af::sol_elliptic_no_zec	(	Param_elliptic &	params,
		const Scalar &	so,
		Scalar &	uu,
		double	val
	)		const

General elliptic solver.

The equation is not solved in the compactified domain.

Parameters

params	[input] : the operators and variables to be uses.
so	[input] : the source.
uu	[output] : the solution.
val	[input] : value at the last shell.

Definition at line 315 of file map_af_elliptic.C.

References Lorene::Scalar::get_etat().

◆ sol_elliptic_only_zec()

void Lorene::Map_af::sol_elliptic_only_zec	(	Param_elliptic &	params,
		const Scalar &	so,
		Scalar &	uu,
		double	val
	)		const

General elliptic solver.

The equation is solved only in the compactified domain.

Parameters

params	[input] : the operators and variables to be uses.
so	[input] : the source.
uu	[output] : the solution.
val	[input] : value at the inner boundary.

Definition at line 371 of file map_af_elliptic.C.

References Lorene::Scalar::get_etat().

◆ sol_elliptic_pseudo_1d()

void Lorene::Map_af::sol_elliptic_pseudo_1d	(	Param_elliptic &	ope_var,
		const Scalar &	source,
		Scalar &	pot
	)		const

General elliptic solver in a pseudo 1d case.

The field is zero at infinity.

Parameters

params	[input] : the operators and variables to be uses.
so	[input] : the source.
uu	[output] : the solution.

Definition at line 62 of file map_af_elliptic_pseudo_1d.C.

References Lorene::Scalar::get_etat().

◆ sol_elliptic_sin_zec()

void Lorene::Map_af::sol_elliptic_sin_zec	(	Param_elliptic &	params,
		const Scalar &	so,
		Scalar &	uu,
		double *	coefs,
		double *	phases
	)		const

General elliptic solver.

The equation is not solved in the compactified domain and the matching is done with an homogeneous solution.

Definition at line 429 of file map_af_elliptic.C.

References Lorene::Scalar::get_etat().

◆ srdsdt() [1/2]

void Lorene::Map_af::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 Lorene::Map.

Definition at line 478 of file map_af_deriv.C.

References Lorene::Cmp::get_etat().

◆ srdsdt() [2/2]

void Lorene::Map_af::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 Lorene::Map.

Definition at line 572 of file map_af_deriv.C.

References Lorene::Scalar::get_etat().

◆ srstdsdp() [1/2]

void Lorene::Map_af::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 Lorene::Map.

Definition at line 636 of file map_af_deriv.C.

References Lorene::Cmp::get_etat().

◆ srstdsdp() [2/2]

void Lorene::Map_af::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 Lorene::Map.

Definition at line 732 of file map_af_deriv.C.

References Lorene::Scalar::get_etat().

◆ stdsdp()

void Lorene::Map_af::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 Lorene::Map.

Definition at line 826 of file map_af_deriv.C.

References Lorene::Scalar::get_etat().

◆ val_lx() [1/2]

void Lorene::Map_af::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 Lorene::Map.

Definition at line 131 of file map_af_radius.C.

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

◆ val_lx() [2/2]

void Lorene::Map_af::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 $(r, \theta, \phi)$ .

Parameters

rr	[input] value of r
theta	[input] value of $\theta$
pphi	[input] value of $\phi$
par	[] unused by the `Map_af` version
l	[output] value of the domain index
xi	[output] value of $\xi$

Implements Lorene::Map.

Definition at line 195 of file map_af_radius.C.

References val_lx().

◆ val_lx_jk()

void Lorene::Map_af::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	[] unused by the `Map_af` version
l	[output] value of the domain index
xi	[output] value of $\xi$

Implements Lorene::Map_radial.

Definition at line 218 of file map_af_radius.C.

References val_lx().

◆ val_r()

double Lorene::Map_af::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 Lorene::Map.

Definition at line 99 of file map_af_radius.C.

References Lorene::Mg3d::get_type_r(), and Lorene::Map::mg.

◆ val_r_jk()

double Lorene::Map_af::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 Lorene::Map_radial.

Definition at line 208 of file map_af_radius.C.

References val_r().

Member Data Documentation

◆ alpha

double* Lorene::Map_af::alpha

private

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

Definition at line 2048 of file map.h.

◆ beta

double* Lorene::Map_af::beta

private

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

Definition at line 2050 of file map.h.

◆ bvect_cart

Base_vect_cart Lorene::Map::bvect_cart

protectedinherited

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 709 of file map.h.

◆ bvect_spher

Base_vect_spher Lorene::Map::bvect_spher

protectedinherited

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 701 of file map.h.

◆ cosp

Coord Lorene::Map::cosp

inherited

$\cos\phi$

Definition at line 736 of file map.h.

◆ cost

Coord Lorene::Map::cost

inherited

$\cos\theta$

Definition at line 734 of file map.h.

◆ d2rdtdx

Coord Lorene::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 1655 of file map.h.

◆ d2rdx2

Coord Lorene::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 1634 of file map.h.

◆ drdt

Coord Lorene::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 1583 of file map.h.

◆ dxdr

Coord Lorene::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 1575 of file map.h.

◆ lapr_tp

Coord Lorene::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 1646 of file map.h.

◆ mg

const Mg3d* Lorene::Map::mg

protectedinherited

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

Definition at line 688 of file map.h.

◆ ori_x

double Lorene::Map::ori_x

protectedinherited

Absolute coordinate x of the origin.

Definition at line 690 of file map.h.

◆ ori_y

double Lorene::Map::ori_y

protectedinherited

Absolute coordinate y of the origin.

Definition at line 691 of file map.h.

◆ ori_z

double Lorene::Map::ori_z

protectedinherited

Absolute coordinate z of the origin.

Definition at line 692 of file map.h.

◆ p_cmp_zero

Cmp* Lorene::Map::p_cmp_zero

protectedinherited

The null Cmp.

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

Definition at line 725 of file map.h.

◆ p_flat_met_cart

Metric_flat* Lorene::Map::p_flat_met_cart

mutableprotectedinherited

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

Definition at line 719 of file map.h.

◆ p_flat_met_spher

Metric_flat* Lorene::Map::p_flat_met_spher

mutableprotectedinherited

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

Definition at line 714 of file map.h.

◆ p_mp_angu

Map_af* Lorene::Map::p_mp_angu

mutableprotectedinherited

Pointer on the "angular" mapping.

Definition at line 727 of file map.h.

◆ phi

Coord Lorene::Map::phi

inherited

$\phi$ coordinate centered on the grid

Definition at line 732 of file map.h.

◆ r

Coord Lorene::Map::r

inherited

r coordinate centered on the grid

Definition at line 730 of file map.h.

◆ rot_phi

double Lorene::Map::rot_phi

protectedinherited

Angle between the x –axis and X –axis.

Definition at line 693 of file map.h.

◆ sinp

Coord Lorene::Map::sinp

inherited

$\sin\phi$

Definition at line 735 of file map.h.

◆ sint

Coord Lorene::Map::sint

inherited

$\sin\theta$

Definition at line 733 of file map.h.

◆ sr2d2rdt2

Coord Lorene::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 1672 of file map.h.

◆ sr2drdt

Coord Lorene::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 1615 of file map.h.

◆ sr2stdrdp

Coord Lorene::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 1623 of file map.h.

◆ srdrdt

Coord Lorene::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 1599 of file map.h.

◆ srstdrdp

Coord Lorene::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 1607 of file map.h.

◆ sstd2rdpdx

Coord Lorene::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 1663 of file map.h.

◆ stdrdp

Coord Lorene::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 1591 of file map.h.

◆ tet

Coord Lorene::Map::tet

inherited

$\theta$ coordinate centered on the grid

Definition at line 731 of file map.h.

◆ x

Coord Lorene::Map::x

inherited

x coordinate centered on the grid

Definition at line 738 of file map.h.

◆ xa

Coord Lorene::Map::xa

inherited

Absolute x coordinate.

Definition at line 742 of file map.h.

◆ xsr

Coord Lorene::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 1564 of file map.h.

◆ y

Coord Lorene::Map::y

inherited

y coordinate centered on the grid

Definition at line 739 of file map.h.

◆ ya

Coord Lorene::Map::ya

inherited

Absolute y coordinate.

Definition at line 743 of file map.h.

◆ z

Coord Lorene::Map::z

inherited

z coordinate centered on the grid

Definition at line 740 of file map.h.

◆ za

Coord Lorene::Map::za

inherited

Absolute z coordinate.

Definition at line 744 of file map.h.

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

Public Member Functions

Public Attributes

Protected Member Functions

Protected Attributes

Private Member Functions

Private Attributes

Friends

Detailed Description

Constructor & Destructor Documentation

◆ Map_af() [1/6]

◆ Map_af() [2/6]

◆ Map_af() [3/6]

◆ Map_af() [4/6]

◆ Map_af() [5/6]

◆ Map_af() [6/6]

◆ ~Map_af()

Member Function Documentation

◆ adapt()

◆ cmp_zero()

◆ comp_p_from_cartesian() [1/2]

◆ comp_p_from_cartesian() [2/2]

◆ comp_r_from_cartesian() [1/2]

◆ comp_r_from_cartesian() [2/2]

◆ comp_t_from_cartesian() [1/2]

◆ comp_t_from_cartesian() [2/2]

◆ comp_x_from_spherical() [1/2]

◆ comp_x_from_spherical() [2/2]

◆ comp_y_from_spherical() [1/2]

◆ comp_y_from_spherical() [2/2]

◆ comp_z_from_spherical() [1/2]

◆ comp_z_from_spherical() [2/2]

◆ convert_absolute()

◆ dalembert()

◆ dec2_dzpuis()

◆ dec_dzpuis()

◆ div_cost()

◆ div_r()

◆ div_r_zec()

◆ div_rsint()

◆ div_sint()

◆ div_tant()

◆ donne_para_poisson_vect()

◆ dsdr() [1/2]

◆ dsdr() [2/2]

◆ dsdradial()

◆ dsdt()

◆ dsdxi() [1/2]

◆ dsdxi() [2/2]

◆ flat_met_cart()

◆ flat_met_spher()

◆ get_alpha()

◆ get_beta()

◆ get_bvect_cart()

◆ get_bvect_spher()

◆ get_mg()

◆ get_ori_x()

◆ get_ori_y()

◆ get_ori_z()

◆ get_rot_phi()

◆ homothetie()

◆ homothetie_interne()

◆ inc2_dzpuis()

◆ inc_dzpuis()

◆ integrale()

◆ integrale_surface() [1/2]

◆ integrale_surface() [2/2]

◆ integrale_surface_infini() [1/2]

◆ integrale_surface_infini() [2/2]

◆ lapang()

◆ laplacien() [1/2]

◆ laplacien() [2/2]

◆ mp_angu()

◆ mult_cost()

◆ mult_r() [1/2]

◆ mult_r() [2/2]

◆ mult_r_zec()

◆ mult_rsint()

◆ mult_sint()

◆ operator=()

◆ operator==()