Multi-domain grid. More...

#include <grilles.h>

Public Member Functions
	Mg3d (int nz, int nbr[], int typr[], int nbt[], int typt, int nbp[], int typp, int *base_r=0x0)
	General constructor. More...

	Mg3d (int nz, int nbr, int nbt, int nbp, int typt, int typp, bool compact, bool legendre=false)
	Simplified constructor for a standard multi-grid. More...

	Mg3d (int nz, int nbr, int nbt, int nbp, int typt, int typp)
	Simplified constructor for a standard multi-grid only with shells and Chebyshev. More...

	Mg3d (const string &filename)
	Constructor from a formatted file, given by its name (string). More...

	Mg3d (FILE *fd, bool read_base=false)
	Constructor from a file (see `sauve(FILE*)`). More...

	Mg3d (const Mg3d &)
	Copy constructor (private and not implemented to make `Mg3d` a non-copyable class) More...

	~Mg3d ()
	Destructor. More...

int	get_nzone () const
	Returns the number of domains. More...

int	get_nr (int l) const
	Returns the number of points in the radial direction ( $\xi$ ) in domain no. l. More...

int	get_nt (int l) const
	Returns the number of points in the co-latitude direction ( $\theta$ ) in domain no. l. More...

int	get_np (int l) const
	Returns the number of points in the azimuthal direction ( $\phi$ ) in domain no. l. More...

int	get_type_r (int l) const
	Returns the type of sampling in the radial direction in domain no. More...

int	get_type_t () const
	Returns the type of sampling in the $\theta$ direction: `SYM` : $\theta\in[0,\pi/2]$ : symmetry with respect to the equatorial plane `NONSYM` : $\theta\in[0,\pi]$ : no symmetry with respect to the equatorial plane. More...

int	get_type_p () const
	Returns the type of sampling in the $\phi$ direction: `SYM` : $\phi\in[0,\pi[$ : symmetry with respect to the transformation $\phi \mapsto \phi + \pi$ `NONSYM` : $\phi\in[0,2\pi[$ : no symmetry with respect to the transformation $\phi \mapsto \phi + \pi$ More...

const Grille3d *	get_grille3d (int l) const
	Returns a pointer on the 3D mono-grid for domain no. l. More...

int	get_colloc_r (int l) const
	Returns the type of collocation points used in domain no. More...

const Mg3d *	get_angu () const
	Returns the pointer on the associated angular grid. More...

const Mg3d *	get_angu_1dom () const
	Returns the pointer on the associated mono-domain angular grid. More...

const Mg3d *	get_radial () const
	Returns the pointer on the associated radial grid. More...

const Mg3d *	get_three_halves () const
	Returns the pointer on the associated grid with 50% points in every direction for dealiasing. More...

const Mg3d *	get_twice () const
	Returns the pointer on the grid which has twice the number of points in each dimension (for desaliasing). More...

const Mg3d *	plus_half () const
	Returns the pointer on the grid which has 50% more points in r dimension (for desaliasing). More...

const Mg3d *	plus_half_angu () const
	Returns the pointer on the grid which has 50% more points in and dimension (for desaliasing). More...

const Mg3d *	get_non_axi () const
	Returns the pointer on the grid which has at least 4 points in the $\phi$ direction and at least 5 in the $\theta$ direction (for tensor rotations). More...

bool	operator== (const Mg3d &) const
	Comparison operator (egality) More...

void	sauve (FILE *fd, bool save_base=false) const
	Saves into a file. More...

bool	operator!= (const Mg3d &) const
	Operator !=. More...

Base_val	std_base_scal () const
	Returns the standard spectral bases for a scalar. More...

Base_val	std_base_scal_odd () const
	Returns the standard odd spectral bases for a scalar. More...

Base_val **	std_base_vect_cart () const
	Returns the standard spectral bases for the Cartesian components of a vector. More...

Base_val **	std_base_vect_spher () const
	Returns the standard spectral bases for the spherical components of a vector. More...

Base_val **	pseudo_base_vect_cart () const
	Returns the standard spectral bases for the Cartesian components of a pseudo-vector. More...

Base_val **	pseudo_base_vect_spher () const
	Returns the standard spectral bases for the spherical components of a pseudo-vector. More...

Protected Member Functions
void	del_deriv () const
	Deletes all the derived quantities (`g_radial` , `g_angu`, `g_twice`, ...) More...

void	set_deriv_0x0 () const
	Sets to `0x0` all the pointers on derived quantities (`g_radial` , `g_angu`, `g_twice`, ... More...

Protected Attributes
int	nzone
	Number of domains (zones) More...

int *	nr
	Array (size: `nzone`) of nb. of points in r ( $\xi$ ) More...

int *	nt
	Array (size: `nzone`) of nb. of points in $\theta$ . More...

int *	np
	Array (size: `nzone`) of nb. of points in $\phi$ . More...

int *	type_r
	Array (size: `nzone`) of type of sampling in r ( $\xi$ ) (`RARE`,`FIN`, `UNSURR`) More...

int	type_t
	Type of sampling in $\theta$ (`SYM`, `NONSYM`) More...

int	type_p
	Type of sampling in $\phi$ (`SYM`, `NONSYM`) More...

int *	colloc_r
	Array (size: `nzone`) of type of collocation points in r ( $\xi$ ) and related decompoisition bases (`BASE_CHEB`, `BASE_LEG`, `BASE_JAC02` ). More...

Grille3d **	g
	Array (size: `nzone`) of pointers on the `Grille3d's`. More...

Mg3d *	g_angu
	Pointer on the associated angular grid. More...

Mg3d *	g_angu_1dom
	Pointer on the associated angular grid with only one domain. More...

Mg3d *	g_radial
	Pointer on the associated radial grid. More...

Mg3d *	g_three_halves
	Pointer on the grid having 50% more points in every direction, for dealiasing. More...

Mg3d *	g_twice
	Pointer on the grid which has twice the number of points in each dimension (for desaliasing). More...

Mg3d *	g_plus_half
	Pointer on the grid which has 50% more points in r dimension (for desaliasing). More...

Mg3d *	g_plus_half_angu
	Pointer on the grid which has 50% more points in and dimension (for desaliasing). More...

Mg3d *	g_non_axi
	Pointer on the grid which has at least 4 points in the $\phi$ direction and at least 5 in the $\theta$ direction (for tensor rotations). More...

Private Member Functions
void	operator= (const Mg3d &)
	Assignement operator (private and not implemented to make `Mg3d` a non-copyable class) More...

Friends
ostream &	operator<< (ostream &, const Mg3d &)
	Display. More...

Detailed Description

Multi-domain grid.

()

A multi-domain grid is a set of 3D grids for the implementation of the multi-domain spectral method described in Bonazzola, Gourgoulhon & Marck, Phys. Rev. D 58, 104020 (1998). Each domain is represented by a 3D mono grid (Grille3d) and is called a zone. For each direction, the Number of Degrees of Freedom (NDF) is a priori independent of the zone. However, some methods or routines may refuse to work if the NDF of some $(\theta, \phi)$ direction is not identical in all the zones. This holds for the type of sampling (symmetry) too.

Version: #$Id: grilles.h,v 1.26 2025/03/26 10:12:20 j_novak Exp $#

Definition at line 276 of file grilles.h.

Constructor & Destructor Documentation

◆ Mg3d() [1/6]

Lorene::Mg3d::Mg3d	(	int	nz,
		int	nbr[],
		int	typr[],
		int	nbt[],
		int	typt,
		int	nbp[],
		int	typp,
		int *	base_r = `0x0`
	)

General constructor.

Parameters

nz	[input] Number of domains (zones).
nbr[]	[input] Array (size: `nz` ) of number of degree of freedom (NDF) in r-direction
typr[]	[input] Array (size: `nz` ) of type of sampling in r -direction
nbt[]	[input] Array (size: `nz` ) of NDF in $\theta$ -direction
typt	[input] Type of sampling in $\theta$ -direction
nbp[]	[input] Array (size: `nz`) of NDF in $\phi$ -direction
typp	[input] Type of sampling in $\phi$ -direction
base_r	[input] Types of r bases in each domain, to define the collocation points: `BASE_CHEB` , `BASE_LEG` or `BASE_JAC02`. If the pointer is null, BASE_CHEB is set.

Definition at line 175 of file mg3d.C.

References colloc_r, and type_r.

◆ Mg3d() [2/6]

Lorene::Mg3d::Mg3d	(	int	nz,
		int	nbr,
		int	nbt,
		int	nbp,
		int	typt,
		int	typp,
		bool	compact,
		bool	legendre = `false`
	)

Simplified constructor for a standard multi-grid.

This provides a multi-grid with the same number of degrees of freedom in all the domains.
The domain of index l = 0 will be a nucleus: $\xi\in [0,1]$ , rarefied sampling (type RARE) near the origin;
domains of indices $1 \le {\tt l} \le {\tt nz}-2$ will be shells: $\xi\in [-1,1]$ , dense sampling (type FIN) near -1 and 1;
if compact == true, the domains of index l = nz-1 will be the outermost compactified shell: $\xi\in [-1,1]$ , dense sampling (type UNSURR) near -1 and 1 for a 1/r discretization.

Parameters

nz	[input] Number of domains (zones).
nbr	[input] Number of degree of freedom (NDF) in r -direction in each domain
nbt	[input] Number of degree of freedom (NDF) in $\theta$ -direction in each domain
nbp	[input] Number of degree of freedom (NDF) in $\phi$ -direction in each domain
typt	[input] Type of sampling in $\theta$ -direction: `SYM` for a sampling in $[0,\pi/2]$ (symmetry with respect to the equatorial plane), `NONSYM` for a sampling in $[0,\pi]$
typp	[input] Type of sampling in $\phi$ -direction: `SYM` for a sampling in $[0,\pi[$ (symmetry with respect to a $\pi$ translation in $\phi$ ) `NONSYM` for a sampling in $[0,2\pi[$
compact	[input] `true` for the last domain to have a 1/r sampling (`UNSURR` ) instead of a r sampling (`FIN` ).
legendre	[input] `true` if the nucleus and shells have Legendre-type collocation points. If `false`, Chebyshev ones shall be used.

Definition at line 221 of file mg3d.C.

References colloc_r, and type_r.

◆ Mg3d() [3/6]

Lorene::Mg3d::Mg3d	(	int	nz,
		int	nbr,
		int	nbt,
		int	nbp,
		int	typt,
		int	typp
	)

Simplified constructor for a standard multi-grid only with shells and Chebyshev.

This provides a multi-grid with the same number of degrees of freedom in all the domains.
ALL DOMAINS ARE TREATED AS SHELLS $\xi\in [-1,1]$ , dense sampling (type FIN) near -1 and 1;
and only Chebyshev bases are considered.

Parameters

nz	[input] Number of domains (zones).
nbr	[input] Number of degree of freedom (NDF) in r -direction in each domain
nbt	[input] Number of degree of freedom (NDF) in $\theta$ -direction in each domain
nbp	[input] Number of degree of freedom (NDF) in $\phi$ -direction in each domain
typt	[input] Type of sampling in $\theta$ -direction: `SYM` for a sampling in $[0,\pi/2]$ (symmetry with respect to the equatorial plane), `NONSYM` for a sampling in $[0,\pi]$
typp	[input] Type of sampling in $\phi$ -direction: `SYM` for a sampling in $[0,\pi[$ (symmetry with respect to a $\pi$ translation in $\phi$ ) `NONSYM` for a sampling in $[0,2\pi[$

Definition at line 279 of file mg3d.C.

References colloc_r, and type_r.

◆ Mg3d() [4/6]

Lorene::Mg3d::Mg3d ( const string & filename )

explicit

Constructor from a formatted file, given by its name (string).

Definition at line 327 of file mg3d.C.

References nzone, Lorene::search_file(), and type_t.

◆ Mg3d() [5/6]

Lorene::Mg3d::Mg3d	(	FILE *	fd,
		bool	read_base = `false`
	)

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

If the boolean flag read_base is false (default) the spectral basis is not saved, for compatibility with older versions. If it is set to true , the basis is saved.

Definition at line 445 of file mg3d.C.

References colloc_r, Lorene::fread_be(), g, np, nr, nt, nzone, type_p, type_r, and type_t.

◆ Mg3d() [6/6]

Lorene::Mg3d::Mg3d ( const Mg3d & )

Copy constructor (private and not implemented to make Mg3d a non-copyable class)

◆ ~Mg3d()

Lorene::Mg3d::~Mg3d ( )

Destructor.

Definition at line 483 of file mg3d.C.

References colloc_r, del_deriv(), g, np, nr, nt, nzone, and type_r.

Member Function Documentation

◆ del_deriv()

void Lorene::Mg3d::del_deriv ( ) const

protected

Deletes all the derived quantities (g_radial , g_angu, g_twice, ...)

Definition at line 577 of file mg3d.C.

References g_angu, g_angu_1dom, g_non_axi, g_plus_half, g_plus_half_angu, g_radial, g_three_halves, g_twice, and set_deriv_0x0().

◆ get_angu()

const Mg3d * Lorene::Mg3d::get_angu ( ) const

Returns the pointer on the associated angular grid.

Definition at line 609 of file mg3d.C.

References colloc_r, g_angu, Mg3d(), np, nt, nzone, type_p, type_r, and type_t.

◆ get_angu_1dom()

const Mg3d * Lorene::Mg3d::get_angu_1dom ( ) const

Returns the pointer on the associated mono-domain angular grid.

This angular grid corresponds to the first domain (index 0).

Definition at line 630 of file mg3d.C.

References g_angu_1dom, np, and nt.

◆ get_colloc_r()

int Lorene::Mg3d::get_colloc_r ( int l ) const

inline

Returns the type of collocation points used in domain no.

l. This type depends on the spectral decomposition basis:

BASE_CHEB : Chebyshev basis and collocation points
BASE_LEG : Legendre basis and collocation points
BASE_JAC02 : Jacobi (0,2) polynomials

Definition at line 530 of file grilles.h.

References colloc_r, and nzone.

◆ get_grille3d()

const Grille3d* Lorene::Mg3d::get_grille3d ( int l ) const

inline

Returns a pointer on the 3D mono-grid for domain no. l.

Definition at line 519 of file grilles.h.

References g, and nzone.

◆ get_non_axi()

const Mg3d * Lorene::Mg3d::get_non_axi ( ) const

Returns the pointer on the grid which has at least 4 points in the $\phi$ direction and at least 5 in the $\theta$ direction (for tensor rotations).

Definition at line 834 of file mg3d.C.

References colloc_r, g_non_axi, Mg3d(), np, nr, nt, nzone, type_p, type_r, and type_t.

◆ get_np()

int Lorene::Mg3d::get_np ( int l ) const

inline

Returns the number of points in the azimuthal direction ( $\phi$ ) in domain no. l.

Definition at line 481 of file grilles.h.

References np, and nzone.

◆ get_nr()

int Lorene::Mg3d::get_nr ( int l ) const

inline

Returns the number of points in the radial direction ( $\xi$ ) in domain no. l.

Definition at line 471 of file grilles.h.

References nr, and nzone.

◆ get_nt()

int Lorene::Mg3d::get_nt ( int l ) const

inline

Returns the number of points in the co-latitude direction ( $\theta$ ) in domain no. l.

Definition at line 476 of file grilles.h.

References nt, and nzone.

◆ get_nzone()

int Lorene::Mg3d::get_nzone ( ) const

inline

Returns the number of domains.

Definition at line 467 of file grilles.h.

References nzone.

◆ get_radial()

const Mg3d * Lorene::Mg3d::get_radial ( ) const

Returns the pointer on the associated radial grid.

Definition at line 654 of file mg3d.C.

References g_radial, Mg3d(), nr, nzone, and type_r.

◆ get_three_halves()

const Mg3d * Lorene::Mg3d::get_three_halves ( ) const

Returns the pointer on the associated grid with 50% points in every direction for dealiasing.

Definition at line 671 of file mg3d.C.

References colloc_r, g_three_halves, Mg3d(), np, nr, nt, nzone, type_p, type_r, and type_t.

◆ get_twice()

const Mg3d * Lorene::Mg3d::get_twice ( ) const

Returns the pointer on the grid which has twice the number of points in each dimension (for desaliasing).

Definition at line 720 of file mg3d.C.

References colloc_r, g_twice, Mg3d(), np, nr, nt, nzone, type_p, type_r, and type_t.

◆ get_type_p()

int Lorene::Mg3d::get_type_p ( ) const

inline

Returns the type of sampling in the $\phi$ direction:
SYM : $\phi\in[0,\pi[$ : symmetry with respect to the transformation $\phi \mapsto \phi + \pi$
NONSYM : $\phi\in[0,2\pi[$ : no symmetry with respect to the transformation $\phi \mapsto \phi + \pi$

Definition at line 514 of file grilles.h.

References type_p.

◆ get_type_r()

int Lorene::Mg3d::get_type_r ( int l ) const

inline

Returns the type of sampling in the radial direction in domain no.

l :
RARE : $\xi\in[0,1]$ : rarefied at the origin
FIN : $\xi\in[-1,1]$ : dense at the two extremities
UNSURR : $\xi\in[-1,1]$ : dense at the two extremities, in view of using $u=1/r$ as radial variable

Definition at line 493 of file grilles.h.

References nzone, and type_r.

◆ get_type_t()

int Lorene::Mg3d::get_type_t ( ) const

inline

Returns the type of sampling in the $\theta$ direction:
SYM : $\theta\in[0,\pi/2]$ : symmetry with respect to the equatorial plane
NONSYM : $\theta\in[0,\pi]$ : no symmetry with respect to the equatorial plane.

Definition at line 504 of file grilles.h.

References type_t.

◆ operator!=()

bool Lorene::Mg3d::operator!= ( const Mg3d & titi ) const

Operator !=.

Definition at line 552 of file mg3d.C.

References colloc_r, np, nr, nt, nzone, type_p, type_r, and type_t.

◆ operator=()

void Lorene::Mg3d::operator= ( const Mg3d & )

private

Assignement operator (private and not implemented to make Mg3d a non-copyable class)

◆ operator==()

bool Lorene::Mg3d::operator== ( const Mg3d & mgi ) const

Comparison operator (egality)

Definition at line 865 of file mg3d.C.

References colloc_r, get_colloc_r(), get_np(), get_nr(), get_nt(), get_nzone(), get_type_p(), get_type_r(), get_type_t(), np, nr, nt, nzone, type_p, type_r, and type_t.

◆ plus_half()

const Mg3d * Lorene::Mg3d::plus_half ( ) const

Returns the pointer on the grid which has 50% more points in r dimension (for desaliasing).

Definition at line 768 of file mg3d.C.

References colloc_r, g_plus_half, Mg3d(), np, nr, nt, nzone, type_p, type_r, and type_t.

◆ plus_half_angu()

const Mg3d * Lorene::Mg3d::plus_half_angu ( ) const

Returns the pointer on the grid which has 50% more points in and dimension (for desaliasing).

Definition at line 796 of file mg3d.C.

References colloc_r, g_plus_half_angu, Mg3d(), np, nr, nt, nzone, type_p, type_r, and type_t.

◆ pseudo_base_vect_cart()

Base_val ** Lorene::Mg3d::pseudo_base_vect_cart ( ) const

Returns the standard spectral bases for the Cartesian components of a pseudo-vector.

Definition at line 800 of file mg3d_std_base.C.

References colloc_r, get_nzone(), and nzone.

◆ pseudo_base_vect_spher()

Base_val ** Lorene::Mg3d::pseudo_base_vect_spher ( ) const

Returns the standard spectral bases for the spherical components of a pseudo-vector.

Definition at line 1120 of file mg3d_std_base.C.

References colloc_r, get_nzone(), and nzone.

◆ sauve()

void Lorene::Mg3d::sauve	(	FILE *	fd,
		bool	save_base = `false`
	)		const

Saves into a file.

By default, if save_base is false, the spectral decomposition basis colloc_r is not saved (for compatibility reasons). If save_base is true, then colloc_r is save, too. The same value for the flag read_base must be given in the contructor reading the file.

Definition at line 503 of file mg3d.C.

References colloc_r, Lorene::fwrite_be(), np, nr, nt, nzone, type_p, type_r, and type_t.

◆ set_deriv_0x0()

void Lorene::Mg3d::set_deriv_0x0 ( ) const

protected

Sets to 0x0 all the pointers on derived quantities (g_radial , g_angu, g_twice, ...

)

Definition at line 592 of file mg3d.C.

References g_angu, g_angu_1dom, g_non_axi, g_plus_half, g_plus_half_angu, g_radial, g_three_halves, and g_twice.

◆ std_base_scal()

Base_val Lorene::Mg3d::std_base_scal ( ) const

Returns the standard spectral bases for a scalar.

Definition at line 107 of file mg3d_std_base.C.

References colloc_r, and nzone.

◆ std_base_scal_odd()

Base_val Lorene::Mg3d::std_base_scal_odd ( ) const

Returns the standard odd spectral bases for a scalar.

Definition at line 137 of file mg3d_std_base.C.

References colloc_r, and nzone.

◆ std_base_vect_cart()

Base_val ** Lorene::Mg3d::std_base_vect_cart ( ) const

Returns the standard spectral bases for the Cartesian components of a vector.

Definition at line 183 of file mg3d_std_base.C.

References colloc_r, get_nzone(), and nzone.

◆ std_base_vect_spher()

Base_val ** Lorene::Mg3d::std_base_vect_spher ( ) const

Returns the standard spectral bases for the spherical components of a vector.

Definition at line 505 of file mg3d_std_base.C.

References colloc_r, get_nzone(), and nzone.

Friends And Related Function Documentation

◆ operator<<

ostream& operator<<	(	ostream &	o,
		const Mg3d &	g
	)

int* Lorene::Mg3d::type_r

protected

Array (size: nzone) of type of sampling in r ( $\xi$ ) (RARE,FIN, UNSURR)

Definition at line 290 of file grilles.h.

◆ type_t

int Lorene::Mg3d::type_t

protected

Type of sampling in $\theta$ (SYM, NONSYM)

Definition at line 293 of file grilles.h.

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

Public Member Functions

Protected Member Functions

Protected Attributes

Private Member Functions

Friends

Detailed Description

Constructor & Destructor Documentation

◆ Mg3d() [1/6]

◆ Mg3d() [2/6]

◆ Mg3d() [3/6]

◆ Mg3d() [4/6]

◆ Mg3d() [5/6]

◆ Mg3d() [6/6]

◆ ~Mg3d()

Member Function Documentation

◆ del_deriv()

◆ get_angu()

◆ get_angu_1dom()

◆ get_colloc_r()

◆ get_grille3d()

◆ get_non_axi()

◆ get_np()

◆ get_nr()

◆ get_nt()

◆ get_nzone()

◆ get_radial()

◆ get_three_halves()

◆ get_twice()

◆ get_type_p()

◆ get_type_r()

◆ get_type_t()

◆ operator!=()

◆ operator=()

◆ operator==()

◆ plus_half()

◆ plus_half_angu()

◆ pseudo_base_vect_cart()

◆ pseudo_base_vect_spher()

◆ sauve()

◆ set_deriv_0x0()

◆ std_base_scal()

◆ std_base_scal_odd()

◆ std_base_vect_cart()

◆ std_base_vect_spher()

Friends And Related Function Documentation

◆ operator<<

Member Data Documentation

◆ colloc_r

◆ g

◆ g_angu

◆ g_angu_1dom

◆ g_non_axi

◆ g_plus_half

◆ g_plus_half_angu

◆ g_radial

◆ g_three_halves

◆ g_twice

◆ np

◆ nr

◆ nt

◆ nzone

◆ type_p

◆ type_r

◆ type_t