scalar_schw_implementation

The implementation of the interfaces defined in scalar_schw.

Uses

- Ancestors:
- scalar_schw
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Functions

function count_digits(l)

Utility routine to count the number of digits in an integer. Used to construct filenames.

Arguments

Type	Intent	Optional	Attributes		Name
integer(kind=ip),	intent(in)			::	l	The integer to count the number of digits in.

Return Value integer(kind=ip)

function construct_filename(l, m)

Construct unique filenames using a base name and the mode numbers l and m for reading in external inital data. The base name is constructed based on the run time parameters input_directory and input_basename.

Arguments

Type	Intent	Optional	Attributes		Name
integer(kind=ip),	intent(in)			::	l	The $\ell$ -mode of this mode.
integer(kind=ip),	intent(in)			::	m	The $m$ -mode of this mode.

Return Value character(len=1024)

The return value is the concatenation of the input_directory and input_basename and the mode information.

function flux(u, C11, C02)

Calculate a flux from the derivative data and the equation coefficient.

Arguments

Type	Intent	Attributes		Name
complex(kind=wp),	intent(in),	dimension(2)	::	u	The input state vector $(\Upsilon,\Pi)$ .
real(kind=wp),	intent(in)		::	C11	The coefficient of the second radial derivative term, $c_{rr}$ .
real(kind=wp),	intent(in)		::	C02	The coefficient of the mixed second derivative term, $c_{tr}$ .

Return Value complex(kind=wp), dimension(2)

On return the flux.

function n_of_l(l)

Calculate the number of m-modes for a given value of l. For the scalar charge in orbit around a Schwarzschild black hole we only need to evolve modes with $\ell+m$ even due to symmetries.

Arguments

Type	Intent	Optional	Attributes		Name
integer(kind=ip),	intent(in)			::	l	The $\ell$ -value.

Return Value integer(kind=ip)

The return value is the number of $m$ -modes that is evolved for this $\ell$ .

function nmodes_of_l(lmin, lmax)

Calculate the total number of modes from lmin to lmax.

Arguments

Type	Intent	Optional	Attributes		Name
integer(kind=ip),	intent(in)			::	lmin	The minimum value of $\ell$ to include in the sum, $\ell_{\mathrm{min}}$ .
integer(kind=ip),	intent(in)			::	lmax	The maximum value of $\ell$ to include in the sum. $\ell_{\mathrm{max}}$ .

Return Value integer(kind=ip)

The return value is to total number of $m$ -modes from all modes from $\ell_{\mathrm{min}}$ to $\ell_{\mathrm{max}}$ .

function linear_extrapolate(x, y)

Utility function for linear extrapolation of data to the horizon and Scri+.

Arguments

Type	Intent	Optional	Attributes		Name
real(kind=wp),	intent(in),		dimension(3)	::	x	A 1d array of size (3) of reals that contains the 3 coordinate locations involved in the extrapolation. The first element is the coordinate where the extrapolation is needed, that last two elements are the locations where data is known.
complex(kind=wp),	intent(in),		dimension(2:3)	::	y	A 1d array of size(2) that contains the known data.

Return Value complex(kind=wp)

The return value is the extrapolated data at the required location.

Subroutines

subroutine set_lm_mode_info(this, lmin, lmax)

Loop over all mode and store it's corresponding $\ell$ and m-values. This should maybe made into a type bound procedure.

Arguments

Type	Intent		Name
type(scal_schw),	intent(inout)	::	this	The mode information will be set for this scal_schw object.
integer(kind=ip),	intent(in)	::	lmin	The mininum $\ell$ -value.
integer(kind=ip),	intent(in)	::	lmax	The mininum $\ell$ -value.

subroutine get_elem_flux(rho, pi, nmodes, mode, r, effs, time_dc, e_lambda, e_s, e_sinv, e_coeffs, r_elem, rho_flux, pi_flux)

Calculate the characteristic fluxes for all elements for a single mode.

Arguments

Type	Intent	Attributes		Name
type(cgf),	intent(in)		::	rho	A complex grid function containing the time derivative variable, $\Upsilon$ .
type(cgf),	intent(in)		::	pi	A complex grid function containing the radial derivative variable, $\Pi$ .
integer(kind=ip),	intent(in)		::	nmodes	The total number of modes.
integer(kind=ip),	intent(in)		::	mode	The mode for which the flux is calculated.
type(rgf),	intent(in)		::	r	A real grid function that contains the Scharzschild radial coordinate.
type(scal_schw_eff),	intent(inout)		::	effs	The effective source object. Needed to add and subtract the derivatives of the singular field when calculating fluxes at the world-tube boundary.
type(tdc)			::	time_dc	The time dependent coordinate object. Needed to transform the derivatives of the field when calculating fluxes at the boundary of the time dependent coordinate region.
type(rgfb),	intent(in),	dimension(:)	::	e_lambda	A 1d array of size (2) of real boundary grid functions that contains the characteristic speeds at the element boundary.
type(rgfb),	intent(in),	dimension(:,:)	::	e_s	A 2d array of size (2,2) of real boundary grid functions that contains the matrix used to convert from characteristic to evolved variables.
type(rgfb),	intent(in),	dimension(:,:)	::	e_sinv	A 2d array of size (2,2) of real boundary grid functions that contains the matrix used to convert from evolved to characteristic variables.
type(rgf),	intent(in),	dimension(:)	::	e_coeffs	A 1d array of real grid functions that contains the coefficients for the wave equation.
type(ref_element),	intent(in)		::	r_elem	The reference element.
type(cgf),	intent(inout)		::	rho_flux	On output contains the $\Upsilon$ component of the characteristic flux.
type(cgf),	intent(inout)		::	pi_flux	On output contains the $\Pi$ component of the characteristic flux.

Module Procedures

module procedure scal_schw_init module subroutine scal_schw_init(this)

Arguments

Type	Intent	Optional	Attributes		Name
class(scal_schw),	intent(inout),		target	::	this	The equation that is being initialized.

module procedure scal_schw_rhs module subroutine scal_schw_rhs(this)

Arguments

Type	Intent	Optional	Attributes		Name
class(scal_schw),	intent(inout)			::	this	The equation for which the RHS is calculated.

module procedure scal_schw_save_globals_1 module subroutine scal_schw_save_globals_1(this)

Arguments

Type	Intent	Optional	Attributes		Name
class(scal_schw),	intent(inout)			::	this	The routine is called on this equation.

module procedure scal_schw_save_globals_2 module subroutine scal_schw_save_globals_2(this)

Arguments

Type	Intent	Optional	Attributes		Name
class(scal_schw),	intent(inout)			::	this	The routine is called on this equation.

module procedure scal_schw_load_globals module subroutine scal_schw_load_globals(this)

Arguments

Type	Intent	Optional	Attributes		Name
class(scal_schw),	intent(inout)			::	this	The routine is called on this equation.

module procedure scal_schw_flux module subroutine scal_schw_flux(this)

Arguments

Type	Intent	Optional	Attributes		Name
class(scal_schw),	intent(inout)			::	this	The routine is called on this equation.

module procedure read_all_modes module subroutine read_all_modes(this)

Arguments

Type	Intent	Optional	Attributes		Name
class(scal_schw),	intent(inout)			::	this	The routine is called on this equation.

module procedure output_coords module subroutine output_coords(this)

Arguments

Type	Intent	Optional	Attributes		Name
class(scal_schw),	intent(inout)			::	this	The routine is called on this equation.

module procedure tortoise_to_hyperboloidal module subroutine tortoise_to_hyperboloidal(this, elem, node, inner, dpsidt, dpsidr)

Arguments

Type	Intent		Name
class(scal_schw),	intent(inout)	::	this	The routine is called on this equation.
integer(kind=ip),	intent(in)	::	elem	The index of the element where the transformation is calculated.
integer(kind=ip),	intent(in)	::	node	The index of the node within that element where the transformation is calculated.
logical,	intent(in)	::	inner	If .true. use the transformation for the inner region. If .false. use the transformation for the outer region.
complex(kind=wp),	intent(inout)	::	dpsidt	On input holds the time derivative in Tortoise coordinates. On output holds the time derivative in hyperboloidal coordinates.
complex(kind=wp),	intent(inout)	::	dpsidr	On input holds the radial derivative in Tortoise coordinates. On output holds the radial derivative in hyperboloidal coordinates.

module procedure convert_var_name module function convert_var_name(var_name, mode)

Arguments

Type	Intent	Optional	Attributes		Name
character(len=*),	intent(in)			::	var_name	The input variable name.
integer(kind=ip),	intent(in)			::	mode	the mode number.

Return Value character(len=len(var_name)+5)

The return value is the converted variable name.

scalar_schw_implementation Submodule

Contents

Functions

Subroutines

Module Procedures

Uses

Ancestors:

Contents

Functions

Subroutines

Module Procedures

Functions

function count_digits(l)

Arguments

Return Value integer(kind=ip)

function construct_filename(l, m)

Arguments

Return Value character(len=1024)

function flux(u, C11, C02)

Arguments

Return Value complex(kind=wp), dimension(2)

function n_of_l(l)

Arguments

Return Value integer(kind=ip)

function nmodes_of_l(lmin, lmax)

Arguments

Return Value integer(kind=ip)

function linear_extrapolate(x, y)

Arguments

Return Value complex(kind=wp)

Subroutines

subroutine set_lm_mode_info(this, lmin, lmax)

Arguments

subroutine get_elem_flux(rho, pi, nmodes, mode, r, effs, time_dc, e_lambda, e_s, e_sinv, e_coeffs, r_elem, rho_flux, pi_flux)

Arguments

Module Procedures

module procedure scal_schw_init module subroutine scal_schw_init(this) Interface →

Arguments

module procedure scal_schw_rhs module subroutine scal_schw_rhs(this) Interface →

Arguments

module procedure scal_schw_save_globals_1 module subroutine scal_schw_save_globals_1(this) Interface →

Arguments

module procedure scal_schw_save_globals_2 module subroutine scal_schw_save_globals_2(this) Interface →

Arguments

module procedure scal_schw_load_globals module subroutine scal_schw_load_globals(this) Interface →

Arguments

module procedure scal_schw_flux module subroutine scal_schw_flux(this) Interface →

Arguments

module procedure read_all_modes module subroutine read_all_modes(this) Interface →

Arguments

module procedure output_coords module subroutine output_coords(this) Interface →

Arguments

module procedure tortoise_to_hyperboloidal module subroutine tortoise_to_hyperboloidal(this, elem, node, inner, dpsidt, dpsidr) Interface →

Arguments

module procedure convert_var_name module function convert_var_name(var_name, mode) Interface →

Arguments

Return Value character(len=len(var_name)+5)

module procedure scal_schw_init module subroutine scal_schw_init(this)

module procedure scal_schw_rhs module subroutine scal_schw_rhs(this)

module procedure scal_schw_save_globals_1 module subroutine scal_schw_save_globals_1(this)

module procedure scal_schw_save_globals_2 module subroutine scal_schw_save_globals_2(this)

module procedure scal_schw_load_globals module subroutine scal_schw_load_globals(this)

module procedure scal_schw_flux module subroutine scal_schw_flux(this)

module procedure read_all_modes module subroutine read_all_modes(this)

module procedure output_coords module subroutine output_coords(this)

module procedure tortoise_to_hyperboloidal module subroutine tortoise_to_hyperboloidal(this, elem, node, inner, dpsidt, dpsidr)

module procedure convert_var_name module function convert_var_name(var_name, mode)