tdc – SelfForce1D

type, public :: tdc

A class that defines a time dependent coordinate transformation for the scalar wave equation on s Schwarzschild spacetime.

Inherits

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Inherited by

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Components

Type	Visibility		Name
type(rgfb),	public	::	dxdlambda_b	A real boundary grid function that stores $\frac{\partial r_*}{\partial \lambda}$ on the element boundaries.
type(rgfb),	public	::	dxdxi_b	A real boundary grid function that stores $\frac{\partial r_*}{\partial \xi}$ on the element boundaries.
real(kind=wp),	public	::	maxspeed	The maximum coordinate speed (needed for CFL timestep condition).
type(rgf),	public	::	dxdlambda	A real grid function that stores $\frac{\partial r_*}{\partial \lambda}$ everywhere.
type(rgf),	public	::	dxdxi	A real grid function that stores $\frac{\partial r_*}{\partial \xi}$ everywhere.
type(rgf),	public	::	d2xdlambda2	A real grid function that stores $\frac{\partial^2 r_*}{\partial \lambda^2}$ everywhere.
type(rgf),	public	::	d2xdxi2	A real grid function that stores $\frac{\partial^2 r_*}{\partial \xi^2}$ everywhere.
type(rgf),	public	::	d2xdlambdadxi	A real grid function that stores $\frac{\partial^2 r_*}{\partial \lambda \partial \xi}$ everywhere.
type(rgf),	public	::	rm2m	A real grid function that stores $r-2M$ everywhere.

Type-Bound Procedures

procedure, public :: init => tdc_init

The initialization routine.

interface

public module subroutine tdc_init(this)

The interface for the initialization routine.

Arguments

Type Intent Optional Attributes Name

class(tdc), intent(inout) :: this
This time dependent coordinate object is being initialized.

Type	Intent	Optional	Attributes		Name
class(tdc),	intent(inout)			::	this	This time dependent coordinate object is being initialized.

procedure, public :: set_coefficients => tdc_set_coefficients

The routine that sets the coefficients for the wave equation.

interface

public module subroutine tdc_set_coefficients(this, coeffs, lcoeffs, lambda, s, sinv, rho, rstar, rschw, ll)

The interface for the routine that sets the coefficient for the scalar wave equation in Schwarzschild spacetime.

Arguments

Type	Intent	Attributes		Name
class(tdc),	intent(inout)		::	this	The routine is called on this time dependent coordinate object.
type(rgf),	intent(inout),	dimension(:)	::	coeffs	A 1d array of real grid functions containing the wave equation coefficients (should be eq_coeffs). On output it will contain $(c_{\xi\xi}, c_{\lambda\xi}, c_{\xi}, c_{\lambda})$ .
type(rgf),	intent(inout),	dimension(:)	::	lcoeffs	A 1d array of real grid functions containing the $\ell$ dependent coefficients (should be eq_lcoeffs). On output it will contain the potential for all modes.
type(rgfb),	intent(inout),	dimension(:)	::	lambda	A 1d array of real boundary grid functions containing the characteristic speeds at the boundary of the elements (should be eq_lambda). On output it will be updated.
type(rgfb),	intent(inout),	dimension(:,:)	::	s	A 2d array of real boundary grid functions containing the matrix used to convert from characteristic to evolved variables (should be eq_s). On output it will be updated.
type(rgfb),	intent(inout),	dimension(:,:)	::	sinv	A 2d array of real boundary grid functions containing the matrix used to convert from evolved to characteristic variables (should be eq_sinv). On output it will be updated.
type(rgf),	intent(in)		::	rho	A real grid function containing the computational radial coordinate, $\rho$ .
type(rgf),	intent(inout)		::	rstar	A real grid function containing the tortoise radial coordinate, $r_*$ . On output this will be updated.
type(rgf),	intent(inout)		::	rschw	A real grid function containing the Schwarzschild radial coodrinate, $r_{\mathrm{schw}}$ . On output this will be updated.
integer(kind=c_int),	intent(in),	dimension(:)	::	ll	A 1d array of c_int containing the $\ell$ -values of all the modes.

procedure, public :: tdc_to_tortoise_cvec => tdc_tdc_to_tortoise_cvec

Routine to transform from $\lambda,\xi)$ to $(t,r_*)$ for complex vector arguments at the boundary of an element.

interface

public module subroutine tdc_tdc_to_tortoise_cvec(this, ielem, dir, dudlambda, dudxi, dudt, dudrstar)

Routine to transform from time dependent $(\lambda,\xi)$ to tortoise coordinates $(t,r_*)$ for complex vector input at element boundaries.

Arguments

Type	Intent	Attributes		Name
class(tdc),	intent(inout)		::	this	The routine is called on this time dependent coordinate object.
integer(kind=ip),	intent(in)		::	ielem	The index of the element that contains the coordinate transformation information.
integer(kind=ip),	intent(in)		::	dir	The index of the boundary within the element that contains the coordinate transformation. Left boundary: 1, right boundary: 2.
complex(kind=wp),	intent(in),	dimension(:)	::	dudlambda	The vector of $\frac{\partial\Psi}{\partial\lambda}$ values to transform.
complex(kind=wp),	intent(in),	dimension(:)	::	dudxi	The vector of $\frac{\partial\Psi}{\partial\xi}$ values to transform.
complex(kind=wp),	intent(out),	dimension(:)	::	dudt	On output contains the $\frac{\partial\Psi}{\partial t}$ vector.
complex(kind=wp),	intent(out),	dimension(:)	::	dudrstar	On output contains the $\frac{\partial\Psi}{\partial r_*}$ vector.

procedure, public :: tdc_to_tortoise_cscal => tdc_tdc_to_tortoise_cscal

Routine to transform from $\lambda,\xi)$ to $(t,r_*)$ for complex scalar arguments at the boundary of an element.

interface

public module subroutine tdc_tdc_to_tortoise_cscal(this, ielem, dir, dudlambda, dudxi, dudt, dudrstar)

Routine to transform from time dependent $(\lambda,\xi)$ to tortoise coordinates $(t,r_*)$ for complex scalar input at element boundaries.

Arguments

Type	Intent		Name
class(tdc),	intent(inout)	::	this	The routine is called on this time dependent coordinate object.
integer(kind=ip),	intent(in)	::	ielem	The index of the element that contains the coordinate transformation information.
integer(kind=ip),	intent(in)	::	dir	The index of the boundary within the element that contains the coordinate transformation. Left boundary: 1, right boundary: 2.
complex(kind=wp),	intent(in)	::	dudlambda	The value of $\frac{\partial\Psi}{\partial\lambda}$ to transform.
complex(kind=wp),	intent(in)	::	dudxi	The value of $\frac{\partial\Psi}{\partial\xi}$ to transform.
complex(kind=wp),	intent(out)	::	dudt	On output contains the $\frac{\partial\Psi}{\partial t}$ value.
complex(kind=wp),	intent(out)	::	dudrstar	On output contains the $\frac{\partial\Psi}{\partial r_*}$ value.

procedure, public :: tdc_to_tortoise_rscal => tdc_tdc_to_tortoise_rscal

Routine to transform from $\lambda,\xi)$ to $(t,r_*)$ for real scalar arguments at the boundary of an element.

interface

public module subroutine tdc_tdc_to_tortoise_rscal(this, ielem, dir, dudlambda, dudxi, dudt, dudrstar)

Routine to transform from time dependent $(\lambda,\xi)$ to tortoise coordinates $(t,r_*)$ for real scalar input at element boundaries.

Arguments

Type	Intent		Name
class(tdc),	intent(inout)	::	this	The routine is called on this time dependent coordinate object.
integer(kind=ip),	intent(in)	::	ielem	The index of the element that contains the coordinate transformation information.
integer(kind=ip),	intent(in)	::	dir	The index of the boundary within the element that contains the coordinate transformation. Left boundary: 1, right boundary: 2.
real(kind=wp),	intent(in)	::	dudlambda	The value of $\frac{\partial\Psi}{\partial\lambda}$ to transform.
real(kind=wp),	intent(in)	::	dudxi	The value of $\frac{\partial\Psi}{\partial\xi}$ to transform.
real(kind=wp),	intent(out)	::	dudt	On output contains the $\frac{\partial\Psi}{\partial t}$ value.
real(kind=wp),	intent(out)	::	dudrstar	On output contains the $\frac{\partial\Psi}{\partial r_*}$ value.

generic, public :: tdc_to_tortoise => tdc_to_tortoise_cvec, tdc_to_tortoise_cscal, tdc_to_tortoise_rscal

Generic name for routines that transform from $\lambda,\xi)$ to $(t,r_*)$ at the boundary of an element.

public interface tdc_tdc_to_tortoise_cvec()

Arguments
None
public interface tdc_tdc_to_tortoise_cscal()

Arguments
None
public interface tdc_tdc_to_tortoise_rscal()

Arguments
None

procedure, public :: tortoise_to_tdc_cvecb => tdc_tortoise_to_tdc_cvecb

Routine to transform from $(t,r_*)$ to $\lambda,\xi)$ for complex vector arguments at the boundary of an element.

interface

public module subroutine tdc_tortoise_to_tdc_cvecb(this, ielem, dir, dudt, dudrstar, dudlambda, dudxi)

Routine to transform from tortoise coordinates $(t,r_*)$ to time dependent $(\lambda,\xi)$ for complex vector input at element boundaries.

Arguments

Type	Intent	Attributes		Name
class(tdc),	intent(inout)		::	this	The routine is called on this time dependent coordinate object.
integer(kind=ip),	intent(in)		::	ielem	The index of the element that contains the coordinate transformation information.
integer(kind=ip),	intent(in)		::	dir	The index of the boundary within the element that contains the coordinate transformation. Left boundary: 1, right boundary: 2.
complex(kind=wp),	intent(in),	dimension(:)	::	dudt	The vector of $\frac{\partial\Psi}{\partial t}$ to transform.
complex(kind=wp),	intent(in),	dimension(:)	::	dudrstar	The vector of $\frac{\partial\Psi}{\partial r_*}$ to transform.
complex(kind=wp),	intent(out),	dimension(:)	::	dudlambda	On output contains the $\frac{\partial\Psi}{\partial\lambda}$ vector.
complex(kind=wp),	intent(out),	dimension(:)	::	dudxi	On output contains the $\frac{\partial\Psi}{\partial\xi}$ vector.

procedure, public :: tortoise_to_tdc_cscalb => tdc_tortoise_to_tdc_cscalb

Routine to transform from $(t,r_*)$ to $\lambda,\xi)$ for complex scalar arguments at the boundary of an element.

interface

public module subroutine tdc_tortoise_to_tdc_cscalb(this, ielem, dir, dudt, dudrstar, dudlambda, dudxi)

Routine to transform from tortoise coordinates $(t,r_*)$ to time dependent $(\lambda,\xi)$ for complex scalar input at element boundaries.

Arguments

Type	Intent		Name
class(tdc),	intent(inout)	::	this	The routine is called on this time dependent coordinate object.
integer(kind=ip),	intent(in)	::	ielem	The index of the element that contains the coordinate transformation information.
integer(kind=ip),	intent(in)	::	dir	The index of the boundary within the element that contains the coordinate transformation. Left boundary: 1, right boundary: 2.
complex(kind=wp),	intent(in)	::	dudt	The value of $\frac{\partial\Psi}{\partial t}$ to transform.
complex(kind=wp),	intent(in)	::	dudrstar	The value of $\frac{\partial\Psi}{\partial r_*}$ to transform.
complex(kind=wp),	intent(out)	::	dudlambda	On output contains the $\frac{\partial\Psi}{\partial\lambda}$ value.
complex(kind=wp),	intent(out)	::	dudxi	On output contains the $\frac{\partial\Psi}{\partial\xi}$ value.

procedure, public :: tortoise_to_tdc_cscal => tdc_tortoise_to_tdc_cscal

Routine to transform from $(t,r_*)$ to $\lambda,\xi)$ for complex scalar arguments at any node in any element.

interface

public module subroutine tdc_tortoise_to_tdc_cscal(this, elem, node, dpsidt, dpsidr)

Routine to transform from tortoise coordinates $(t,r_*)$ to time dependent $(\lambda,\xi)$ for complex scalar input.

Arguments

Type	Intent		Name
class(tdc),	intent(inout)	::	this	The routine is called on this time dependent coordinate object.
integer(kind=ip),	intent(in)	::	elem	The element index of the point to transform.
integer(kind=ip),	intent(in)	::	node	The node index of the point to transform.
complex(kind=wp),	intent(inout)	::	dpsidt	On input contains: $\frac{\partial\Psi}{\partial t}$ . On output contains $\frac{\partial\Psi}{\partial\lambda}$ .
complex(kind=wp),	intent(inout)	::	dpsidr	On input contains: $\frac{\partial\Psi}{\partial r_*}$ . On output contains $\frac{\partial\Psi}{\partial\xi}$ .

generic, public :: tortoise_to_tdc => tortoise_to_tdc_cvecb, tortoise_to_tdc_cscalb, tortoise_to_tdc_cscal

Generic name for routines that transform from $(t,r_*)$ to $\lambda,\xi)$ .

public interface tdc_tortoise_to_tdc_cvecb()

Arguments
None
public interface tdc_tortoise_to_tdc_cscalb()

Arguments
None
public interface tdc_tortoise_to_tdc_cscal()

Arguments
None

Source Code

  type :: tdc
  !! A class that defines a time dependent coordinate transformation for the
  !! scalar wave equation on s Schwarzschild spacetime.
    type(rgfb) :: dxdlambda_b
    !! A real boundary grid function that stores
    !! \(\frac{\partial r_*}{\partial \lambda}\) on the element boundaries.
    type(rgfb) :: dxdxi_b
    !! A real boundary grid function that stores
    !! \(\frac{\partial r_*}{\partial \xi}\) on the element boundaries.
    real(wp) :: maxspeed
    !! The maximum coordinate speed (needed for CFL timestep condition).
    type(rgf) :: dxdlambda
    !! A real grid function that stores
    !! \(\frac{\partial r_*}{\partial \lambda}\) everywhere.
    type(rgf) :: dxdxi
    !! A real grid function that stores
    !! \(\frac{\partial r_*}{\partial \xi}\) everywhere.
    type(rgf) :: d2xdlambda2
    !! A real grid function that stores
    !! \(\frac{\partial^2 r_*}{\partial \lambda^2}\) everywhere.
    type(rgf) :: d2xdxi2
    !! A real grid function that stores
    !! \(\frac{\partial^2 r_*}{\partial \xi^2}\) everywhere.
    type(rgf) :: d2xdlambdadxi
    !! A real grid function that stores
    !! \(\frac{\partial^2 r_*}{\partial \lambda \partial \xi}\) everywhere.
    type(rgf) :: rm2m
    !! A real grid function that stores \(r-2M\) everywhere.
  contains
    procedure :: init => tdc_init
    !! The initialization routine.
    procedure :: set_coefficients => tdc_set_coefficients
    !! The routine that sets the coefficients for the wave equation.
    procedure :: tdc_to_tortoise_cvec => tdc_tdc_to_tortoise_cvec
    !! Routine to transform from \(\lambda,\xi)\) to \((t,r_*)\) for complex
    !! vector arguments at the boundary of an element.
    procedure :: tdc_to_tortoise_cscal => tdc_tdc_to_tortoise_cscal
    !! Routine to transform from \(\lambda,\xi)\) to \((t,r_*)\) for complex
    !! scalar arguments at the boundary of an element.
    procedure :: tdc_to_tortoise_rscal => tdc_tdc_to_tortoise_rscal
    !! Routine to transform from \(\lambda,\xi)\) to \((t,r_*)\) for real
    !! scalar arguments at the boundary of an element.
    generic :: tdc_to_tortoise => tdc_to_tortoise_cvec, tdc_to_tortoise_cscal, &
                                  tdc_to_tortoise_rscal
    !! Generic name for routines that transform from \(\lambda,\xi)\) to
    !! \((t,r_*)\) at the boundary of an element.
    procedure :: tortoise_to_tdc_cvecb => tdc_tortoise_to_tdc_cvecb
    !! Routine to transform from \((t,r_*)\) to \(\lambda,\xi)\) for complex
    !! vector arguments at the boundary of an element.
    procedure :: tortoise_to_tdc_cscalb => tdc_tortoise_to_tdc_cscalb
    !! Routine to transform from \((t,r_*)\) to \(\lambda,\xi)\) for complex
    !! scalar arguments at the boundary of an element.
    procedure :: tortoise_to_tdc_cscal => tdc_tortoise_to_tdc_cscal
    !! Routine to transform from \((t,r_*)\) to \(\lambda,\xi)\) for complex
    !! scalar arguments at any node in any element.
    generic :: tortoise_to_tdc => tortoise_to_tdc_cvecb, &
                                  tortoise_to_tdc_cscalb, &
                                  tortoise_to_tdc_cscal
    !! Generic name for routines that transform from \((t,r_*)\) to
    !! \(\lambda,\xi)\).
  end type tdc

tdc Derived Type

Contents

Variables

Type-Bound Procedures

Source Code

type, public :: tdc

Inherits

Inherited by

Contents

Variables

Type-Bound Procedures

Source Code

Components

Type-Bound Procedures

procedure, public :: init => tdc_init

interface

public module subroutine tdc_init(this) Implementation →

Arguments

procedure, public :: set_coefficients => tdc_set_coefficients

interface

public module subroutine tdc_set_coefficients(this, coeffs, lcoeffs, lambda, s, sinv, rho, rstar, rschw, ll) Implementation →

Arguments

procedure, public :: tdc_to_tortoise_cvec => tdc_tdc_to_tortoise_cvec

interface

public module subroutine tdc_tdc_to_tortoise_cvec(this, ielem, dir, dudlambda, dudxi, dudt, dudrstar) Implementation →

Arguments

procedure, public :: tdc_to_tortoise_cscal => tdc_tdc_to_tortoise_cscal

interface

public module subroutine tdc_tdc_to_tortoise_cscal(this, ielem, dir, dudlambda, dudxi, dudt, dudrstar) Implementation →

Arguments

procedure, public :: tdc_to_tortoise_rscal => tdc_tdc_to_tortoise_rscal

interface

public module subroutine tdc_tdc_to_tortoise_rscal(this, ielem, dir, dudlambda, dudxi, dudt, dudrstar) Implementation →

Arguments

generic, public :: tdc_to_tortoise => tdc_to_tortoise_cvec, tdc_to_tortoise_cscal, tdc_to_tortoise_rscal

public interface tdc_tdc_to_tortoise_cvec()

Arguments

public interface tdc_tdc_to_tortoise_cscal()

Arguments

public interface tdc_tdc_to_tortoise_rscal()

Arguments

procedure, public :: tortoise_to_tdc_cvecb => tdc_tortoise_to_tdc_cvecb

interface

public module subroutine tdc_tortoise_to_tdc_cvecb(this, ielem, dir, dudt, dudrstar, dudlambda, dudxi) Implementation →

Arguments

procedure, public :: tortoise_to_tdc_cscalb => tdc_tortoise_to_tdc_cscalb

interface

public module subroutine tdc_tortoise_to_tdc_cscalb(this, ielem, dir, dudt, dudrstar, dudlambda, dudxi) Implementation →

Arguments

procedure, public :: tortoise_to_tdc_cscal => tdc_tortoise_to_tdc_cscal

interface

public module subroutine tdc_tortoise_to_tdc_cscal(this, elem, node, dpsidt, dpsidr) Implementation →

Arguments

generic, public :: tortoise_to_tdc => tortoise_to_tdc_cvecb, tortoise_to_tdc_cscalb, tortoise_to_tdc_cscal

public interface tdc_tortoise_to_tdc_cvecb()

Arguments

public interface tdc_tortoise_to_tdc_cscalb()

Arguments

public interface tdc_tortoise_to_tdc_cscal()

Arguments

Source Code

public module subroutine tdc_init(this)

public module subroutine tdc_set_coefficients(this, coeffs, lcoeffs, lambda, s, sinv, rho, rstar, rschw, ll)

public module subroutine tdc_tdc_to_tortoise_cvec(this, ielem, dir, dudlambda, dudxi, dudt, dudrstar)

public module subroutine tdc_tdc_to_tortoise_cscal(this, ielem, dir, dudlambda, dudxi, dudt, dudrstar)

public module subroutine tdc_tdc_to_tortoise_rscal(this, ielem, dir, dudlambda, dudxi, dudt, dudrstar)

public module subroutine tdc_tortoise_to_tdc_cvecb(this, ielem, dir, dudt, dudrstar, dudlambda, dudxi)

public module subroutine tdc_tortoise_to_tdc_cscalb(this, ielem, dir, dudt, dudrstar, dudlambda, dudxi)

public module subroutine tdc_tortoise_to_tdc_cscal(this, elem, node, dpsidt, dpsidr)