Module that defines an equation class for evolving the spherical harmonic decomposed field of a scalar point charge moving in a Schwarzschild spacetime. From the starting point of the wave equation in Tortoise coordinates, the class supports the use of hyperboloidal coordinates in regions near the horizon and near future null infinity as well as time dependent coordinates for the case of a particle on a non-circular orbit. The class interfaces with an effective source provided as C++ routines.
The wave equation is written in first order in time and space form with the evolved variables being where is the radial coordinate and is the time.
The implementation is found in submodule_scalar_schw_implementation.f90.
| Type | Visibility | Attributes | Name | Initial | |||
|---|---|---|---|---|---|---|---|
| complex(kind=wp), | public, | dimension(:,:), allocatable | :: | drho | A 2d array of reals used to store the radial derivative of for all modes in a single element. The size when allocated is (order+1:nmodes). |
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| complex(kind=wp), | public, | dimension(:,:), allocatable | :: | dpi | A 2d array of reals used to store the radial derivative of for all modes in a single element. The size when allocated is (order+1:nmodes). |
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| complex(kind=wp), | public, | dimension(:,:,:), allocatable | :: | flux_result | A 3d array of complex used to store fluxes for all modes at the boundary of a single element. The size when allocated is (order+1:2:nmodes). |
A helper function that produces unique file names by adding the mode number to a variable name.
| Type | Intent | Optional | Attributes | Name | ||
|---|---|---|---|---|---|---|
| character(len=*), | intent(in) | :: | var_name | The input variable name. |
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| integer(kind=ip), | intent(in) | :: | mode | the mode number. |
The return value is the converted variable name.
The interface for the scal_schw version of init. This interface is consistent with eq_init_interface.
| Type | Intent | Optional | Attributes | Name | ||
|---|---|---|---|---|---|---|
| class(scal_schw), | intent(inout), | target | :: | this | The equation that is being initialized. |
The interface for the scal_schw version of rhs. This interface is consistent with eq_rhs_interface.
| Type | Intent | Optional | Attributes | Name | ||
|---|---|---|---|---|---|---|
| class(scal_schw), | intent(inout) | :: | this | The equation for which the RHS is calculated. |
The interface for the scal_schw version of save_globals_1. This interface is consistent with eq_save_globals_1.
| Type | Intent | Optional | Attributes | Name | ||
|---|---|---|---|---|---|---|
| class(scal_schw), | intent(inout) | :: | this | The routine is called on this equation. |
The interface for the scal_schw version of save_globals_2. This interface is consistent with eq_save_globals_2.
| Type | Intent | Optional | Attributes | Name | ||
|---|---|---|---|---|---|---|
| class(scal_schw), | intent(inout) | :: | this | The routine is called on this equation. |
The interface for the scal_schw version of load_globals. This interface is consistent with eq_load_globals.
| Type | Intent | Optional | Attributes | Name | ||
|---|---|---|---|---|---|---|
| class(scal_schw), | intent(inout) | :: | this | The routine is called on this equation. |
The interface for the scal_schw_flux routine for calculating fluxes. Can be called under the generic name flux.
| Type | Intent | Optional | Attributes | Name | ||
|---|---|---|---|---|---|---|
| class(scal_schw), | intent(inout) | :: | this | The routine is called on this equation. |
The interface for the read_all_modes routine that reads external initial data.
| Type | Intent | Optional | Attributes | Name | ||
|---|---|---|---|---|---|---|
| class(scal_schw), | intent(inout) | :: | this | The routine is called on this equation. |
The interface for the output_coords routine that writes out the coordinates for an external python frequency domain code that calculates initial data.
| Type | Intent | Optional | Attributes | Name | ||
|---|---|---|---|---|---|---|
| class(scal_schw), | intent(inout) | :: | this | The routine is called on this equation. |
The interface for the tortoise_to_hyperboloidal routine that converts from Tortoise to hyperboloidal coordinates when reading in external initial data.
| Type | Intent | Optional | Attributes | Name | ||
|---|---|---|---|---|---|---|
| class(scal_schw), | intent(inout) | :: | this | The routine is called on this equation. |
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| integer(kind=ip), | intent(in) | :: | elem | The index of the element where the transformation is calculated. |
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| integer(kind=ip), | intent(in) | :: | node | The index of the node within that element where the transformation is calculated. |
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| logical, | intent(in) | :: | inner | If .true. use the transformation for the inner region. If .false. use the transformation for the outer region. |
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| complex(kind=wp), | intent(inout) | :: | dpsidt | On input holds the time derivative in Tortoise coordinates. On output holds the time derivative in hyperboloidal coordinates. |
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| complex(kind=wp), | intent(inout) | :: | dpsidr | On input holds the radial derivative in Tortoise coordinates. On output holds the radial derivative in hyperboloidal coordinates. |
A class that defines the evolution equations for a scalar field produced by a point charge in Schwarzschild coordinates decomposed into spherical harmonics.
| Type | Visibility | Attributes | Name | Initial | |||
|---|---|---|---|---|---|---|---|
| integer(kind=ip), | public | :: | ntmp | The number of temporary storage variables to allocate. |
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| character(len=:), | public, | allocatable | :: | ename | The name of the system of equations |
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| integer(kind=ip), | public | :: | nmodes | The number of spherical harmonic modes. Should be moved to the specific implementation of the equation as this class should not be limited to systems using spherical harmonic decomposition. |
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| integer(kind=ip), | public | :: | nvars | = | 3 | The number of variables per mode. Should probably be changed to be the total number of variables in order to make this independent of spherical harmonic decomposition. And the value should be set by the equation implementation. |
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| type(cgf), | public, | dimension(:,:), allocatable | :: | eq_data | A 2d array of complex grid functions that contains the data variables for the equation system. Should probably be changed to a 1d array to make this independent of spherical harmonic decomposition. |
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| type(cgf), | public, | dimension(:,:), allocatable | :: | eq_rhs_data | A 2d array of complex grid functions that contains the rhs variables for the equation system. Should probably be changed to a 1d array to make this independent of spherical harmonic decomposition. |
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| type(cgf), | public, | dimension(:,:,:), allocatable | :: | eq_tmp_data | A 3d array of complex grid functions that contains the temporary variables needed by the time integrator. Should probably be changed to a 2d array to make this independent of spherical harmonic decomposition. |
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| type(cgf_pointer), | public, | dimension(:,:,:), allocatable | :: | data_pointer | A 3d array of pointers to complex grid functions that points to the RHS variables (:,:,-1), the data variables (:,:,0) and the temporary variables (:,:,1:ntmp) for the equation system. Should probably be changed to a 2d array to make this independent of spherical harmonic decomposition. |
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| integer(kind=c_int), | public, | dimension(:), allocatable | :: | ll | A 1d array of c_int containing the l values of all the evolved modes. |
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| integer(kind=c_int), | public, | dimension(:), allocatable | :: | mm | A 1d array of c_int containing the m values of all the evolved modes. |
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| type(ref_element), | public | :: | refelem | The ref_element contains the derivative matrix needed for approximating partial derivatives as well as the routines needed for calculating characteristic fluxes. |
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| type(cgf), | public, | dimension(:,:), allocatable | :: | eq_flux_data | A 2d array of complex grid functions that stores flux data for the system. |
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| type(rgf), | public, | dimension(:), allocatable | :: | eq_coeffs | A 1d array of real grid functions that stores the equation coefficients. |
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| type(rgf), | public, | dimension(:), allocatable | :: | eq_lcoeffs | A 1d array of real grid functions that stores the l-dependent potential. |
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| type(rgfb), | public, | dimension(:), allocatable | :: | eq_lambda | A 1d array of real boundary grid functions that stores the characteristic speeds at the element boundaries. |
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| type(rgfb), | public, | dimension(:,:), allocatable | :: | eq_s | A 2d array of real boundary grid functions that stores the matrix used to convert from characteristic to evolved variables. |
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| type(rgfb), | public, | dimension(:,:), allocatable | :: | eq_sinv | A 2d array of real boundary grid functions that stores the matrix used to convert from evolve to characteristic variables. |
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| type(rgf), | public | :: | r_schw | A real grid function that stores the Schwarzschild radial coordinate. |
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| type(rgf), | public | :: | r_star | A real grid function that stores the tortoise radial coordinate. |
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| type(scal_schw_eff), | public | :: | effs | The effective source for a scalar point charge on generic orbits in a Schwarzschild spacetime. |
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| type(tdc), | public | :: | time_dep_coord | A time dependent coordinate class for the scalar wave equation in Tortoise coordinates. |
| procedure, public :: set_to_zero => cpde_set_to_zero | The set_to_zero routine is provided by cpde_set_to_zero. |
| procedure, public :: update_vars => cpde_update_vars | The update_vars routine is provided by cpde_update_vars. |
| procedure, public :: output => cpde_output | The output routine is provided by cpde_output. |
| procedure, public :: print_data => cpde_print_data | The print_data routine is provided by cpde_print_data. |
| procedure, public :: init => scal_schw_init | The init routine is provided by scal_schw_init. |
| procedure, public :: rhs => scal_schw_rhs | The rhs routine is provided by scal_schw_rhs. |
| procedure, public :: save_globals_1 => scal_schw_save_globals_1 | The save_globals_1 routine is provided by scal_schw_save_globals_1. |
| procedure, public :: save_globals_2 => scal_schw_save_globals_2 | The save_globals_2 routine is provided by scal_schw_save_globals_2. |
| procedure, public :: load_globals => scal_schw_load_globals | The load_globals routine is provided by scal_schw_load_globals. |
| generic, public :: flux => scal_schw_flux | A routine to calculate fluxes is provided by scal_schw_flux under the generic name flux. |
| procedure, public :: scal_schw_flux | Provides a routine to calculate fluxes. |
| procedure, public :: read_all_modes | Provides a routine to read in external initial data. |
| procedure, public :: output_coords | Provides a routine to output the coordinates in a format needed for a frequency domain python code that can provide initial data. |
| procedure, public :: tortoise_to_hyperboloidal | Provides a routine to transform from tortoise to hyperboloid that is used when reading in external data. |