Procedures

The constructor for a complex data type grid function.

The constructor for a complex data type boundary grid function.

Routine that chooses an integrator by pointing to one of the available ones.

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.

Routine that converts the particle location and time derivatives in Schwarszschild coordinates to Tortoise coordinates.

Routine that calculates the Tortoise coordinates $(t,r_*)$ from time dependent coordinates $(\lambda,\xi)$ where the particle is kept at a fixed coordinate location as well as the informtation needed to transform the wave equation to time dependent coordinates.

Function that fits higher order terms to data containing amplitude as function of l-values and corrects the sum over the evolved l-modes with the contribution from the not evolved l-modes.

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

Initialize the differentiation matrix for a reference element of order $n$.

The constructor for the complex element boundary data class.

The constructor for the integer element boundary data class.

The constructor for the real element boundary data class.

The constructor for the complex element data class.

The constructor for the real element data class.

Double precision version of a function that returns the convergence criterium.

Quad precision version of a function that returns the convergence criterium.

Single precision version of a function that returns the convergence criterium.

A simple factorial function. Use only for small values of $n$ as no consideration of efficiency has been made.

Create an exponential filter matrix that can be used to filter out high-frequency noise.

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

Routine to calculate the integration weights for the Gauss-Lobatto Quadrature points.

Function that generates a head key or heading to add to the top of output files for an observer.

Routine that gets the 4-acceleration.

Routine that gets $\chi$.

Function to get the current $\Delta t$

Function to get the current quad precision time, $t$.

Function to get the current working precision time, $t$.

Routine that gets the second coordinate time derivative of the 4-acceleration.

Routine that gets the coordinate time derivative of the 4-acceleration.

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

Routine that gets the self-force variable.

Routine that gets all the orbit variables except for $\chi$.

Evaluate the derivative of the Jacobi polynomial of type $(\alpha,\beta)>-1$ at points $x$ for order $n$.

Initialize the gradient of the modal basis $j$ at $r_i$.

The constructor for an integer data type boundary grid function.

Routine to increment $t$ by $\Delta t$.

Routine to initialize the time variables.

Helper function that calculates the inverse of a matrix.

Routine to convert from Energy and Angular momentum per unit mass to semi-latus rectum and eccentricity.

Function to invert the tortoise radius as a function of Schwarzschild radius.

Calculate the Jacobian for transforming derivatives from the reference element to the physical element.

Routine that sets up the physical coordinates as well as the Jacobian and inverse Jacobian to convert derivatives between reference element and physical element.

Compute the n'th order Gauss Lobatto quadrature points, $x$, associated with the Jacobi polynomial of type $(\alpha,\beta)>-1$.

Compute the n'th order Gauss quadrature points, $x$ and weights, $w$, associated with the Jacobi polynomial of type $(\alpha,\beta)>-1$.

Function to evaluate Jacobi Polynomial $P^{(\alpha,\beta)}_n$ of type $(\alpha,\beta)>-1$ (with $\alpha+\beta\neq -1$) at points $x$ for order $n$.

Function to calculate Lambert's W-function.

Function that calculates the higher order terms, $c_n(\ell)$ in the self-force expansion over $\ell$.

Initialize the lift matrix, $L_{ij}$, used to compute surface integral terms in the Discontinuous Galerkin formulation.

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

Function that calculates the sum of higher order terms, $c_n(\ell)$, provided by ldep from $\ell_{\mathrm{min}}$ to $\infty$.

Function that interfaces with the ntemp functions provided by the individual integrators. This function can be called before choose_integrator is called.

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.

Helper function that finds the number of unique values in a 1d integer array.

Function that provides the next available file unit.

Calculate the total number of modes from lmin to lmax.

Routine that performs output of the self-force.

Read in the run-time parameters from a file. The name of the file is read from the first command line option. If no command line options are given, use 'input.par'.

Function that releases the last assigned file unit.

Routine to restore and increment a backup copy of the time.

The constructor for a real data type grid function.

The constructor for a real data type boundary grid function.

Function to invert the tortoise radius as a function of Schwarzschild radius.

Function to calculate the tortoise radius, $r_*$, as function of the Schwarzschild radius, $r_{\mathrm{schw}}$.

Routine to make a backup copy of the time.

Routine that sets the 4-acceleration and the inner product of the 4-velovity and the self-force.

Routine that sets the second coordinate time derivative of the 4-acceleration.

Routine that sets the coordinate time derivative of the 4-acceleration.

Routine that sets $\Delta t$.

Routine that sets the self-force variable.

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

Routine that sets all the orbit variables.

Routine to calculate a smooth "Gaussian" type time window function, $f_t$ and it's first $f_t'$ and second $f_t''$ time derivative.

Routine to calculate the smooth transition function, $fT$, and it's first $fT'$ and second $fT''$ derivative with respect to the computational coordinate, $\rho$.

Initialize the 1D Vandermonde matrix, $\mathcal{V}_{ij}=P_j(x_i)$ for the Legendre-Gauss-Lobatto quadrature points.