time_dependent_coordinate_implementation Submodule

The lower boundary location of the time dependent coordinate region.

The upper boundary location of the time dependent coordinate region.

The current particle location in Tortoise coordinates, $r^{\mathrm{p}}_*$.

The constant particle location in time dependent coordinates, $\xi^{\mathrm{p}}$.

The current time derivative of the particle location in Tortoise coordinates, $\frac{d r_*^{\mathrm{p}}}{dt}$.

The current second time derivative of the particle location in Tortoise coordinates, $\frac{d^2 r_*^{\mathrm{p}}}{dt^2}$.

A 1d array containing coordinate values $\xi_i$.

A 1d array that on output contains the Tortoise coordinates $(r_*)_i$.

A 1d array that on outout contains $\frac{d r_*}{dt}$.

A 1d array that on outout contains $\frac{d r_*}{d\xi}$.

A 1d array that on outout contains $\frac{d^2 r_*}{dt^2}$.

A 1d array that on outout contains $\frac{d^2 r_*}{d\xi^2}$.

A 1d array that on outout contains $\frac{d^2 r_*}{dt d\xi}$.

On input the particle location in Schwarschild coordinates, $r^{\mathrm{p}}$. On output the particle location in Tortoise coordinates, $r_*^{\mathrm{p}}$.

On input the time derivative of the particle location in Schwarschild coordinates, $\frac{dr^{\mathrm{p}}}{dt}$. On output the time derivative of the particle location in Tortoise coordinates, $\frac{dr_*^{\mathrm{p}}}{dt}$.

On input the second time derivative of the particle location in Schwarschild coordinates, $\frac{d^2r^{\mathrm{p}}}{dt^2}$. On output the second time derivative of the particle location in Tortoise coordinates, $\frac{d^2r_*^{\mathrm{p}}}{dt^2}$.

This time dependent coordinate object is being initialized.

The routine is called on this time dependent coordinate object.

A 1d array of real grid functions containing the wave equation coefficients (should be eq_coeffs). On output it will contain $(c_{\xi\xi}, c_{\lambda\xi}, c_{\xi}, c_{\lambda})$.

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.

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.

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.

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.

A real grid function containing the computational radial coordinate, $\rho$.

A real grid function containing the tortoise radial coordinate, $r_*$. On output this will be updated.

A real grid function containing the Schwarzschild radial coodrinate, $r_{\mathrm{schw}}$. On output this will be updated.

A 1d array of c_int containing the $\ell$-values of all the modes.

The routine is called on this time dependent coordinate object.

The index of the element that contains the coordinate transformation information.

The index of the boundary within the element that contains the coordinate transformation. Left boundary: 1, right boundary: 2.

The vector of $\frac{\partial\Psi}{\partial\lambda}$ values to transform.

The vector of $\frac{\partial\Psi}{\partial\xi}$ values to transform.

On output contains the $\frac{\partial\Psi}{\partial t}$ vector.

On output contains the $\frac{\partial\Psi}{\partial r_*}$ vector.

The routine is called on this time dependent coordinate object.

The index of the element that contains the coordinate transformation information.

The index of the boundary within the element that contains the coordinate transformation. Left boundary: 1, right boundary: 2.

The value of $\frac{\partial\Psi}{\partial\lambda}$ to transform.

The value of $\frac{\partial\Psi}{\partial\xi}$ to transform.

On output contains the $\frac{\partial\Psi}{\partial t}$ value.

On output contains the $\frac{\partial\Psi}{\partial r_*}$ value.

The routine is called on this time dependent coordinate object.

The index of the element that contains the coordinate transformation information.

The index of the boundary within the element that contains the coordinate transformation. Left boundary: 1, right boundary: 2.

The value of $\frac{\partial\Psi}{\partial\lambda}$ to transform.

The value of $\frac{\partial\Psi}{\partial\xi}$ to transform.

On output contains the $\frac{\partial\Psi}{\partial t}$ value.

On output contains the $\frac{\partial\Psi}{\partial r_*}$ value.

The routine is called on this time dependent coordinate object.

The index of the element that contains the coordinate transformation information.

The index of the boundary within the element that contains the coordinate transformation. Left boundary: 1, right boundary: 2.

The vector of $\frac{\partial\Psi}{\partial t}$ to transform.

The vector of $\frac{\partial\Psi}{\partial r_*}$ to transform.

On output contains the $\frac{\partial\Psi}{\partial\lambda}$ vector.

On output contains the $\frac{\partial\Psi}{\partial\xi}$ vector.

The routine is called on this time dependent coordinate object.

The index of the element that contains the coordinate transformation information.

The index of the boundary within the element that contains the coordinate transformation. Left boundary: 1, right boundary: 2.

The value of $\frac{\partial\Psi}{\partial t}$ to transform.

The value of $\frac{\partial\Psi}{\partial r_*}$ to transform.

On output contains the $\frac{\partial\Psi}{\partial\lambda}$ value.

On output contains the $\frac{\partial\Psi}{\partial\xi}$ value.

The routine is called on this time dependent coordinate object.

The element index of the point to transform.

The node index of the point to transform.

On input contains: $\frac{\partial\Psi}{\partial t}$. On output contains $\frac{\partial\Psi}{\partial\lambda}$.

On input contains: $\frac{\partial\Psi}{\partial r_*}$. On output contains $\frac{\partial\Psi}{\partial\xi}$.