bssn_formulation Module

Conformal traceless extrinsic curvature $A_{ij}$

Connection constraint computed with the \(\mathrm{ID}\) on the mesh

Integral of the connection constraint computed with the \(\mathrm{ID}\) on the mesh

$\ell_2$ norm of the connection constraint computed with the \(\mathrm{ID}\) on the mesh

$\ell_\infty$ norm, i.e., supremum of the absolute value, of the connection constraint computed with the \(\mathrm{ID}\) on the mesh

Connection constraint computed with the \(\mathrm{BSSNOK}\) \(\mathrm{ID}\) on the mesh, and the hydrodynamical \(\mathrm{ID}\) mapped from the particles to the mesh

Integral of the connection constraint computed with the \(\mathrm{BSSNOK}\) \(\mathrm{ID}\) on the mesh, and the hydrodynamical \(\mathrm{ID}\) mapped from the particles to the mesh with the \(\mathrm{ID}\) on the mesh

$\ell_2$ norm of the connection constraint computed with the \(\mathrm{BSSNOK}\) \(\mathrm{ID}\) on the mesh, and the hydrodynamical \(\mathrm{ID}\) mapped from the particles to the mesh

$\ell_\infty$ norm, i.e., supremum of the absolute value, of the connection constraint computed with the \(\mathrm{BSSNOK}\) \(\mathrm{ID}\) on the mesh, and the hydrodynamical \(\mathrm{ID}\) mapped from the particles to the mesh

Conformal connection $\bar{\Gamma} ^i_{jk}$

Grid scalar function storing the Hamiltonian constraint (violations) computed using the ID on the mesh

Integral the Hamiltonian constraint computed using the stress-energy tensor mapped from the particles

$\ell_2$ norm of the Hamiltonian constraint computed on the mesh

$\ell_\infty$ norm of the Hamiltonian constraint computed on the mesh (i.e., its maximum)

Grid scalar function storing the Hamiltonian constraint (violations) computed using the stress-energy tensor mapped from the particles to the mesh

Integral the Hamiltonian constraint computed on the mesh

$\ell_2$ norm of the Hamiltonian constraint computed on the mesh, using the stress-energy tensor mapped from the particles

$\ell_\infty$ norm of the Hamiltonian constraint computed on the mesh, using the stress-energy tensor mapped from the particles (i.e., its maximum)

Grid function storing the extrinsic curvature

Grid function storing the momentum constraint (violations) computed using the ID on the mesh

Integral of the momentum constraint computed on the mesh

$\ell_2$ norm of the momentum constraint computed on the mesh

$\ell_\infty$ norm of the momentum constraint computed on the mesh (i.e., its maximum)

Grid function storing the momentum constraint (violations) computed using the stress-energy tensor mapped from the particles to the mesh

Integral of the momentum constraint computed using the stress-energy tensor mapped from the particles

$\ell_2$ norm of the Hamiltonian constraint computed on the mesh, using the stress-energy tensor mapped from the particles

$\ell_\infty$ norm of the momentum constraint computed on the mesh, using the stress-energy tensor mapped from the particles (i.e., its maximum)

Ricci tensor $R_{ij}$

Ricci scalar $R^\mu{}_nu$

Grid function storing the matter source in the momentum constraint computed using the ID on the mesh, multiplied by $8\pi$

Grid function storing the matter source in the momentum constraint computed using the stress-energy tensor mapped from the particles to the mesh, multiplied by $8\pi$

Timer that times how long it takes to compute the \(\mathrm{BSSNOK}\) variables on the refined mesh

Flag set to a value different than 0 if the SUBROUTINE compute_and_print_bssn_variables is called

Constraint violations are printed to file every cons_step-th grid point

Grid function storing the Cartesian coordinates

.TRUE. if the binary files for SPHINCS_BSSN are to be exported, .FALSE. otherwise

.TRUE. if the constraint violations are to be printed to file, .FALSE. otherwise

.TRUE. if the points at which the constraints violations are within the intervals $[0,10^{-7}],[10^3,\infty],[10^n,10^m]$, with $n\in\{-7,2\}$ and $m=n+1$, are to be printed to file; .FALSE. otherwise

.TRUE. if only the constrain violations on the $x$ axis are to be

.TRUE. if only the constrain violations on the $xy$ plane are to be

.TRUE. if the \(\mathrm{ID}\) in the formatted files is to be on the x axis only, .FALSE. otherwise

.TRUE. if the \(\mathrm{ID}\) in the formatted files is to be on the xy plane only, .FALSE. otherwise

Conformal spatial metric $\gamma_{ij}$

Grid function storing the spatial metric

Timer that times how long it takes to set up the grid and allocate the grid functions

Timer that times how long it takes to import the \(\texttt{LORENE}\) ID on the mesh

Grid scalar function storing the lapse function

Array containing the information on each refinement level

Number of matter objects in the physical system

Number of refinement levels

Array containing the number of mesh points of the highest-resolution refinement level across the x-axis-size of the matter objects

Conformal factor $\phi$

Grid scalar function storing the radial coordinates of each grid point

Grid scalar function storing the matter source in the Hamiltonian constraint computed using the ID on the mesh, multiplied by $16\pi$

Grid scalar function storing the matter source in the Hamiltonian constraint computed using the stress-energy tensor mapped from the particles to the mesh, multiplied by $16\pi$

Grid function storing the shift vector

Negative integer that identifies the tpo object

Trace of extrinsic curvature $K$

Destructor; finalizes members from both TYPES tpo and bssn, by calling destruct_bssn

Analyze a constraint (or an arbitrary scalar grid function) by examining its values at the refined mesh. Computes the number of mesh points at which the scalar grid function has values lying within predefined (hard-coded) intervals

Computes an estimate of the $\mathrm{ADM}$ linear momentum of the fluid using the \(\mathrm{SPH}\) hydro fields, and the spacetime metric mapped from the mesh

Overloaded PROCEDURE to compute the constraints using only the \(\mathrm{ID}\) on the refined mesh, or the spacetime \(\mathrm{ID}\) on the refined mesh and the hydrodynamical \(\mathrm{ID}\) mapped from the particles to the refined mesh

Computes the \(\mathrm{BSSNOK}\) constraints using the full \(\mathrm{ID}\) on the refined mesh, prints a summary with the statistics for the constraints. Optionally, prints the constraints to a formatted file to be read by $\texttt{gnuplot}$, and analyze the constraints by calling analyze_constraint

Computes the \(\mathrm{BSSNOK}\) constraints using the \(\mathrm{BSSNOK}\) \(\mathrm{ID}\) on the refined mesh and the hydrodynamical \(\mathrm{ID}\) mapped from the particles to the mesh, prints a summary with the statistics for the constraints. Optionally, prints the constraints to a formatted file to be read by $\texttt{gnuplot}$, and analyze the constraints by calling analyze_constraint

Computes the \(\mathrm{BSSNOK}\) variables at the particle positions, and optionally prints them to a binary file to be read by $\texttt{SPHINCS_BSSN}$ and $\texttt{splash}$, and to a formatted file to be read by $\texttt{gnuplot}$, by calling print_formatted_id_tpo_variables

Computes the Ricci tensor and the Ricci scalar on the mesh

Deallocates memory for the bssn member arrays

Deallocates memory for the standard 3+1 fields

Allocates memory for the bssn member grid functions

Destructor for the EXTENDED TYPE bssn, not ABSTRACT TYPE tpo

Prints the \(\mathrm{BSSNOK}\) \(\mathrm{ID}\) to a formatted file

Prints a summary about the features of the refined mesh

Reads the binary \(\mathrm{ID}\) file printed by compute_and_print_tpo_variables

Set up the refined mesh by reading the gravity_grid_parameter.dat parameter file, and read the standard 3+1 \(\mathrm{ID}\) using the given idbase object, on the refined mesh

Computes the conserved variables from the physical ones, and vice versa, to test that the recovered physical variables are the same to those computed from the \(\mathrm{ID}\). Uses the metric mapped from the grid to the particles.