sphereint calculates the numerical volume in a sphere. It provides a weight for each grid position based on whether or not it is in (weight = 1), out (weight = 0), or partially in (weight in between 0 and 1) a sphere of a given radius. A cubic cell is placed around each grid position and the volume of the cell in the sphere (assuming a flat surface in the cell) is calculated and normalized by the cell volume to obtain the weight.

ICPertFLRW, a Cactus code (ascl:1102.013) thorn, provides as initial conditions an FLRW metric perturbed with the comoving curvature perturbation Rc in the synchronous comoving gauge. Rc is defined as a sum of sinusoidals (20 in each x, y, and z direction) whose amplitude, wavelength, and phase shift are all parameters in param.ccl. While the metric and extrinsic curvature only have first order scalar perturbations, the energy density is computed exactly in full from the Hamiltonian constraint, hence vector and tensor perturbations are initially present at higher order. These are then passed to the CT_Dust thorn to be evolved.

EBWeyl computes the electric and magnetic parts of the Weyl tensor, Eαβ and Bαβ, using a 3+1 slicing formulation. The module provides a Finite Differencing class with 4th (default) and 6th order backward, centered, and forward schemes. Periodic boundary conditions are used by default; otherwise, a combination of the 3 schemes is available. It also includes a Weyl class that computes for a given metric the variables of the 3+1 formalism, the spatial Christoffel symbols, spatial Ricci tensor, electric and magnetic parts of the Weyl tensor projected along the normal to the hypersurface and fluid flow, the Weyl scalars and invariant scalars. EBWeyl can also compute the determinant and inverse of a 3x3 or 4x4 matrice in every position of a data box.