Efficient Parallel Numerical Simulations of the Einstein Equations in Spherical Coordinates

We present a new parallel filter that we use to ameliorate the severe

CFL limitation due to the non-constant cell volumes in spherical coordinate grids,

which is implemented inside our new code, SphericalNR. With the filter, we are

able to evolve the system with a larger time step, without sacrificing the accuracy

of the numerical solution. Our new filter is fully parallelized to avoid restrictions

on the number of processors in both the azimuthal and latitude directions.

We validate the filter by demonstrating it passes a variety of challenging code tests

in static and dynamical spacetimes.