Numerical relativity simulations of compact binaries: Comparison of cell- and vertex-centered adaptive meshes

Given the compact binary evolution problem of numerical relativity, in the finite-difference, block-based, adaptive mesh refinement context, choices must be made on how evolved fields are to be discretized. In -thena++, the space-time solver was previously fixed to be vertex centered. Here, our recent extensions to a cell-centered treatment are described. Simplifications in the handling of variables during the treatment of general relativistic magneto-hydrodynamical (GRMHD) evolution are found. A novelty is that performance comparison for the two choices of grid sampling is made within a single code base. In the case of a binary black hole inspiral-merger problem, by evolving geometric fields on vertex centers, an average <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"> <a:mo>∼</a:mo> <a:mn>20</a:mn> <a:mo>%</a:mo> </a:math> speed increase is observed, when compared against cell-centered sampling. The opposite occurs in the GRMHD setting. A binary neutron star inspiral-merger-collapse problem, representative of typical production simulations, is considered. We find that cell-centered sampling for the space-time solver improves performance, by a similar factor.