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

TL;DR

This paper compares cell-centered and vertex-centered adaptive mesh refinement techniques in numerical relativity simulations, finding that the optimal choice depends on the specific physical scenario, with performance benefits observed for each method in different contexts.

Contribution

The paper introduces a novel comparison of cell-centered and vertex-centered grid sampling within a single code-base for numerical relativity simulations, highlighting their respective performance advantages.

Findings

Vertex-centered sampling yields ~20% faster binary black hole inspiral-merger simulations.

Cell-centered sampling improves performance in binary neutron star merger simulations.

Performance benefits vary depending on the physical scenario and grid sampling method.

Abstract

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 GR-Athena++, 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 $\sim 20\%$ 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.