Lessons for adaptive mesh refinement in numerical relativity

TL;DR

This paper evaluates the Berger-Rigoutsos AMR algorithm in the GRChombo code for numerical relativity, demonstrating high-quality gravitational waveform generation and discussing technical challenges and best practices for adaptive mesh refinement.

Contribution

It showcases the flexibility of the Berger-Rigoutsos AMR algorithm in GRChombo, compares its performance with established codes, and provides practical guidelines for effective mesh refinement in complex simulations.

Findings

GRChombo produces high-quality binary black-hole waveforms

Different refinement criteria impact numerical accuracy and efficiency

Guidelines are provided for choosing tagging criteria in various scenarios

Abstract

We demonstrate the flexibility and utility of the Berger-Rigoutsos Adaptive Mesh Refinement (AMR) algorithm used in the open-source numerical relativity code GRChombo for generating gravitational waveforms from binary black-hole inspirals, and for studying other problems involving non-trivial matter configurations. We show that GRChombo can produce high quality binary black-hole waveforms through a code comparison with the established numerical relativity code Lean. We also discuss some of the technical challenges involved in making use of full AMR (as opposed to, e.g. moving box mesh refinement), including the numerical effects caused by using various refinement criteria when regridding. We suggest several "rules of thumb" for when to use different tagging criteria for simulating a variety of physical phenomena. We demonstrate the use of these different criteria through example evolutions of a scalar field theory. Finally, we also review the current status and general capabilities of GRChombo.