Code generation for AMReX with applications to numerical relativity

TL;DR

This paper introduces a Python/SymPy code generator for creating numerical solvers for PDEs in AMReX, applied to numerical relativity, and demonstrates its effectiveness through stability tests and black hole simulations.

Contribution

A novel Python/SymPy based code generator for PDEs in AMReX, tailored for numerical relativity applications, enabling efficient and accurate simulation of complex spacetime phenomena.

Findings

Generated spacetime solvers are stable and accurate.

Successfully simulated black hole collisions and gravitational waves.

Demonstrated applicability to complex numerical relativity problems.

Abstract

We present a new python/SymPy based code generator for producing executable numerical expressions for partial differential equations in AMReX-based applications. We demonstrate the code generator capabilities for the case of $3+1$ ADM formulations of numerical relativity for the constraint damped, conformal Z4 formulations (Z4c and CCZ4). The generated spacetime solvers are examined for stability and accuracy using a selection of checks from the standard Apples with Apples testbeds for numerical relativity applications. We also explore physically interesting vacuum spacetimes including head-on and inspiraling black hole binary collisions, and investigate the simulated gravitational waveforms from such events with the Newman-Penrose formulation of waveform extraction.