Code generation for AMReX with applications to numerical relativity

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.