Code generation for AMReX with applications to numerical relativity

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.

Automated summary

This article presents a new code generator based on python/SymPy for producing executable numerical expressions to solve partial differential equations. The generator is applied to the constraint damped and conformal Z4 formulations in 3+1 ADM numerical relativity. The generated solvers are tested for stability and accuracy and applied to physically interesting vacuum spacetimes and gravitational waveforms.