Towards an exascale code for GRMHD on dynamical spacetimes

TL;DR

This paper introduces ExaHyPE, an exascale hyperbolic PDE engine designed to simulate dynamical spacetimes of black holes and neutron stars, employing advanced numerical schemes and formulations for Einstein's equations.

Contribution

The paper presents the first implementation of an exascale PDE engine for dynamical spacetimes using a novel formulation of Einstein's equations and a communication-avoiding numerical scheme.

Findings

Code passes tests in special relativity

Code demonstrates initial capabilities in general relativity

Employs innovative divergence-cleaning and adaptive schemes

Abstract

We present the first results on the construction of an exascale hyperbolic PDE engine (ExaHyPE), a code for the next generation of supercomputers with the objective to evolve dynamical spacetimes of black holes, neutron stars and binaries. We solve a novel first order formulation of Einstein field equations in the conformal and constraint damping Z4 formulation (CCZ4) coupled to ideal general relativistic magnetohydrodynamics (GRMHD), using divergence-cleaning. We adopt a novel communication-avoiding one-step ADER-DG scheme with an a-posteriori subcell finite volume limiter on adaptive spacetrees. Despite being only at its first stages, the code passes a number of tests in special and general relativity.