A Simflowny-based finite-difference code for high-performance computing in Relativity

TL;DR

This paper introduces Simflowny, a platform that automatically generates parallel, high-order, adaptive mesh refinement codes for simulating Einstein and matter equations in high-performance computing environments, enabling efficient gravitational-wave modeling.

Contribution

The paper presents a novel automated code generation platform, Simflowny, tailored for high-performance adaptive mesh refinement simulations of relativistic physics.

Findings

Successfully validated codes with wave equation, MHD, and Einstein equations.

Achieved high scalability and efficiency in simulations.

Demonstrated applicability to complex physical systems in relativity.

Abstract

The tremendous challenge of comparing our theoretical models with the gravitational-wave observations in the new era of multimessenger astronomy requires accurate and fast numerical simulations of complicated physical systems described by the Einstein and the matter equations. These requirements can only be satisfied if the simulations can be parallelized efficiently on a large number of processors and advanced computational strategies are adopted. To achieve this goal we have developed Simflowny, an open platform for scientific dynamical models which automatically generates parallel code for different simulation frameworks, allowing the use of HPC infrastructures to non-specialist scientists. One of these frameworks is SAMRAI, a mature patch-based structured adaptive mesh refinement infrastructure, capable of reaching exascale in some specific problems. Here we present the numerical techniques that we have implemented on this framework by using Simflowny in order to perform fast, efficient, accurate and highly-scalable simulations. These techniques involve high-order schemes for smooth and non-smooth solutions, Adaptive Mesh Refinement with arbitrary resolution ratios and an optimal strategy for the sub-cycling in time. We validate the automatically generated codes for the SAMRAI infrastructure with some simple test examples (i.e., wave equation and Newtonian MHD) and finally with the Einstein equations.