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

Extension of the subgrid-scale gradient model for compressible magnetohydrodynamics turbulent instabilities

“…We have generated our computational code by using the platform Simflowny 66,67 , endowed with HRSC high-order finite-difference schemes commonly used in numerical relativity applications, already described in depth in our previous work 71 . We stress that we use methods that may not be optimal for periodic box turbulence, but are adequate in astrophysical simulations with the development of strong shocks.…”

Gravitational waves from dark boson star binary mergers

“…These equations have been introduced in the platform Simflowny [35][36][37][38] to automatically generate parallel code for the SAMRAI infrastructure [39][40][41]. SAM-RAI provides parallelization and Adaptive Mesh Refinement (AMR), which are crucial to obtain accurate solutions in an efficient manner by adding more resolution only where it is required (i.e., in the regions encompassing each BSs).…”

A Simflowny-based high-performance 3D code for the generalized induction equation

“…The novelty of our code lies in: (i) the use of a Cartesian 3D grid to solve at the same time all the regions of the star, including the magnetosphere; (ii) the efficient implementation, using high-order numerical schemes, on the infrastructure SAMRAI which allows for high-scalability parallelization and AMR [38,55]; (iii) the divergence cleaning method to ensure the constraint ∇ · B = 0; (iv) the generalization of the induction equation, including all possible terms that can act, either independently or combined.…”

“…The time integration of the resulting semi-discrete equations is performed by using a 4 th -order Runge-Kutta scheme, which ensures the stability and convergence of the solution for a small enough time step ∆t. We defer the reader to [55] for further details on the numerical schemes and an extensive analysis of the performance with different discretization schemes for different problems, including MHD.…”