Evolutions in 3D numerical relativity using fixed mesh refinement

TL;DR

This paper demonstrates that fixed mesh refinement in 3D numerical relativity simulations maintains accuracy and stability while reducing computational costs, introducing new techniques for interface handling and initial data interpolation.

Contribution

It introduces a new fixed mesh refinement system, 'Carpet', integrated into Cactus, with improved interface handling and higher-order initial data interpolation methods.

Findings

FMR achieves comparable accuracy and stability to unigrid simulations.

FMR reduces computational resources needed for high-resolution simulations.

Buffer zones help maintain convergence at grid interfaces.

Abstract

We present results of 3D numerical simulations using a finite difference code featuring fixed mesh refinement (FMR), in which a subset of the computational domain is refined in space and time. We apply this code to a series of test cases including a robust stability test, a nonlinear gauge wave and an excised Schwarzschild black hole in an evolving gauge. We find that the mesh refinement results are comparable in accuracy, stability and convergence to unigrid simulations with the same effective resolution. At the same time, the use of FMR reduces the computational resources needed to obtain a given accuracy. Particular care must be taken at the interfaces between coarse and fine grids to avoid a loss of convergence at higher resolutions, and we introduce the use of "buffer zones" as one resolution of this issue. We also introduce a new method for initial data generation, which enables higher-order interpolation in time even from the initial time slice. This FMR system, "Carpet", is a driver module in the freely available Cactus computational infrastructure, and is able to endow generic existing Cactus simulation modules ("thorns") with FMR with little or no extra effort.