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Evolutions in 3D numerical relativity using fixed mesh refinement

Evolutions in 3D numerical relativity using fixed mesh refinement
Evolutions in 3D numerical relativity using fixed mesh refinement
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.
0264-9381
1465-1488
Schnetter, Erik
fa61f1d3-135d-47af-80e2-4285f37a1e24
Hawley, Scott H.
5ded26e9-ff46-447a-b337-e70db8b6076e
Hawke, Ian
fc964672-c794-4260-a972-eaf818e7c9f4
Schnetter, Erik
fa61f1d3-135d-47af-80e2-4285f37a1e24
Hawley, Scott H.
5ded26e9-ff46-447a-b337-e70db8b6076e
Hawke, Ian
fc964672-c794-4260-a972-eaf818e7c9f4

Schnetter, Erik, Hawley, Scott H. and Hawke, Ian (2004) Evolutions in 3D numerical relativity using fixed mesh refinement. Classical and Quantum Gravity, 21 (6), 1465-1488. (doi:10.1088/0264-9381/21/6/014).

Record type: Article

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.

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Published date: 2004

Identifiers

Local EPrints ID: 29316
URI: http://eprints.soton.ac.uk/id/eprint/29316
ISSN: 0264-9381
PURE UUID: 461f3335-0b72-4074-a07b-acf4d30125b9
ORCID for Ian Hawke: ORCID iD orcid.org/0000-0003-4805-0309

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Date deposited: 11 May 2006
Last modified: 10 Jan 2022 02:50

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Contributors

Author: Erik Schnetter
Author: Scott H. Hawley
Author: Ian Hawke ORCID iD

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