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  A multi-block infrastructure for three-dimensional time-dependent numerical relativity

Schnetter, E., Diener, P., Dorband, E. N., & Tiglio, M. (2006). A multi-block infrastructure for three-dimensional time-dependent numerical relativity. Classical and Quantum Gravity, 23, S553-S578.

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Item Permalink: http://hdl.handle.net/11858/00-001M-0000-0013-4BC1-0 Version Permalink: http://hdl.handle.net/11858/00-001M-0000-0013-4BC2-E
Genre: Journal Article

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 Creators:
Schnetter, Erik, Author
Diener, Peter1, Author
Dorband, Ernst Nils1, Author              
Tiglio, Manuel, Author
Affiliations:
1Astrophysical Relativity, AEI-Golm, MPI for Gravitational Physics, Max Planck Society, ou_24013              

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 Abstract: We describe a generic infrastructure for time evolution simulations in numerical relativity using multiple grid patches. After a motivation of this approach, we discuss the relative advantages of global and patch-local tensor bases. We describe both our multi-patch infrastructure and our time evolution scheme, and comment on adaptive time integrators and parallelisation. We also describe various patch system topologies that provide spherical outer and/or multiple inner boundaries. We employ penalty inter-patch boundary conditions, and we demonstrate the stability and accuracy of our three-dimensional implementation. We solve both a scalar wave equation on a stationary rotating black hole background and the full Einstein equations. For the scalar wave equation, we compare the effects of global and patch-local tensor bases, different finite differencing operators, and the effect of artificial dissipation onto stability and accuracy. We show that multi-patch systems can directly compete with the so-called fixed mesh refinement approach; however, one can also combine both. For the Einstein equations, we show that using multiple grid patches with penalty boundary conditions leads to a robustly stable system. We also show long-term stable and accurate evolutions of a one-dimensional non-linear gauge wave. Finally, we evolve weak gravitational waves in three dimensions and extract accurate waveforms, taking advantage of the spherical shape of our grid lines. Comment of the Author: Invited papers on numerical relativity, related to the Banff International Research Station programme 16–21 April 2005 and the Newton Institute programme 8 August–23 December 2005

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Language(s): eng - English
 Dates: 2006
 Publication Status: Published in print
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 Identifiers: eDoc: 254736
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Title: Classical and Quantum Gravity
Source Genre: Journal
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Pages: - Volume / Issue: 23 Sequence Number: - Start / End Page: S553 - S578 Identifier: -