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  Constructing Reference Metrics on Multicube Representations of Arbitrary Manifolds

Lindblom, L., Taylor, N. W., & Rinne, O. (2016). Constructing Reference Metrics on Multicube Representations of Arbitrary Manifolds. Journal of Computational Physics, 313, 31-56. doi:10.1016/j.jcp.2016.02.029.

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Item Permalink: http://hdl.handle.net/11858/00-001M-0000-0024-65CA-C Version Permalink: http://hdl.handle.net/11858/00-001M-0000-002A-6318-7
Genre: Journal Article

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1411.6785.pdf (Preprint), 706KB
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 Creators:
Lindblom, Lee, Author
Taylor, Nicholas W., Author
Rinne, Oliver1, Author              
Affiliations:
1Geometric Analysis and Gravitation, AEI-Golm, MPI for Gravitational Physics, Max Planck Society, escidoc:24012              

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Free keywords: Physics, Computational Physics, physics.comp-ph,General Relativity and Quantum Cosmology, gr-qc,Mathematics, Differential Geometry, math.DG
 Abstract: Reference metrics are used to define the differential structure on multicube representations of manifolds, i.e., they provide a simple and practical way to define what it means globally for tensor fields and their derivatives to be continuous. This paper introduces a general procedure for constructing reference metrics automatically on multicube representations of manifolds with arbitrary topologies. The method is tested here by constructing reference metrics for compact, orientable two-dimensional manifolds with genera between zero and five. These metrics are shown to satisfy the Gauss-Bonnet identity numerically to the level of truncation error (which converges toward zero as the numerical resolution is increased). These reference metrics can be made smoother and more uniform by evolving them with Ricci flow. This smoothing procedure is tested on the two-dimensional reference metrics constructed here. These smoothing evolutions (using volume-normalized Ricci flow with DeTurck gauge fixing) are all shown to produce reference metrics with constant scalar curvatures (at the level of numerical truncation error).

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 Dates: 2014-11-252015-01-022016
 Publication Status: Published in print
 Pages: 37 pages, 16 figures
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 Rev. Method: -
 Identifiers: arXiv: 1411.6785
DOI: 10.1016/j.jcp.2016.02.029
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Title: Journal of Computational Physics
Source Genre: Journal
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Pages: - Volume / Issue: 313 Sequence Number: - Start / End Page: 31 - 56 Identifier: -