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  Symmetry without symmetry: Numerical simulation of axisymmetric systems using Cartesian grids.

Alcubierre, M., Brandt, S., Brügmann, B., Holz, D., Seidel, E., Takahashi, R., et al. (2001). Symmetry without symmetry: Numerical simulation of axisymmetric systems using Cartesian grids. International Journal of Modern Physics D, 10(3), 273-289. doi:10.1142/S0218271801000834.

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Item Permalink: http://hdl.handle.net/11858/00-001M-0000-0013-559C-A Version Permalink: http://hdl.handle.net/11858/00-001M-0000-0013-559D-8
Genre: Journal Article

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Int.Journ.Mod.Phys.D.10.3.pdf (Publisher version), 374KB
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 Creators:
Alcubierre, Miguel1, Author
Brandt, Steven1, Author
Brügmann, Bernd1, Author
Holz, Daniel1, Author
Seidel, Edward1, Author
Takahashi, Ryoji1, Author
Thornburg, Jonathan, Author
Affiliations:
1Astrophysical Relativity, AEI-Golm, MPI for Gravitational Physics, Max Planck Society, escidoc:24013              

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 Abstract: We present a new technique for the numerical simulation of axisymmetric systems. This technique avoids the coordinate singularities which often arise when cylindrical or polar-spherical coordinate finite difference grids are used, particularly in simulating tenser partial differential equations like those of 3 + 1 numerical relativity. For a system axisymmetric about the r axis, the basic idea is to use a three-dimensional Cartesian (x,y,z) coordinate grid which covers (say) the y = 0 plane, but is only one finite-difference-molecule-width thick in the y direction. The field variables in the central y = 0 grid plane can be updated using normal (x, y, z)-coordinate finite differencing, while those in the y not equal 0 grid planes can be computed from those in the central plane by using the axisymmetry assumption and interpolation. We demonstrate the effectiveness of the approach on a set of fully nonlinear test computations in 3 + 1 numerical general relativity, involving both black holes and collapsing gravitational waves.

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 Dates: 2001-06
 Publication Status: Published in print
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 Identifiers: eDoc: 206107
URI: http://xxx.lanl.gov/archive/gr-qc/
Other: 16362
DOI: 10.1142/S0218271801000834
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Title: International Journal of Modern Physics D
Source Genre: Journal
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Pages: - Volume / Issue: 10 (3) Sequence Number: - Start / End Page: 273 - 289 Identifier: ISSN: 0218-2718