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  A Fully Pseudospectral Scheme for Solving Singular Hyperbolic Equations on Conformally Compactified Space-times

Hennig, J., & Ansorg, M. (2009). A Fully Pseudospectral Scheme for Solving Singular Hyperbolic Equations on Conformally Compactified Space-times. Journal of Hyperbolic Differential Equations, 6, 161-184. doi:10.1142/S0219891609001769.

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Item Permalink: http://hdl.handle.net/11858/00-001M-0000-0013-4579-8 Version Permalink: http://hdl.handle.net/11858/00-001M-0000-0013-457A-6
Genre: Journal Article

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 Creators:
Hennig, Jörg1, Author              
Ansorg, Marcus1, Author
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1Geometric Analysis and Gravitation, AEI-Golm, MPI for Gravitational Physics, Max Planck Society, ou_24012              

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 Abstract: With the example of the spherically symmetric scalar wave equation on Minkowski space-time we demonstrate that a fully pseudospectral scheme (i.e. spectral with respect to both spatial and time directions) can be applied for solving hyperbolic equations. The calculations are carried out within the framework of conformally compactified space-times. In our formulation, the equation becomes singular at null infinity and yields regular boundary conditions there. In this manner it becomes possible to avoid "artificial" conditions at some numerical outer boundary at a finite distance. We obtain highly accurate numerical solutions possessing exponential spectral convergence, a feature known from solving elliptic PDEs with spectral methods. Our investigations are meant as a first step towards the goal of treating time evolution problems in General Relativity with spectral methods in space and time.

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 Dates: 2009
 Publication Status: Published in print
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Title: Journal of Hyperbolic Differential Equations
Source Genre: Journal
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Pages: - Volume / Issue: 6 Sequence Number: - Start / End Page: 161 - 184 Identifier: -