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          Institute: MPI für Gravitationsphysik     Collection: Geometric Analysis and Gravitation     Display Documents



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ID: 360692.0, MPI für Gravitationsphysik / Geometric Analysis and Gravitation
A Fully Pseudospectral Scheme for Solving Singular Hyperbolic Equations on Conformally Compactified Space-times
Authors:Hennig, Jörg; Ansorg, Marcus
Date of Publication (YYYY-MM-DD):2009
Title of Journal:Journal of Hyperbolic Differential Equations
Volume:6
Start Page:161
End Page:184
Review Status:not specified
Audience:Not Specified
Abstract / Description: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.
External Publication Status:published
Document Type:Article
Communicated by:Gerhard Huisken
Affiliations:MPI für Gravitationsphysik/Geometric Analysis and Gravitation
Identifiers:LOCALID:arXiv:0801.1455
DOI:10.1142/S0219891609001769
URL:http://www.worldscinet.com/cgi-bin/details.cgi?id=...
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