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Discrete boundary treatment for the shifted wave equation

Discrete boundary treatment for the shifted wave equation
Discrete boundary treatment for the shifted wave equation
We present strongly stable semi-discrete finite difference approximations to the quarter space problem (x > 0, t > 0) for the first order in time, second order in space wave equation with a shift term. We consider space-like (pure outflow) and time-like boundaries, with either second- or fourth-order accuracy. These discrete boundary conditions suggest a general prescription for boundary conditions in finite difference codes approximating first order in time, second order in space hyperbolic problems, such as those that appear in numerical relativity. As an example we construct boundary conditions for the Nagy–Ortiz–Reula formulation of the Einstein equations coupled to a scalar field in spherical symmetry.
0264-9381
S343-S368
Calabrese, Gioel
b6d18b27-64cd-426f-b86e-1b3a848f03ed
Gundlach, Carsten
586f1eb5-3185-4b2b-8656-c29c436040fc
Calabrese, Gioel
b6d18b27-64cd-426f-b86e-1b3a848f03ed
Gundlach, Carsten
586f1eb5-3185-4b2b-8656-c29c436040fc

Calabrese, Gioel and Gundlach, Carsten (2006) Discrete boundary treatment for the shifted wave equation. Classical and Quantum Gravity, 23 (16), S343-S368. (doi:10.1088/0264-9381/23/16/S04).

Record type: Article

Abstract

We present strongly stable semi-discrete finite difference approximations to the quarter space problem (x > 0, t > 0) for the first order in time, second order in space wave equation with a shift term. We consider space-like (pure outflow) and time-like boundaries, with either second- or fourth-order accuracy. These discrete boundary conditions suggest a general prescription for boundary conditions in finite difference codes approximating first order in time, second order in space hyperbolic problems, such as those that appear in numerical relativity. As an example we construct boundary conditions for the Nagy–Ortiz–Reula formulation of the Einstein equations coupled to a scalar field in spherical symmetry.

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More information

Submitted date: 22 October 2005
Published date: 21 August 2006

Identifiers

Local EPrints ID: 48962
URI: https://eprints.soton.ac.uk/id/eprint/48962
ISSN: 0264-9381
PURE UUID: b53e4a72-67db-41b4-91fe-4e8ad940d83c
ORCID for Carsten Gundlach: ORCID iD orcid.org/0000-0001-9585-5375

Catalogue record

Date deposited: 18 Oct 2007
Last modified: 20 Jul 2018 00:34

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