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Introduction to 3+1 Numerical Relativity$
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Miguel Alcubierre

Print publication date: 2008

Print ISBN-13: 9780199205677

Published to Oxford Scholarship Online: September 2008

DOI: 10.1093/acprof:oso/9780199205677.001.0001

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HYPERBOLIC REDUCTIONS OF THE FIELD DQUATIONS

HYPERBOLIC REDUCTIONS OF THE FIELD DQUATIONS

Chapter:
(p.155) 5 HYPERBOLIC REDUCTIONS OF THE FIELD DQUATIONS
Source:
Introduction to 3+1 Numerical Relativity
Author(s):

Miguel Alcubierre

Publisher:
Oxford University Press
DOI:10.1093/acprof:oso/9780199205677.003.0005

From the early 1990s, a large number of alternative formulations of the 3+1 evolution equations have been proposed. There are currently more formulations than there are numerical groups capable of testing them. This chapter discusses a small number of formulations, chosen both because they are a representative sample of the different approaches used, and because they correspond to the formulations used by the majority of numerical evolution codes that exist today. Topics covered include well-posedness, the concept of hyperbolicity, hyperbolicity of the ADM equations, the Bona–Masso and NOR formulations, hyperbolicity of BSSNOK, the Kidder–Scheel–Teukolsky family, higher derivative formulations, the Z4 formulation, boundary conditions, radiative boundary conditions, maximally dissipative boundary conditions, and constraint preserving boundary conditions.

Keywords:   well-posedness, hyperbolicity, Bona–Masso formulation, NOR formulation, derivative formulations, boundary conditions

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