Spectral methods in general relativistic astrophysics.
TLDR
In this paper, the authors present spectral methods developed in their group to solve three-dimensional partial differential equations arising from astrophysical problems in the framework of general relativity, where the emphasis is laid on equations arising in the universe.About:
This article is published in Journal of Computational and Applied Mathematics.The article was published on 1999-09-30 and is currently open access. It has received 62 citations till now. The article focuses on the topics: Spectral method & General relativity.read more
Citations
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Journal ArticleDOI
Coalescence of Black Hole-Neutron Star Binaries
Masaru Shibata,Keisuke Taniguchi +1 more
TL;DR: The current status of general relativistic studies for the coalescence of black hole-neutron star (BH-NS) binaries is reviewed and understanding for the merger and/or tidal disruption processes, the criterion for tidal disruption, and the properties of the remnant formed after the tidal disruption are summarized.
Journal ArticleDOI
Numerical Hydrodynamics and Magnetohydrodynamics in General Relativity
TL;DR: A comprehensive summary of astrophysical simulations in strong gravitational fields is presented, detailed in three basic sections, namely gravitational collapse, black-hole accretion, and neutron-star evolutions; despite the boundaries, these sections may (and in fact do) overlap throughout the discussion.
Journal ArticleDOI
Spectral Methods for Numerical Relativity
TL;DR: This paper focuses on a class called spectral methods in which, typically, the various functions are expanded in sets of orthogonal polynomials or functions, and presents results obtained by various groups in the field of general relativity by means of spectral methods.
Journal ArticleDOI
Numerical relativity and compact binaries
TL;DR: Numerical relativity is the most promising tool for theoretically modeling the inspiral and coalescence of neutron star and black hole binaries, which, in turn, are among the promising sources of gravitational radiation for future detection by gravitational wave observatories as mentioned in this paper.
Journal ArticleDOI
Numerical Hydrodynamics in General Relativity
TL;DR: The present update provides additional information on numerical schemes, and extends the discussion of astrophysical simulations in general relativistic hydrodynamics, with special mention of conservative and hyperbolic formulations well- adapted to advanced numerical methods.
References
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Book
Spectral Methods in Fluid Dynamics
M. Y. Hussaini,Thomas A. Zang +1 more
TL;DR: Spectral methods have been widely used in simulation of stability, transition, and turbulence as discussed by the authors, and their applications to both compressible and incompressible flows, to viscous as well as inviscid flows, and also to chemically reacting flows are surveyed.
Journal ArticleDOI
Spectral Methods in Fluid Dynamics.
TL;DR: In this article, the authors present a set of methods for the estimation of two-dimensional fluid flow, including a Fourier Galerkin method and a Chebyshev Collocation method.
Difference methods for initial-value problems
Robert D. Richtmyer,K. W. Morton +1 more
TL;DR: In this article, differentielles and stabilite were used for differentiable transport in the context of transfert de chaleur and ondes Reference Record created on 2005-11-18, modified on 2016-08-08
MonographDOI
Numerical analysis of spectral methods : theory and applications
David Gottlieb,Steven A. Orszag +1 more
TL;DR: Spectral Methods Survey of Approximation Theory Review of Convergence Theory Algebraic Stability Spectral Methods Using Fourier Series Applications of algebraic stability analysis Constant Coefficient Hyperbolic Equations Time Differencing Efficient Implementation of Spectral Method as discussed by the authors.