Astronomy and Astrophysics – Astrophysics – General Relativity and Quantum Cosmology
Scientific paper
2007-06-15
Living Reviews in Relativity (2009) lrr-1009-1
Astronomy and Astrophysics
Astrophysics
General Relativity and Quantum Cosmology
This new version has been accepted for publication in Living Reviews in Relativity
Scientific paper
Equations arising in General Relativity are usually too complicated to be solved analytically and one has to rely on numerical methods to solve sets of coupled partial differential equations. Among the possible choices, this paper focuses on a class called spectral methods where, typically, the various functions are expanded onto sets of orthogonal polynomials or functions. A theoretical introduction on spectral expansion is first given and a particular emphasis is put on the fast convergence of the spectral approximation. We present then different approaches to solve partial differential equations, first limiting ourselves to the one-dimensional case, with one or several domains. Generalization to more dimensions is then discussed. In particular, the case of time evolutions is carefully studied and the stability of such evolutions investigated. One then turns to results obtained by various groups in the field of General Relativity by means of spectral methods. First, works which do not involve explicit time-evolutions are discussed, going from rapidly rotating strange stars to the computation of binary black holes initial data. Finally, the evolutions of various systems of astrophysical interest are presented, from supernovae core collapse to binary black hole mergers.
Grandclement Philippe
Novak Jerome
No associations
LandOfFree
Spectral Methods for Numerical Relativity does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Spectral Methods for Numerical Relativity, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Spectral Methods for Numerical Relativity will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-549585