Spectral Methods for Numerical Relativity

Details Spectral Methods for Numerical Relativity Spectral Methods for Numerical Relativity

Jan 2009

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2009lrr....12....1g&link_type=abstract

Living Reviews in Relativity, vol. 12, no. 1

Statistics

Computation

16

Numerical Relativity, Numerical Methods

Scientific paper

Equations arising in general relativity are usually too complicated to be solved analytically and one must 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 in which, typically, the various functions are expanded in sets of orthogonal polynomials or functions. First, a theoretical introduction of spectral expansion is given with a particular emphasis on the fast convergence of the spectral approximation. We then present different approaches to solving partial differential equations, first limiting ourselves to the one-dimensional case, with one or more 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. We then present results obtained by various groups in the field of general relativity by means of spectral methods. Work, which does not involve explicit time-evolutions, is discussed, going from rapidly-rotating strange stars to the computation of black-hole binary initial data. Finally, the evolution of various systems of astrophysical interest are presented, from supernovae core collapse to black-hole binary mergers.

Affiliated with

Also associated with

No associations

Rating

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.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-1139031