The University of Southampton
University of Southampton Institutional Repository

Convergence and stability in numerical relativity

Convergence and stability in numerical relativity
Convergence and stability in numerical relativity
It is often the case in numerical relativity that schemes that are known to be convergent for well posed systems are used in evolutions of weakly hyperbolic (WH) formulations of Einstein's equations. Here we explicitly show that with several of the discretizations that have been used through out the years, this procedure leads to non-convergent schemes. That is, arbitrarily small initial errors are amplified without bound when resolution is increased, independently of the amount of numerical dissipation introduced. The lack of convergence introduced by this instability can be particularly subtle, in the sense that it can be missed by several convergence tests, especially in 3+1 dimensional codes. We propose tests and methods to analyze convergence that may help detect these situations.
1550-7998
1-4
Calabrese, Gioel
b6d18b27-64cd-426f-b86e-1b3a848f03ed
Pullin, Jorge
4c0fa15e-1ba7-49c4-bfc6-f46944951a9f
Sarbach, Olivier
9b1b946c-5ff3-4eeb-b685-915c662edff8
Tiglio, Manuel
70c1e9ee-b30c-4354-af43-1bd3b4b6af24
Calabrese, Gioel
b6d18b27-64cd-426f-b86e-1b3a848f03ed
Pullin, Jorge
4c0fa15e-1ba7-49c4-bfc6-f46944951a9f
Sarbach, Olivier
9b1b946c-5ff3-4eeb-b685-915c662edff8
Tiglio, Manuel
70c1e9ee-b30c-4354-af43-1bd3b4b6af24

Calabrese, Gioel, Pullin, Jorge, Sarbach, Olivier and Tiglio, Manuel (2002) Convergence and stability in numerical relativity. Physical Review D, 66 (4), 1-4. (doi:10.1103/PhysRevD.66.041501).

Record type: Article

Abstract

It is often the case in numerical relativity that schemes that are known to be convergent for well posed systems are used in evolutions of weakly hyperbolic (WH) formulations of Einstein's equations. Here we explicitly show that with several of the discretizations that have been used through out the years, this procedure leads to non-convergent schemes. That is, arbitrarily small initial errors are amplified without bound when resolution is increased, independently of the amount of numerical dissipation introduced. The lack of convergence introduced by this instability can be particularly subtle, in the sense that it can be missed by several convergence tests, especially in 3+1 dimensional codes. We propose tests and methods to analyze convergence that may help detect these situations.

This record has no associated files available for download.

More information

Published date: 2002

Identifiers

Local EPrints ID: 40859
URI: http://eprints.soton.ac.uk/id/eprint/40859
ISSN: 1550-7998
PURE UUID: 3b7898b3-ef78-4569-bcfb-a018c84a2c86

Catalogue record

Date deposited: 11 Jul 2006
Last modified: 15 Mar 2024 08:23

Export record

Altmetrics

Contributors

Author: Gioel Calabrese
Author: Jorge Pullin
Author: Olivier Sarbach
Author: Manuel Tiglio

Download statistics

Downloads from ePrints over the past year. Other digital versions may also be available to download e.g. from the publisher's website.

View more statistics

Atom RSS 1.0 RSS 2.0

Contact ePrints Soton: eprints@soton.ac.uk

ePrints Soton supports OAI 2.0 with a base URL of http://eprints.soton.ac.uk/cgi/oai2

This repository has been built using EPrints software, developed at the University of Southampton, but available to everyone to use.

We use cookies to ensure that we give you the best experience on our website. If you continue without changing your settings, we will assume that you are happy to receive cookies on the University of Southampton website.

×