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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.

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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

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Date deposited: 11 Jul 2006
Last modified: 15 Jul 2019 18:58

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