General-covariant evolution formalism for numerical relativity

Bona, Carles; Ledvinka, Tomáš; Palenzuela, Carlos; Žáček, M.

doi:10.1103/physrevd.67.104005

Cited by 180 publications

(238 citation statements)

References 38 publications

(134 reference statements)

Supporting

Mentioning

232

Contrasting

Order By: Relevance

“…Notice also that the special (harmonic) case f = 1, λ = 2 has been shown in [25] to be symmetric hyperbolic for the parameter choice ζ = −1. The corresponding energy function can be written as but notice that this expression is far from being unique.…”

Section: B Gowdy Wavesmentioning

confidence: 85%

Symmetry-breaking mechanism for the Z4 general-covariant evolution system

et al. 2004

Self Cite

View full text Add to dashboard Cite

The general-covariant Z4 formalism is further analyzed. The gauge conditions are generalized with a view to Numerical Relativity applications and the conditions for obtaining strongly hyperbolic evolution systems are given both at the first and the second order levels. A symmetry-breaking mechanism is proposed that allows one, when applied in a partial way, to recover previously proposed strongly hyperbolic formalisms, like the BSSN and the Bona-Massó ones. When applied in its full form, the symmetry breaking mechanism allows one to recover the full five-parameter family of first order KST systems. Numerical codes based in the proposed formalisms are tested. A robust stability test is provided by evolving random noise data around Minkowski space-time. A strong field test is provided by the collapse of a periodic background of plane gravitational waves, as described by the Gowdy metric.

show abstract

Section: B Gowdy Wavesmentioning

confidence: 85%

Symmetry-breaking mechanism for the Z4 general-covariant evolution system

et al. 2004

Self Cite

View full text Add to dashboard Cite

show abstract

“…The same family of solutions that was used to show instability of the discretized ADM equations can be used for the standard discretization of the linearized Z4 system [19] o t a ¼ Àf ðK À mHÞ;…”

Section: The Z4 Systemmentioning

confidence: 99%

Numerical stability for finite difference approximations of Einstein’s equations

Calabrese

Hinder

Husa

2006

Journal of Computational Physics

102

View full text Add to dashboard Cite

We extend the notion of numerical stability of finite difference approximations to include hyperbolic systems that are first order in time and second order in space, such as those that appear in numerical relativity and, more generally, in Hamiltonian formulations of field theories. By analyzing the symbol of the second order system, we obtain necessary and sufficient conditions for stability in a discrete norm containing one-sided difference operators. We prove stability for certain toy models and the linearized Nagy-Ortiz-Reula formulation of Einstein's equations.We also find that, unlike in the fully first order case, standard discretizations of some well-posed problems lead to unstable schemes and that the Courant limits are not always simply related to the characteristic speeds of the continuum problem. Finally, we propose methods for testing stability for second order in space hyperbolic systems.

show abstract

“…It turns out to be related with the variableΓ i of the BSSN system, defined by Eq. (21) in [14]. (See also [16].)…”

Section: Introductionmentioning

confidence: 99%

Strongly hyperbolic second order Einstein’s evolution equations

2004

View full text Add to dashboard Cite

BSSN-type evolution equations are discussed. The name refers to the Baumgarte, Shapiro, Shibata, and Nakamura version of the Einstein evolution equations, without introducing the conformaltraceless decomposition but keeping the three connection functions and including a densitized lapse. It is proved that a pseudo-differential first order reduction of these equations is strongly hyperbolic. In the same way, densitized Arnowitt-Deser-Misner evolution equations are found to be weakly hyperbolic. In both cases, the positive densitized lapse function and the spacelike shift vector are arbitrary given fields. This first order pseudodifferential reduction adds no extra equations to the system and so no extra constraints.

show abstract

General-covariant evolution formalism for numerical relativity

Cited by 180 publications

References 38 publications

Symmetry-breaking mechanism for the Z4 general-covariant evolution system

Symmetry-breaking mechanism for the Z4 general-covariant evolution system

Numerical stability for finite difference approximations of Einstein’s equations

Strongly hyperbolic second order Einstein’s evolution equations

Contact Info

Product

Resources

About