A New Generalized Harmonic Evolution System

Lindblom, Lee; Scheel, Mark A.; Kidder, Lawrence E.; Owen, Robert; Rinne, Oliver

doi:10.1142/9789812772923_0003

Cited by 64 publications

(245 citation statements)

References 25 publications

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“…slices, and N and N i are the lapse function and shift vector, respectively. The parameter γ 2 was introduced in [6] in order to damp violations of the three-index constraint…”

Section: The Generalized Harmonic Evolution Systemmentioning

confidence: 99%

“…where P C is a projection operator of rank 4 (cf [6]). Here n i now refers to the outwardpointing unit spatial normal to the boundary, l a = (t a + n a )/ √ 2, k a = (t a − n a )/ √ 2, and .…”

Section: Construction Of Boundary Conditionsmentioning

confidence: 99%

“…Here P P is a projection operator of rank 2 that is orthogonal to P C [6]. We remark that (12) still causes some, albeit very small, spurious reflections of gravitational radiation.…”

Section: Construction Of Boundary Conditionsmentioning

confidence: 99%

“…The remaining four components correspond to gauge degrees of freedom. In the past we chose simply to freeze those components in time [6],…”

Section: Construction Of Boundary Conditionsmentioning

confidence: 99%

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Testing outer boundary treatments for the Einstein equations

Rinne¹,

Lindblom²,

Scheel³

2007

Class. Quantum Grav.

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179

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Various methods of treating outer boundaries in numerical relativity are compared using a simple test problem: a Schwarzschild black hole with an outgoing gravitational wave perturbation. Numerical solutions computed using different boundary treatments are compared to a 'reference' numerical solution obtained by placing the outer boundary at a very large radius. For each boundary treatment, the full solutions including constraint violations and extracted gravitational waves are compared to those of the reference solution, thereby assessing the reflections caused by the artificial boundary. These tests are based on a first-order generalized harmonic formulation of the Einstein equations and are implemented using a pseudo-spectral collocation method. Constraint-preserving boundary conditions for this system are reviewed, and an improved boundary condition on the gauge degrees of freedom is presented. Alternate boundary conditions evaluated here include freezing the incoming characteristic fields, Sommerfeld boundary conditions, and the constraint-preserving boundary conditions of Kreiss and Winicour. Rather different approaches to boundary treatments, such as sponge layers and spatial compactification, are also tested. Overall the best treatment found here combines boundary conditions that preserve the constraints, freeze the Newman-Penrose scalar 0 , and control gauge reflections.

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“…slices, and N and N i are the lapse function and shift vector, respectively. The parameter γ 2 was introduced in [6] in order to damp violations of the three-index constraint…”

Section: The Generalized Harmonic Evolution Systemmentioning

confidence: 99%

Section: Construction Of Boundary Conditionsmentioning

confidence: 99%

“…Here P P is a projection operator of rank 2 that is orthogonal to P C [6]. We remark that (12) still causes some, albeit very small, spurious reflections of gravitational radiation.…”

Section: Construction Of Boundary Conditionsmentioning

confidence: 99%

“…The remaining four components correspond to gauge degrees of freedom. In the past we chose simply to freeze those components in time [6],…”

Section: Construction Of Boundary Conditionsmentioning

confidence: 99%

See 2 more Smart Citations

Testing outer boundary treatments for the Einstein equations

Rinne¹,

Lindblom²,

Scheel³

2007

Class. Quantum Grav.

Self Cite

179

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show abstract

“…(11)- (13). On this shell we will use the Chebyshev basis (8) in the radial direction and the Fourier basis (9) and (10) in the angular directions. As before, we will evolve the Cartesian components of all variables on this spherical grid without rewriting the evolution equations in spherical coordinates.…”

Section: Evolving a Single Black Hole With The Bssn Systemmentioning

confidence: 99%

Black hole evolution with the BSSN system by pseudospectral methods

Tichy

2006

Phys. Rev. D

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We present a new pseudo-spectral code for the simulation of evolution systems that are second order in space. We test this code by evolving a non-linear scalar wave equation. These non-linear waves can be stably evolved using very simple constant or radiative boundary conditions, which we show to be well-posed in the scalar wave case. The main motivation for this work, however, is to evolve black holes for the first time with the BSSN system by means of a spectral method. We use our new code to simulate the evolution of a single black hole using all applicable methods that are usually employed when the BSSN system is used together with finite differencing methods. In particular, we use black hole excision and test standard radiative and also constant outer boundary conditions. Furthermore, we study different gauge choices such as 1 + log and constant densitized lapse. We find that these methods in principle do work also with our spectral method. However, our simulations fail after about 100M due to unstable exponentially growing modes. The reason for this failure may be that we evolve the black hole on a full grid without imposing any symmetries. Such full grid instabilities have also been observed when finite differencing methods are used to evolve excised black holes with the BSSN system.

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