Implementation of standard testbeds for numerical relativity

Babiuc, Maria; Husa, S.; Alic, Daniela; Hinder, Ian; Lechner, Christiane; Schnetter, Erik; Szilágyi, Béla; Zlochower, Yosef; Dorband, Nils; Pollney, Denis; Winicour, Jeffrey

doi:10.1088/0264-9381/25/12/125012

Cited by 56 publications

(97 citation statements)

References 48 publications

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“…We endorse in this way some recent claims (by Winicour and others) that the current code crosscomparison efforts [22,23] should be extended to the boundaries treatment. A convergence test is performed against this exact strong-field solution, showing the expected convergence rate (second order for our simple SBP method).…”

supporting

confidence: 72%

“…In order to test the strong field regime, we will consider the Gowdy solution [20], which describes a space-time containing plane polarized gravitational waves. This is one of the test cases that is used in numerical code cross-comparison with periodic boundary conditions [22,23]. One of the advantages is that it allows for periodic and/or reflecting boundary conditions, which can be applied to the modes which are not in the energy-momentum constraint sector.…”

Section: Gowdy Waves As a Strong Field Testmentioning

confidence: 99%

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Constraint-preserving boundary conditions in the3+1first-order approach

Bona

Bona-Casas

2010

Phys. Rev. D

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A set of energy-momentum constraint-preserving boundary conditions is proposed for the first-order Z4 case. The stability of a simple numerical implementation is tested in the linear regime (robust stability test), both with the standard corner and vertex treatment and with a modified finite-differences stencil for boundary points which avoids corners and vertices even in cartesian-like grids. Moreover, the proposed boundary conditions are tested in a strong field scenario, the Gowdy waves metric, showing the expected rate of convergence. The accumulated amount of energy-momentum constraint violations is similar or even smaller than the one generated by either periodic or reflection conditions, which are exact in the Gowdy waves case. As a side theoretical result, a new symmetrizer is explicitly given, which extends the parametric domain of symmetric hyperbolicity for the Z4 formalism. The application of these results to first-order BSSN-like formalisms is also considered.

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supporting

confidence: 72%

Section: Gowdy Waves As a Strong Field Testmentioning

confidence: 99%

Constraint-preserving boundary conditions in the3+1first-order approach

Bona

Bona-Casas

2010

Phys. Rev. D

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“…We expect to recover full convergence of the moving puncture formalism in the unigrid limit performing tests similar to those in Ref. [83].…”

Section: Discussionmentioning

confidence: 77%

Accuracy issues for numerical waveforms

2012

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We study the convergence properties of our implementation of the moving punctures approach at very high resolutions for an equal-mass, nonspinning, black-hole binary. We find convergence of the Hamiltonian constraint on the horizons and the L2 norm of the Hamiltonian constraint in the bulk for sixth-and eighth-order finite difference implementations. The momentum constraint is more sensitive, and its L2 norm shows clear convergence for a system with consistent sixth-order finite differencing, while the momentum and BSSN constraints on the horizons show convergence for both sixth-and eighth-order systems. We analyze the gravitational waveform error from the late inspiral, merger, and ringdown. We find that using several lower-order techniques for increasing the speed of numerical relativity simulations actually lead to apparently nonconvergent errors. Even when using standard high-accuracy techniques, rather than seeing clean convergence, where the waveform phase is a monotonic function of grid resolution, we find that the phase tends to oscillate with resolution, possibly due to stochastic errors induced by grid refinement boundaries. Our results seem to indicate that one can obtain gravitational waveform phases to within 0.05 rad. (and possibly as small as 0.015 rad.), while the amplitude error can be reduced to 0.1%. We then compare with the waveforms obtained using the CCZ4 formalism. We find that the CCZ4 waveforms have larger truncation errors for a given resolution, but the Richardson extrapolation phase of the CCZ4 and BSSN waveforms agrees to within 0.01 rad., even during the ringdown.

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“…The color scheme follows kcut = c∆k, for c = 2, 4,8,10,12,14,16,20,40, from blue to red (bottom to top). Note that as we initialize more modes, we are also increasing σρ/ρ.…”

Section: Resultsmentioning

confidence: 99%

Integration of inhomogeneous cosmological spacetimes in the BSSN formalism

2016

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We present cosmological-scale numerical simulations of an evolving universe in full general relativity (GR) and introduce a new numerical tool, CosmoGRaPH, which employs the BaumgarteShapiro-Shibata-Nakamura (BSSN) formalism on a 3-dimensional grid. Using CosmoGRaPH, we calculate the effect of an inhomogeneous matter distribution on the evolution of a spacetime. We also present the results of a set of standard stability tests to demonstrate the robustness of our simulations.

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Implementation of standard testbeds for numerical relativity

Cited by 56 publications

References 48 publications

Constraint-preserving boundary conditions in the3+1first-order approach

Constraint-preserving boundary conditions in the3+1first-order approach

Accuracy issues for numerical waveforms

Integration of inhomogeneous cosmological spacetimes in the BSSN formalism

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