Stable Characteristic Evolution of Generic Three-Dimensional Single-Black-Hole Spacetimes

Gómez, Roberto; Lehner, Luis; Marsa, R. L.; Winicour, Jeffrey; Abrahams, Andrew M.; Anderson, Arlen; Anninos, Peter; Baumgarte, Thomas W.; Bishop, Nigel T.; Brandt, Steven R.; Browne, James C.; Camarda, Karen; Choptuik, Matthew W.; Cook, G.G.; Correll, R. R.; Evans, Charles R.; Finn, L. S.; Fox, Geoffrey; Haupt, T.; Huq, M.; Kidder, Lawrence E.; Klasky, Scott; Laguna, Pablo; Landry, Walter; Lenaghan, Jonathan; Massó, Joan; Matzner, Richard A.; Mitra, S.; Papadopoulos, Philippos; Parashar, Manish; Rezzolla, Luciano; Rupright, M. E.; Saied, Faisal; Saylor, Paul E.; Scheel, Mark A.; Seidel, Edward; Shapiro, Stuart L.; Shoemaker, D. M.; Smarr, Larry; Szilágyi, Béla; Teukolsky, Saul A.; Putten, Maurice H. P. M. van; Walker, Paul; York, James W.

doi:10.1103/physrevlett.80.3915

Cited by 93 publications

(50 citation statements)

References 22 publications

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“…The characteristic approach to numerical relativity is based on null coordinates x α = (u, r, x A ), with u the retarded time, r a luminosity distance and x A coordinates on the sphere [1, 2,3,4,5,6,7,8,12,13]. In its 3-dimensional implementation, the angular coordinates chosen are stereographic coordinates x A = (ζ,ζ) on the sphere, which is covered with two stereographic coordinate patches, as first presented in Ref.…”

Section: The Standard Eth Approach In Characteristic Numerical Rementioning

confidence: 99%

“…Since the past light cones tilts outwards once inside the horizon, the values computed just inside the horizon can never affect those points of the grid that lie outside. This scheme provides then an extremely simple and effective form of excision, as discussed in [4,5,42] in the context of characteristic evolution, and in [43] in the context of 3+1 simulations in the Bondi-Sachs gauge.…”

Section: Boundary Treatment For the Evolved Fieldsmentioning

confidence: 99%

“…The characteristic approach has been used successfully to carry out numerical simulations of space-times with and without sources [1, 2,3,4,5,6,7,8]. A significant computational effort is nevertheless necessary to extend its range of applicability to the simulation of astrophysically relevant sources of gravitational radiation, such as the black hole -neutron star binary problem, where the approach can be most useful.…”

Section: Introductionmentioning

confidence: 99%

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Framework for large-scale relativistic simulations in the characteristic approach

2007

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We present a new computational framework (LEO), that enables us to carry out the very first large-scale, high-resolution computations in the context of the characteristic approach in numerical relativity. At the analytic level, our approach is based on a new implementation of the "eth" formalism, using a non-standard representation of the spin-raising and lowering angular operators in terms of non-conformal coordinates on the sphere; we couple this formalism to a partially firstorder reduction (in the angular variables) of the Einstein equations. The numerical implementation of our approach supplies the basic building blocks for a highly parallel, easily extensible numerical code. We demonstrate the adaptability and excellent scaling of our numerical code by solving, within our numerical framework, for a scalar field minimally coupled to gravity (the Einstein-KleinGordon problem) in the 3-dimensions. The nonlinear code is globally second-order convergent, and has been extensively tested using as reference a calibrated code with the same boundary-initial data and radial marching algorithm. In this context, we show how accurately we can follow quasi-normal mode ringing. In the linear regime, we show energy conservation for a number of initial data sets with varying angular structure. A striking result that arises in this context is the saturation of the flow of energy through the Schwarzschild radius. As a final calibration check we perform a large simulation with resolution never achieved before.

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Section: The Standard Eth Approach In Characteristic Numerical Rementioning

confidence: 99%

Section: Boundary Treatment For the Evolved Fieldsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Framework for large-scale relativistic simulations in the characteristic approach

2007

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“…Many different systems such as gauge waves, gravitational waves and Schwarzschild black hole systems are solved using Numerical Relativity [1][2][3]. With the 2005 breakthroughs, the binary Schwarzschild black holes and merger simulations last long enough to extract gravitational waves and study their forms [4,5].…”

Section: Introductionmentioning

confidence: 99%

Lattice Boltzmann model for numerical relativity

Ilseven

Mendoza

2016

Phys. Rev. E

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In the Bona-Masso formulation, Einstein equations are written as a set of flux conservative first order hyperbolic equations that resemble fluid dynamics equations. Based on this formulation, we construct a lattice Boltzmann model for Numerical Relativity. Our model is validated with wellestablished tests, showing good agreement with analytical solutions. Furthermore, we show that by increasing the relaxation time, we gain stability at the cost of losing accuracy, and by decreasing the lattice spacings while keeping a constant numerical diffusivity, the accuracy and stability of our simulations improves. Finally, in order to show the potential of our approach a linear scaling law for parallelisation with respect to number of CPU cores is demonstrated. Our model represents the first step in using lattice kinetic theory to solve gravitational problems.

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“…Gómez et al [10] use two overlapping stereographic patches to discretize the angular direction using the eth formalism. This was later used by Gómez et al [11] to evolve a single, non-stationary black hole in a stable manner in three dimensions with a characteristic formulation. Thornburg [12] evolves a stationary Kerr black hole in three dimensions using multiple grid patches using a Cauchy formulation.…”

Section: Introductionmentioning

confidence: 99%

A multi-block infrastructure for three-dimensional time-dependent numerical relativity

Schnetter

Diener

Dorband

et al. 2006

Class. Quantum Grav.

112

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We describe a generic infrastructure for time evolution simulations in numerical relativity using multiple grid patches. After a motivation of this approach, we discuss the relative advantages of global and patch-local tensor bases. We describe both our multi-patch infrastructure and our time evolution scheme, and comment on adaptive time integrators and parallelization. We also describe various patch system topologies that provide spherical outer and/or multiple inner boundaries. We employ penalty inter-patch boundary conditions, and we demonstrate the stability and accuracy of our three-dimensional implementation. We solve both a scalar wave equation on a stationary rotating black hole background and the full Einstein equations. For the scalar wave equation, we compare the effects of global and patch-local tensor bases, different finite differencing operators and the effect of artificial dissipation onto stability and accuracy. We show that multi-patch systems can directly compete with the so-called fixed mesh refinement approach; however, one can also combine both. For the Einstein equations, we show that using multiple grid patches with penalty boundary conditions leads to a robustly stable system. We also show long-term stable and accurate evolutions of a one-dimensional nonlinear gauge wave. Finally, we evolve weak gravitational waves in three dimensions and extract accurate waveforms, taking advantage of the spherical shape of our grid lines.

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Stable Characteristic Evolution of Generic Three-Dimensional Single-Black-Hole Spacetimes

Cited by 93 publications

References 22 publications

Framework for large-scale relativistic simulations in the characteristic approach

Framework for large-scale relativistic simulations in the characteristic approach

Lattice Boltzmann model for numerical relativity

A multi-block infrastructure for three-dimensional time-dependent numerical relativity

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