Numerical relativity on a transputer array

Bishop, Nigel T.; Clarke, Christopher J.; d’Inverno, Ray

doi:10.1088/0264-9381/7/2/001

Cited by 20 publications

(24 citation statements)

References 4 publications

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“…The formalism for the numerical evolution of Einstein's equations, in null cone coordinates, is well known [21,23,24] (see also [25,26,27,28,29]). For the sake of completeness, we give here a summary of the formalism, including some of the necessary equations.…”

Section: Summary Of Previous Results and Notationmentioning

confidence: 99%

Numerical relativistic model of a massive particle in orbit near a Schwarzschild black hole

et al. 2003

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We present a method for computing the evolution of a spacetime containing a massive particle and a black hole. The essential idea is that the gravitational field is evolved using full numerical relativity, with the particle generating a non-zero source term in the Einstein equations. The matter fields are not evolved by hydrodynamic equations. Instead the particle is treated as a quasi-rigid body whose center follows a geodesic. The necessary theoretical framework is developed and then implemented in a computer code that uses the null-cone, or characteristic, formulation of numerical relativity. The performance of the code is illustrated in test runs, including a complete orbit (near r = 9M ) of a Schwarzschild black hole.

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Section: Summary Of Previous Results and Notationmentioning

confidence: 99%

Numerical relativistic model of a massive particle in orbit near a Schwarzschild black hole

et al. 2003

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“…Although of potential importance for the accuracy of gravitational waveforms, such a study lies outside the scope of the present work. [16][17][18][19][20]. The solid line corresponds to the energy content E(u) at successive times, the dashed line to the sum of the energy radiated through the inner (Ein(u)) and outer (Eout(u)) boundaries, and the dotdashed line to the sum, Σ(u) = E(u) + Ein(u) + Eout(u), respectively.…”

Section: Concluding Remarks and Outlook Of Future Workmentioning

confidence: 99%

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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“…It should be noted that the PITT code is not the only approach to characteristic numerical relativity -for example, see [7,8,9,10,11,12]. The PITT code exhibits long-term stability in evolving single black hole spacetimes [13], and has also been successfully applied to the problem of nonlinear scattering of gravitational radiation by a black hole [14].…”

Section: Introductionmentioning

confidence: 99%

Linearized solutions of the Einstein equations within a Bondi–Sachs framework, and implications for boundary conditions in numerical simulations

Bishop¹

2005

Class. Quantum Grav.

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We linearize the Einstein equations when the metric is Bondi-Sachs, when the background is Schwarzschild or Minkowski, and when there is a matter source in the form of a thin shell whose density varies with time and angular position. By performing an eigenfunction decomposition, we reduce the problem to a system of linear ordinary differential equations which we are able to solve. The solutions are relevant to the characteristic formulation of numerical relativity: (a) as exact solutions against which computations of gravitational radiation can be compared; and (b) in formulating boundary conditions on the r = 2M Schwarzschild horizon.

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Numerical relativity on a transputer array

Cited by 20 publications

References 4 publications

Numerical relativistic model of a massive particle in orbit near a Schwarzschild black hole

Numerical relativistic model of a massive particle in orbit near a Schwarzschild black hole

Framework for large-scale relativistic simulations in the characteristic approach

Linearized solutions of the Einstein equations within a Bondi–Sachs framework, and implications for boundary conditions in numerical simulations

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