A Dissipative Algorithm for Wave-like Equations in the Characteristic Formulation

Lehner, Luis

doi:10.1006/jcph.1998.6137

Cited by 18 publications

(29 citation statements)

References 26 publications

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“…In the case of a square stereographic patch, whose boundary aligns with the grid lines, the dissipation built into the characteristic radial integration scheme is sufficient for this purpose [35]. However, because a circular boundary fits into a stereographic grid in an irregular way, angular dissipation is also necessary in order to suppress the resulting high frequency error introduced by the interpolations between stereographic patches.…”

Section: A Angular Dissipationmentioning

confidence: 99%

Strategies for the characteristic extraction of gravitational waveforms

et al. 2009

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We develop, test, and compare new numerical and geometrical methods for improving the accuracy of extracting waveforms using characteristic evolution. The new numerical method involves use of circular boundaries to the stereographic grid patches which cover the spherical cross sections of the outgoing null cones. We show how an angular version of numerical dissipation can be introduced into the characteristic code to damp the high frequency error arising form the irregular way the circular patch boundary cuts through the grid. The new geometric method involves use of the Weyl tensor component É 4 to extract the waveform as opposed to the original approach via the Bondi news function. We develop the necessary analytic and computational formula to compute the Oð1=rÞ radiative part of É 4 in terms of a conformally compactified treatment of null infinity. These methods are compared and calibrated in test problems based upon linearized waves.

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Section: A Angular Dissipationmentioning

confidence: 99%

Strategies for the characteristic extraction of gravitational waveforms

et al. 2009

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“…For more details on the convergence properties of the radial evolution algorithm, see [44]. The simulations reported in this and subsequent sections are all carried out in compactified, outgoing (retarded) null coordinates.…”

Section: Tests Of Second Order Convergencementioning

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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“…Dissipation cannot be added to the {2 + 1 + 1} format of characteristic evolution in this standard way for {3 + 1} Cauchy evolution. In the original version of the PITT code, which used square stereographic patches with boundaries aligned with the grid, numerical dissipation was only introduced in the radial direction [163]. This was sufficient to establish numerical stability.…”

Section: D Characteristic Evolutionmentioning

confidence: 99%

Characteristic Evolution and Matching

Winicour

2009

Living Rev. Relativ.

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I review the development of numerical evolution codes for general relativity based upon the characteristic initial value problem. Progress is traced from the early stage of 1D feasibility studies to 2D axisymmetric codes that accurately simulate the oscillations and gravitational collapse of relativistic stars and to current 3D codes that provide pieces of a binary black hole spacetime. Cauchy codes have now been successful at simulating all aspects of the binary black hole problem inside an artificially constructed outer boundary. A prime application of characteristic evolution is to eliminate the role of this artificial outer boundary via Cauchy-characteristic matching, by which the radiated waveform can be computed at null infinity. Progress in this direction is discussed.

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A Dissipative Algorithm for Wave-like Equations in the Characteristic Formulation

Cited by 18 publications

References 26 publications

Strategies for the characteristic extraction of gravitational waveforms

Strategies for the characteristic extraction of gravitational waveforms

Framework for large-scale relativistic simulations in the characteristic approach

Characteristic Evolution and Matching

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