Open AccessDissertation
Constrained evolution in numerical relativity
Matthew Anderson
- pp 3496
TLDR
In this paper, the authors propose a method to solve the problem of "uniformity" and "uncertainty" in the context of health care, and propose a solution.Abstract:
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Citations
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Characteristic evolutions in numerical relativity using six angular patches
TL;DR: In this article, the authors investigate the use of a six-patch angular coordinate system in characteristic numerical relativity, by comparing an existing two-patch implementation (using second-order finite differencing throughout) with a new sixpatch implementation using either second- or fourth-order FDFD for the angular derivatives, and compare these different codes by monitoring the Einstein constraint equations, numerically evaluated independently from the evolution.
Journal ArticleDOI
Extended Lifetime in Computational Evolution of Isolated Black Holes
TL;DR: In this paper, it was shown that for large domains, neither constraint-subtracted nor constrained solutions can stabilize long-term single-hole evolutions, and the failure appears to arise from features at the inner excision boundary; the behavior does generally improve with resolution.
Journal ArticleDOI
Excising a boosted rotating black hole with overlapping grids
Gioel Calabrese,David Neilsen +1 more
TL;DR: In this article, the authors use the overlapping grids method to construct a fourth order accurate discretization of a first order reduction of the Klein-Gordon scalar field equation on a boosted spinning black hole blackground in axisymmetry.
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Hyperbolicity and constrained evolution in linearized gravity
TL;DR: In this paper, the authors present an analysis for one method of constrained evolution, applied to a simple vacuum system, linearized gravitational waves, and give explicit analytical construction of the effect of initial data setting and constrained evolution for linearised gravitational waves.
References
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Journal ArticleDOI
Über die partiellen Differenzengleichungen der mathematischen Physik
TL;DR: In this paper, the authors present a Gebrauch bestimmt ausschließlich für den persönlichen, nicht kommerziellen Gebrauchs, which is a rechtschutzbestimmter gebrauch, and gilt vorbehaltlich der folgenden Einschränkungen.
Book
Adaptive mesh refinement for hyperbolic partial differential equations
Marsha Berger,Joseph Oliger +1 more
TL;DR: This work presents an adaptive method based on the idea of multiple, component grids for the solution of hyperbolic partial differential equations using finite difference techniques based upon Richardson-type estimates of the truncation error, which is a mesh refinement algorithm in time and space.
Journal ArticleDOI
Republication of: The dynamics of general relativity
TL;DR: The Golden Oldie as discussed by the authors is an unretouched version of the Witten formulation of General Relativity, originally published as Chap. 7, pp. 227-264, in Gravitation: an introduction to current research, L. Witten, ed.
Efficient Management of Parallelism in Object-Oriented Numerical Software Libraries.
TL;DR: The concepts discussed are appropriate for all scalable computing systems and provide many of the data structures and numerical kernels required for the scalable solution of PDEs, offering performance portability.
BookDOI
Time Dependent Problems and Difference Methods
TL;DR: Time-Dependent Problems and Difference Methods, Second Edition as discussed by the authors provides guidance for the analysis of difference methods for computing approximate solutions to partial differential equations for time-dependent problems, and provides a more useful analysis of numerical methods.