A time-domain fourth-order-convergent numerical algorithm to integrate black hole perturbations in the extreme-mass-ratio limit

Lousto, Carlos O.

doi:10.1088/0264-9381/22/15/001

Cited by 38 publications

(59 citation statements)

References 39 publications

(96 reference statements)

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“…2. Briefly, for second order global accuracy I use a standard diamond-cell integration scheme [16,33,34,37,55,56,84], while for fourth order global accuracy I use a modified version of the scheme described by Lousto [55] and Haas [38]. I describe the finite differencing schemes in detail in Appendix A.…”

Section: Unigrid Finite Differencingmentioning

confidence: 99%

“…To discretize the wave equation (3) to fourth order global accuracy in the grid spacing , I use a scheme based on that of Haas [38] (see also [55]), but modified in its treatment of cells near the particle. The modification makes the scheme fully explicit, removing the need for an iterative computation at each cell intersecting the particle.…”

Section: A2 Fourth Order Global Accuracymentioning

confidence: 99%

“…That is (following [55] and [38]) I first define the new grid function G ≡ V φ. I then interpolate G hh via Haas's equation (2.7), which in my notation reads…”

Section: A21 |I − I P | ≥ 3 (Cell Far From the Particle)mentioning

confidence: 99%

“…To discretize the wave equation (3) to second order global accuracy in the grid spacing , I use a standard diamond-cell integration scheme [16,33,34,37,55,56,84]:…”

Section: Appendix A: Details Of the Unigrid Finite Differencing Schemementioning

confidence: 99%

“…For the more generic case where r p is time-dependent, then in general the particle worldline would pass obliquely through the cell. As discussed by, for example, Martel and Poisson[58], Lousto[55] and Haas[38], this would considerably complicate the finite differencing of cells intersecting the particle worldline. However, it would not alter the overall character of the AMR algorithm.…”

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confidence: 99%

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Adaptive mesh refinement for characteristic grids

Thornburg

2010

Gen Relativ Gravit

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I consider techniques for Berger-Oliger adaptive mesh refinement (AMR) when numerically solving partial differential equations with wave-like solutions, using characteristic (double-null) grids. Such AMR algorithms are naturally recursive, and the best-known past Berger-Oliger characteristic AMR algorithm, that of Pretorius and Lehner (J Comp Phys 198:10, 2004), recurses on individual "diamond" characteristic grid cells. This leads to the use of fine-grained memory management, with individual grid cells kept in two-dimensional linked lists at each refinement level. This complicates the implementation and adds overhead in both space and time. Here I describe a Berger-Oliger characteristic AMR algorithm which instead recurses on null slices. This algorithm is very similar to the usual Cauchy Berger-Oliger algorithm, and uses relatively coarse-grained memory management, allowing entire null slices to be stored in contiguous arrays in memory. The algorithm is very efficient in both space and time. I describe discretizations yielding both second and fourth order global accuracy. My code implementing the algorithm described here is included in the electronic supplementary materials accompanying this paper, and is freely available to other researchers under the terms of the GNU general public license. This paper is dedicated to the memory of Thomas Radke, my late friend and colleague in many computational adventures. Electronic supplementary materialThe online version of this article (

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Section: Unigrid Finite Differencingmentioning

confidence: 99%

Section: A2 Fourth Order Global Accuracymentioning

confidence: 99%

“…That is (following [55] and [38]) I first define the new grid function G ≡ V φ. I then interpolate G hh via Haas's equation (2.7), which in my notation reads…”

Section: A21 |I − I P | ≥ 3 (Cell Far From the Particle)mentioning

confidence: 99%

“…To discretize the wave equation (3) to second order global accuracy in the grid spacing , I use a standard diamond-cell integration scheme [16,33,34,37,55,56,84]:…”

Section: Appendix A: Details Of the Unigrid Finite Differencing Schemementioning

confidence: 99%

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confidence: 99%

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