A pseudospectral matrix method for time-dependent tensor fields on a spherical shell

JOURNAL OF COMPUTATIONAL PHYSICS

卷:235

Article

Bruegmann, Bernd

关键词: Pseudospectral;    Double Fourier;    Spin-weighted spherical harmonics;    GPU computing;    Numerical relativity;   

DOI  :  10.1016/j.jcp.2012.11.007

来源: Elsevier

【 摘 要 】

We construct a pseudospectral method for the solution of time-dependent, non-linear partial differential equations on a three-dimensional spherical shell. The problem we address is the treatment of tensor fields on the sphere. As a test case we consider the evolution of a single black hole in numerical general relativity. A natural strategy would be the expansion in tensor spherical harmonics in spherical coordinates. Instead, we consider the simpler and potentially more efficient possibility of a double Fourier expansion on the sphere for tensors in Cartesian coordinates. As usual for the double Fourier method, we employ a filter to address time-step limitations and certain stability issues. We find that a tensor filter based on spin-weighted spherical harmonics is successful, while two simplified, non-spin-weighted filters do not lead to stable evolutions. The derivatives and the filter are implemented by matrix multiplication for efficiency. A key technical point is the construction of a matrix multiplication method for the spin-weighted spherical harmonic filter. As example for the efficient parallelization of the double Fourier, spin-weighted filter method we discuss an implementation on a GPU, which achieves a speed-up of up to a factor of 20 compared to a single core CPU implementation. (c) 2012 Elsevier Inc. All rights reserved.

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