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Numerical evolutions of fields on the 2-sphere using a spectral method based on spin-weighted spherical harmonics

机译:用光谱法研究2球面上场的数值演化   基于自旋加权球谐函数

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摘要

Many applications in science call for the numerical simulation of systems onmanifolds with spherical topology. Through use of integer spin weightedspherical harmonics we present a method which allows for the implementation ofarbitrary tensorial evolution equations. Our method combines two numericaltechniques that were originally developed with different applications in mind.The first is Huffenberger and Wandelt's spectral decomposition algorithm toperform the mapping from physical to spectral space. The second is theapplication of Luscombe and Luban's method, to convert numerically divergentlinear recursions into stable nonlinear recursions, to the calculation ofreduced Wigner d-functions. We give a detailed discussion of the theory andnumerical implementation of our algorithm. The properties of our method areinvestigated by solving the scalar and vectorial advection equation on thesphere, as well as the 2+1 Maxwell equations on a deformed sphere.
机译:科学中的许多应用都要求对具有球形拓扑的流形系统进行数值模拟。通过使用整数自旋加权球谐函数,我们提出了一种方法,该方法可以实现任意张量演化方程。我们的方法结合了两种数值技术,这些数值技术最初是针对不同的应用而开发的。第一种是Huffenberger和Wandelt的光谱分解算法,以执行从物理空间到光谱空间的映射。第二是应用Luscombe和Luban方法,将数值发散线性递归转换为稳定的非线性递归,以计算简化的Wigner d函数。我们将详细讨论算法的理论和数值实现。通过求解球面上的标量和矢量对流方程以及变形球面上的2 + 1麦克斯韦方程,研究了我们方法的性质。

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