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.
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