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This paper concerns a numerical solution for the diffusion equation on the unit sphere. The given method is
based on the spherical basis function approximation and the
Petrov-Galerkin test discretization. The method is meshless
because spherical triangulation is not required neither for
approximation nor for numerical integration. This feature is
achieved through the spherical basis function approximation
and the use of local weak forms instead of a global variational
formulation. The local Petrov-Galerkin formulation allows to
compute the integrals on small independent spherical caps
without any dependence on a connected background mesh.
Experimental results show the accuracy and the efficiency of
the new method.
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