Spherical harmonic expansion of fundamental solutions and their derivatives for homogenous elliptic operators

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Abstract

In this work, a unified scheme for computing the fundamental solutions of a three-dimensionalhomogeneous elliptic partial differential operator is presented. The scheme is based on the Rayleighexpansion and on the Fourier representation of a homogeneous function. The scheme has the advantage ofexpressing the fundamental solutions and their derivatives up to the desired order without any term-by-termdifferentiation. Moreover, the coefficients of the series need to be computed only once, thus making thepresented scheme attractive for numerical implementation. The scheme is employed to compute thefundamental solution of isotropic elasticity showing that the spherical harmonics expansions provide theexact expressions. Then, the accuracy of the scheme is assessed by computing the fundamental solutions of agenerally anisotropic magneto-electro-elastic material.
Original languageEnglish
Pages33-38
Number of pages6
Publication statusPublished - 2017

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