In this work, a unified scheme for computing the fundamental solutions of a three-dimensional homogeneous elliptic partial differential operator is presented. The scheme is based on the Rayleigh expansion and on the Fourier representation of a homogeneous function. The scheme has the advantage of expressing the fundamental solutions and their derivatives up to the desired order without any term-by-term differentiation. Moreover, the coefficients of the series need to be computed only once, thus making the presented scheme attractive for numerical implementation. The scheme is employed to compute the fundamental solution of isotropic elasticity showing that the spherical harmonics expansions provide the exact expressions. Then, the accuracy of the scheme is assessed by computing the fundamental solutions of a generally anisotropic magneto-electro-elastic material.

Gulizzi, V., Milazzo, A., Benedetti, I. (2017). Spherical harmonic expansion of fundamental solutions and their derivatives for homogenous elliptic operators. In Advances In Boundary Element and Meshless Techniques XVIII (pp.33-38). Eastleigh, SO53 4HJ : EC, Ltd, UK.

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

Gulizzi, Vincenzo;MILAZZO, Alberto;BENEDETTI, Ivano
2017-01-01

Abstract

In this work, a unified scheme for computing the fundamental solutions of a three-dimensional homogeneous elliptic partial differential operator is presented. The scheme is based on the Rayleigh expansion and on the Fourier representation of a homogeneous function. The scheme has the advantage of expressing the fundamental solutions and their derivatives up to the desired order without any term-by-term differentiation. Moreover, the coefficients of the series need to be computed only once, thus making the presented scheme attractive for numerical implementation. The scheme is employed to compute the fundamental solution of isotropic elasticity showing that the spherical harmonics expansions provide the exact expressions. Then, the accuracy of the scheme is assessed by computing the fundamental solutions of a generally anisotropic magneto-electro-elastic material.
International Conference on Boundary Element and Meshless Techniques XVIII
Bucarest (Romania)
11-13 luglio 2017
XVIII
2017
6
Gulizzi, V., Milazzo, A., Benedetti, I. (2017). Spherical harmonic expansion of fundamental solutions and their derivatives for homogenous elliptic operators. In Advances In Boundary Element and Meshless Techniques XVIII (pp.33-38). Eastleigh, SO53 4HJ : EC, Ltd, UK.
Proceedings (atti dei congressi)
Gulizzi, V.; Milazzo, A.; Benedetti, I.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10447/240528
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