Extending the method of fundamental solutions to non-homogeneous elastic wave problems

Alves, Carlos J. S.; Martins, Nuno F. M.; Valtchev, Svilen

http://hdl.handle.net/10400.8/13682

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Authors

Alves, Carlos J. S.

Martins, Nuno F. M.

Valtchev, Svilen

Abstract(s)

Two meshfree methods are developed for the numerical solution of the non-homogeneous Cauchy–Navier equations of elastodynamics in an isotropic material. The two approaches differ upon the choice of the basis functions used for the approximation of the unknown wave amplitude. In the first case, the solution is approximated in terms of a linear combination of fundamental solutions of the Navier differential operator with different source points and test frequencies. In the second method the solution is approximated by superposition of acoustic waves, i.e. fundamental solutions of the Helmholtz operator, with different source points and test frequencies. The applicability of the two methods is justified in terms of density results and a convergence result is proven. The accuracy of the methods is illustrated through 2D numerical examples. Applications to interior elastic wave scattering problems are also presented.

Keywords

Elastic wave scattering Meshfree method Method of fundamental solutions Non-homogeneous problems

URI

http://hdl.handle.net/10400.8/13682

Citation

Carlos J.S. Alves, Nuno F.M. Martins, Svilen S. Valtchev, Extending the method of fundamental solutions to non-homogeneous elastic wave problems, Applied Numerical Mathematics, Volume 115, 2017, Pages 299-313, ISSN 0168-9274, https://doi.org/10.1016/j.apnum.2016.06.002.