The method of fundamental solutions (MFS) is a meshfree numerical method for the approximate solution of homogeneous boundary value problems, where the unknown solution is approximated in terms of a linear combination of fundamental solutions of  the underlying differential operator, with singularities located in the exterior of the domain.

In this work we extend the range of applicability of the MFS to non-homogeneous elastic wave propagation problems in isotropic media. In particular, basis functions with different test frequencies are included in the linear combination. A theoretical justification for the method is provided in terms of density results and an error bound is also formulated. The accuracy of the proposed method is illustrated for 2D interior elastic wave scattering problems.

Authors: Alves CJS, Martins NFM, Valtchev SS

Journal: Applied Numerical Mathematics