A meshfree method with fundamental solutions for inhomogeneous elastic wave problems

We consider the numerical solution of the inhomogeneous Cauchy-Navier equations of elastodynamics for an isotropic material. The corresponding elliptic PDE, posed in a bounded simply connected domain, is coupled with boundary conditions and solved trough a meshfree method, based on the Method of Fundamental Solutions. In partic- ular, the displacement field is approximated in terms of a linear combination of fundamental solutions of the underlying differential operator with different source points and test frequencies. The applicability of the numerical method is justified in terms of density results and its accuracy is illustrated through 2D numerical simulations. Interior elastic wave scattering problems are also addressed.