Density results using the method of fundamental solutions for a fluid-structure interaction problem

We propose two numerical methods i.e., the method of fundamental solutions (MFS) and the coupling of the MFS and the plane waves method, for solving a fluid-structure interaction scattering problem numerically in two and three dimensions, which are both free of irregular frequencies. It is shown that the acoustic fields can be approximated in the $H^1$-norm by the fundamental solutions of the Helmholtz equation placed at distinct source points, whereas elastic fields are approximated in the same norm either by the fundamental solutions of the Navier equations at different locations or by the plane waves of the Navier equations with distinct directions. Some numerical examples are performed to show the behaviors of our methods for the two-dimensional case.