A finite element contour integral method for computing the scattering resonances of fluid-solid interaction problem

The paper considers the computation of scattering resonances of the fluid-solid interaction problem. Scattering resonances are the replacement of discrete spectral data for problems on non-compact domains which are very important in many areas of science and engineering. For the special disk case, we get the analytical solution which can be used as reference solutions. For the general case, we truncate the unbounded domain using the Dirichlet-to-Neumann (DtN) mapping. Standard linear Lagrange element is used to do the discretization which leads to nonlinear algebraic eigenvalue problems. We then solve the nonlinear algebraic eigenvalue problems by the parallel spectral indicator methods. Finally, numerical examples are presented.