An adaptive finite element PML method for the acoustic-elastic interaction in three dimensions
For researchers in computational wave scattering, this provides a rigorous and efficient numerical method for a challenging 3D interaction problem.
The paper develops an adaptive finite element PML method for 3D acoustic-elastic scattering, proving well-posedness and exponential convergence, with numerical experiments showing competitive performance.
Consider the scattering of a time-harmonic acoustic incident wave by a bounded, penetrable, and isotropic elastic solid, which is immersed in a homogeneous compressible air or fluid. The paper concerns the numerical solution for such an acoustic-elastic interaction problem in three dimensions. An exact transparent boundary condition (TBC) is developed to reduce the problem equivalently into a boundary value problem in a bounded domain. The perfectly matched layer (PML) technique is adopted to truncate the unbounded physical domain into a bounded computational domain. The well-posedness and exponential convergence of the solution are established for the truncated PML problem by using a PML equivalent TBC. An a posteriori error estimate based adaptive finite element method is developed to solve the scattering problem. Numerical experiments are included to demonstrate the competitive behavior of the proposed method.