A Fictitious Domain Method with Operator Splitting for Wave Problems in Mixed Form

We propose a novel operator splitting scheme for time discretization, combined with a new fictitious domain method involving a distributed Lagrange multiplier for the solution of a wave scattering problem. The symmetrized operator splitting scheme decouples the propagation of the wave, and the enforcement of the Dirichlet boundary condition on the obstacle. We employ mixed finite elements for the substeps which propagate the wave. The accuracy of the method is demonstrated via a numerical example.