An arbitrary-order Virtual Element Method for the Helmholtz equation applied to wave field calculation in port

The Virtual Element Method (VEM), as a high-order polytopal method, offers significant advantages over traditional Finite Element Methods (FEM). In particular, it allows the handling of polytopal or non-conforming meshes which greatly simplificates the mesh generation procedure. In this paper, the VEM is used for the discretization of the Helmholtz equations with a Robin-type absorbing boundary condition. This problem is crucial in various fields, including coastal engineering, oceanography and the design of offshore structures. Details of the VEM implementation with Robin boundary condition are given. Numerical results on test cases with analytical solutions show that the methods can provide optimal convergence rates for smooth solutions. Then, as a more realistic test case, the computation of the eigenmodes of the port of Cherbourg is carried out.