An explicit Wave Based - Finite element model as alterna- tive to the DtN finite element method

The solution of unbounded Helmholtz problems is the subject of substantial research. If these problems are to be solved using a domain-based discretisation technique like the finite element method (FEM), the computational domain has to be truncated to a bounded region. The unbounded nature of the problem exterior to this truncation is simulated by an appropriate condition on the truncation. A common method to derive this condition is the Dirichlet-to-Neumann (DtN) map. In this paper, a alternative is presented where an explicit model of the unbounded domain exterior to the truncation is constructed. The Wave Based Method (WBM), a novel technique for solving Helmholtz problems, is used for the unbounded part, yielding a hybrid FE-WB model. This new approach is compared to the DtN FE method, considering both accuracy and computational efficiency. A numerical example illustrate the advantageous properties of the hybrid method.