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

摘要

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.