An explicit Wave based model as alternative to the DtN map for solving unbounded Helmholtz problems with the finite element method

摘要

When using a domain-based method for solving problems in unbounded domains, the computational domain has to be truncated to a bounded region. On the truncation, suitable conditions must be imposed to ensure the solution of the truncated problem is equivalent to the solution of the unbounded problem. This paper proposes to derive these conditions based on an explicit model of the unbounded domain exterior to the truncation. The Wave Based Method (WBM), a Trefftz-based prediction technique for solving Helmholtz problems, is used to construct this unbounded model. The WBM has proven to be an efficient alternative for element based techniques and therefore can be applied towards mid-frequency problems. The obtained method is compared to the DtN FE method, where it is shown that the obtained accuracy is equivalent, but the proposed hybrid FE-WB framework allows for a more efficient construction and solution of the model.