Author:

Keywords:

Science & Technology, Technology, Physical Sciences, Engineering, Multidisciplinary, Mathematics, Interdisciplinary Applications, Engineering, Mathematics, Trefftz method, Wave based method, Helmholtz problems, Semi-unbounded problems, FINITE-ELEMENT METHODS, PREDICTION TECHNIQUE, COLLOCATION, 2D, 0102 Applied Mathematics, 0905 Civil Engineering, 0913 Mechanical Engineering, Applied Mathematics, 4005 Civil engineering, 4017 Mechanical engineering, 4901 Applied mathematics

Abstract:

The wave based method (WBM), which is based on an indirect Trefftz approach, is a deterministic prediction method posed as an alternative to the element-based methods. It uses wave functions, which are exact solutions of the underlying differential equation, to describe the dynamic field variables. This way, it can avoid the pollution errors associated with the polynomial element-based approximations. As a consequence, a dense element discretization is no longer required, yielding a smaller numerical system. The resulting enhanced computational efficiency of the WBM as compared to the element based methods has been proven for the analysis of both bounded and unbounded acoustic problems. This paper extends the applicability of the WBM to semi-infinite domains. An appropriate function set is proposed, together with a calculation procedure for both semi-infinite radiation and scattering problems, and transmission or diffraction problems containing a rigid baffle. The resulting technique is validated on two numerical examples.