This paper presents a novel hybrid approach for the efficient solution of bounded acoustic problems with arbitrarily shaped inclusions. The hybrid method couples the Wave Based Method (WBM) and the Boundary Element Method (BEM) in order to benefit from the prominent advantages of both. The WBM is based on an indirect Trefftz approach; as such, it uses exact solutions of the governing equations to approximate the field variables. It has a high computational advantage as compared to conventional element based methods, when applied on moderately complex geometries. The BEM, on the other hand, can tackle complex geometries with ease. However, it can be computationally expensive. The hybrid Boundary Element-Wave Based Method (BE-WBM) combines the best properties of the two; it makes use of the efficient WBM for the moderately complex bounded domains and utilizes the flexibility of the BEM for the complex objects that reside in the bounded domains. The accuracy and the efficiency of the method is demonstrated with three numerical examples, where the hybrid BE-WBM is shown to be more efficient than a quadratic Finite Element Method (FEM). While the hybrid method provides efficient solution for the bounded problems with inclusions, it also brings certain conceptual advantages over the FEM. The fact that it is a boundary-type method with an easy refinement concept reduces the modeling effort on the preprocessing step. Moreover, for certain optimization scenarios such as optimization of the position of inclusions, the FEM becomes disadvantageous because of its domain discretization requirements for each iteration. On the other hand, the hybrid method allows reusing of the fixed geometries and only needs recalculation of the coupling matrices without a further need of preprocessing. As such, the hybrid method combines efficiency with versatility.
Atak, O., Jonckheere, S., Deckers, E., Huybrechs, D., Pluymers, B., & Desmet, W. (2015). A hybrid Boundary Element-Wave Based Method for an efficient solution of bounded acoustic problems with inclusions. Computer Methods in Applied Mechanics and Engineering, 283, 1260–1277. https://doi.org/10.1016/j.cma.2014.08.019