A multi-level wave based numerical modelling framework for the steady-state dynamic analysis of bounded Helmholtz problems with multiple inclusions

The Wave Based Method (WBM) is an alternative numerical prediction method for both interior and exterior steady-state dynamic problems, which is based on an indirect Trefftz approach. It applies wave functions, which are exact solutions of the governing differential equation, to describe the dynamic field variables. The smaller system of equations and the absence of pollution errors make the WBM very suitable for the treatment of Helmholtz problems in the mid-frequency range, where element-based methods are no longer feasible due to the associated computational costs. A sufficient condition for convergence of the method is the convexity of the considered problem domain. As a result, only problems of moderate geometrical complexity can be considered and some geometrical features cannot be handled at all. In this paper, these limitations are alleviated through the development of a general modelling framework based on existing WBM methodologies which allows for the efficient introduction of inclusion configurations in bounded WBM models for problems governed by one or more Helmholtz equations. The feasibility and efficiency of the method is illustrated by means of numerical verification studies in which the methodology is applied to two types of dynamic problems. On the one hand, a single Helmholtz equation associated with the steady-state dynamic behaviour of acoustic cavities is studied. On the other hand, the framework is applied to the solution of the Navier system of partial differential equations that describe the elastodynamic response of two-dimensional perforated solids.