The Wave Based Method: current state of the art

Most commonly, element based prediction techniques, such as the Finite Element Method and the Boundary Element Method are used to solve steady state dynamic problems. These procedures divide the problem domain or its boundary into a large number of small elements in which the dynamic fields are described using simple, most often polynomial, shape functions. When frequency increases and the wavelengths shorten, the mesh needs to be refined to obtain accurate solutions, due to interpolation and pollution errors. The sizes of the system matrices, and consequently the computational load, increase accordingly. From a certain frequency on, the models become computationally too demanding, such that the element based techniques are limited for solution at lower frequencies. The Wave Based Method is also a deterministic numerical prediction technique to solve steady-state dynamic problems, developed to overcome some of these frequency limitations imposed by the use of small elements and simple interpolation functions. The method belongs to the family of indirect Trefftz approaches and uses a weighted sum of so-called wave functions, which are exact solutions of the governing partial differential equations, to approximate the dynamic field variables. Contrarily to element based techniques, the problem domain is subdivided into a small number of large, convex subdomains. By minimising the errors on boundary and interface conditions, a system of equations is obtained which can be solved for the unknown contribution factors of each wave function. As a result, the system of equations is smaller and a higher convergence rate and lower computational loads are obtained as compared to conventional prediction techniques. On the other hand, the method shows its full efficiency for moderately complex geometries. Various enhancements have been made to the method through the years, in order to extend the applicability of the Wave Based Method. This paper aims to give an overview of the current state of the art of the Wave Based Method, its modelling procedure, application areas and extensions to the method such as hybrid and multi-level approaches.status: publishe