The wave based method: An overview of 15 years of research

• Published in: Wave motion Vol. 51; no. 4; pp. 550 - 565
• Main Authors: Deckers, Elke, Atak, Onur, Coox, Laurens, D’Amico, Roberto, Devriendt, Hendrik, Jonckheere, Stijn, Koo, Kunmo, Pluymers, Bert, Vandepitte, Dirk, Desmet, Wim
• Format: Journal Article
• Language: English
• Published: Elsevier B.V 01.06.2014
• Subjects: Acoustics; Approximation; Biot theory; Boundaries; Convergence; Dynamical systems; Dynamics; Exact solutions; Mathematical analysis; Mathematical models; Structural dynamics; Trefftz approach; Wave based method; Wave functions; Wave based method; Trefftz approach; Structural dynamics; Acoustics; Biot theory
• ISSN: 0165-2125; 1878-433X
• DOI: 10.1016/j.wavemoti.2013.12.003

The Wave Based Method is a deterministic prediction technique to solve steady-state dynamic problems and is developed to overcome some of the frequency limitations imposed by element-based prediction techniques. 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. 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 rather moderately complex geometries. As a result, various enhancements have been made to the method through the years, in order to extend the applicability of the Wave Based Method. This paper gives an overview of the current state of the art of the Wave Based Method, elaborating on the modelling procedure, a comparison of the properties of the Wave Based Method and element-based prediction techniques, application areas, extensions to the method such as hybrid and multi-level approaches and the most recent developments. •The state of the art for the Wave Based Method is reviewed.•The procedure of the WBM is shown for a generalised Helmholtz problem.•The method is compared to the Finite Element and Boundary Element Method.•Current applications, along with hybrid and multi-level extensions are listed.•In view of the recent advancements, future research topics are given.