Trefftz-Based Methods for Time-Harmonic Acoustics

Abstract

Over the last decade, Computer Aided Engineering (CAE) tools have become essential in the assessment and optimization of the acoustic characteristics of products and processes. The possibility of evaluating these characteristics on virtual prototypes at almost any stage of the design process reduces the need for very expensive and time consuming physical prototype testing. However, despite their steady improvements and extensions, CAE techniques are still primarily used by analysis specialists. In order to turn them into easy-to-use, versatile tools that are also easily accessible for designers, several bottlenecks have to be resolved. The latter include, amongst others, the lack of efficient numerical techniques for solving system-level functional performance models in a wide frequency range. This paper reviews the CAE modelling techniques which can be used for the analysis of time-harmonic acoustic problems and focusses on techniques which have the Trefftz approach as baseline methodology. The basic properties of the different methods are highlighted and their strengths and limitations are discussed. Furthermore, an overview is given of the state-of-the-art of the extensions and the enhancements which have been recently investigated to enlarge the application range of the different techniques. Specific attention is paid to one very promising Trefftz-based technique, which is the so-called wave based method. This method has all the necessary attributes for putting a next step in the evolution towards truly virtual product design.

Hybrid-Trefftz six-node triangular finite element models for Helmholtz problem

“…To better tackle the issue, a number of wave-based approaches that make use of the solution sets for the wave or Helmholtz equations have been proposed. While a brief survey will be presented in the subsequent paragraphs, the readers may like to consult reference [16] for a more comprehensive review.…”

“…Following the success of the Trefftz boundary element methods for Helmholtz problems [11][12][13][14][15][16], a number of Trefftz finite element methods can be noted in literature. A core issue of the Trefftz finite element methods is the enforcement of inter-element continuity of the domain or intra-element variable.…”

“…The term "tractionframe" inherits the fact that the boundary variable for elasticity problems is the boundary traction [13,14,16,24]. It is also possible to use the displacement-frame in which the boundary and domain variables are both Helmholtz variables in a way analogous to the hybrid-displacement finite element models commonly used to deal with stress singularity problems, see (1), (2) and references [2][3][4].…”

Sound pressure attenuation provided by a 3D rigid acoustic barrier on a building façade: the influence of its longitudinal shape

“…The works by Marburg and Nolte [1], Cheng and Cheng [2] and Pluymers et al [3] and the reference book by Jensen et al [4] give a good general overview of the developments in this field.…”

Trefftz collocation for frequency domain elastodynamic problems

“…Trefftz collocation methods have essentially been applied to the case of acoustics, that is, the scalar Helmholtz case (see Li [11]). Galerkin type Trefftz methods have been applied to the acoustic case (see Pluymers et al [12], Cheung et al [13]) but also to the elastodynamic case (Freitas and Cismasiu [14]) amongst others.…”