Spline-based boundaries: A first step towards generic geometric domain descriptions for efficient mid-frequency acoustic analysis using the Wave Based Method

Abstract

The application of numerical simulation techniques for the analysis and optimization of the acoustic behavior of all kinds of products has become very important in almost every phase of a design process. The large computational burden associated with the Finite Element Method (FEM) limits its applicability to low-frequency problems. Recently, the Wave Based Method (WBM) was proposed as an efficient alternative to the element based methods. This method is based on an indirect Trefftz approach, using an expansion of exact solutions of the governing differential equation to describe the dynamic field variables. An important disadvantage of the WBM is the limited geometrical flexibility as compared to the element based techniques. This paper aims to alleviate the geometrical restrictions by using B-splines for the efficient description of curved edges. The introduction of B-splines within the WBM requires an adaptation of the numerical integration procedure used to evaluate the weighted residual formulation. To this end, different types of numerical integration techniques are studied: the Gauss–Legendre and the Romberg integration procedure. A comparative study with the finite element method and the original WBM indicates that the application of B-splines and the adapted numerical integration procedure leads to accurate and computationally affordable WB models.