Boundary element method for efficient acoustic simulation

Discretization methods such as the finite element method (FEM) or the boundary element method (BEM) are usually used for the numerical simulation of acoustic problems. The BEM offers the advantage that no unwanted reflections of the sound waves occur at the edges of the model during a simulation in infinite areas, as the formulation automatically fulfills Sommerfeld's radiation condition. In addition, only the boundary of the area under investigation needs to be discretized.

Typically, a numerical simulation begins with the creation of a discretization using elements of different orders based on Lagrange polynomials. This step leads to an approximation of the geometry and the resulting errors. In addition, this procedure is very time-consuming and takes up a large part of the processing time in practical applications. The direct use of so-called "Non Uniformal Rational B-Splines" (NURBS) within the BEM formulation (IGABEM) offers a new possibility. The accuracy of the method depends on the description of the geometry, with the typical procedure being the generation of an acoustic surface mesh from existing CAD data. Such geometries are described by the NURBS, which enable the exact recording of a geometry, especially in the area of round components.

In addition to accuracy, computing time plays an important role in numerical simulation. In particular, the investigation of three-dimensional systems with large dimensions, as is often the case with external space problems, as well as questions in the high-frequency range, also lead to systems of equations that have to be processed with iterative solvers when using the BEM. However, these require frequent matrix-vector multiplications, resulting in a quadratic complexity O(N²). To reduce this complexity, fast BEM methods such as the Fast Multipole Method (FMM) or H-matrices can be used.

Since 2010, the Institute for Modeling and Computation at TUHH has been developing BEM software for calculating acoustic problems in cooperation with Novicos GmbH. The research focus is on the aforementioned IGABEM and the fast BEM methods. In this context, various topics for Bachelor's, Master's or project work are possible.