In the numerical simulation of acoustic problems, discretization methods such as the Finite Element Method (FEM) or the Boundary Element Method (BEM) are mostly used. The BEM offers the advantage that no unwanted reflections of the sound waves at the model boundaries occur during a simulation in infinite domains, since the formulation automatically satisfies Sommerfeld's radiation condition. Furthermore, only the boundary of the area under investigation needs to be discretized.
Typically, a numerical simulation starts with the creation of a discretization by elements of different order based on Lagrange polynomials. This step leads to an approximation of the geometry and to resulting errors. In addition, this procedure is very time-consuming and takes up a large part of the processing time in practical applications. A new possibility offers the direct use of so-called "Non Uniform Rational B-Splines" (NURBS) within the BEM formulation (IGABEM). The accuracy of the method depends on the description of the geometry, the typical procedure being the generation of an acoustic surface mesh from existing CAD data. Such geometries are described by the NURBS, which allow the exact registration of a geometry, especially in the area of round components.
In addition to accuracy, computation time plays an important role in numerical simulation. In particular, the investigation of three-dimensional systems with large dimensions, as they often occur in outdoor space problems, as well as problems in the high-frequency range also lead to systems of equations when using BEM, which have to be processed with iterative solvers. However, these require frequent performance of 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 the H-matrices, can be used.
Since 2010, the Institute for Modeling and Computation at TUHH, in cooperation with Novicos GmbH, has been developing BEM software for the computation of acoustic problems. The research focus is on the previously mentioned IGABEM and fast BEM methods. In this context, different topics for bachelor, master or project theses are possible.
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