Onur Atak

Coupling of Boundary Element and Wave Based Methods for the efficient solution of complex multiple scattering problems

A novel hybrid method for the efficient solution of complex acoustic multiple scattering problems is proposed in this paper. The Wave Based Method and the Boundary Element Method are coupled to benefit from the strengths of both. The former is an indirect Trefftz approach, which has a faster convergence rate and lower computational load compared to element based methods when applied on geometries of moderate complexity. The latter is the state-of-the-art technique for unbounded acoustic problems and can handle very complex geometries. The idea behind the hybrid method is to take advantage of the fast WBM solution for scatterers of moderate complexity and take advantage of the BEM@?s capability for handling scatterers of high complexity. For the BEM part, the indirect variational formulation is used which allows modeling of open boundary problems (zero thickness walls). In addition, the WBM makes it possible to easily add heterogeneities (domain inclusions) to the problem. Therefore, the hybrid method does not only aim for better efficiency but also for extending the variety of configurations that can be tackled by both methods with ease. The accuracy and the performance of the method are demonstrated with three examples, both in 2D and 3D. It is shown that when complex and simple scatterers coexist, the hybrid method is more efficient than the WBM, the BEM and the Fast-Multipole BEM while it is able to provide accuracy of similar level.

A wave based method to predict the absorption, reflection and transmission coefficient of two-dimensional rigid frame porous structures with periodic inclusions

This paper presents an extension to the Wave Based Method to predict the absorption, reflection and transmission coefficients of a porous material with an embedded periodic set of inclusions. The porous unit cell is described using the Multi-Level methodology and by embedding Bloch-Floquet periodicity conditions in the weighted residual scheme. The dynamic pressure field in the semi-infinite acoustic domains is approximated using a novel wave function set that fulfils the Helmholtz equation, the Bloch-Floquet periodicity conditions and the Sommerfeld radiation condition. The method is meshless and computationally efficient, which makes it well suited for optimisation studies.

High-order 2D mesh curving methods with a piecewise linear target and application to Helmholtz problems

Abstract High-order simulation techniques typically require high-quality curvilinear meshes. In most cases, mesh curving methods assume that the exact geometry is known. However, in some situations only a fine linear FEM mesh is available and the connection to the CAD geometry is lost. In other applications, the geometry may be represented as a set of scanned points. In this paper, two curving methods are described that take a piecewise fine linear mesh as input: a least squares approach and a continuous optimization in the H 1 -seminorm. Hierarchic, modal shape functions are used as basis for the geometric approximation. This approach allows to create very high-order curvilinear meshes efficiently ( q > 4 ) without having to optimize the location of non-vertex nodes. The methods are compared on two test geometries and then used to solve a Helmholtz problem at various input frequencies. Finally, the main steps for the extension to 3D are outlined.