Langer S., Hampel S.

The coupling of boundary elements and a raytracing procedure using the method of fundamental solutions is presented here. As results the Boundary Element analysis gives the nodal values of the primary variable (e.g. sound pressure) and of the secondary variable (e.g. sound flux) on the boundary and on demand - using a postprocessing step - the sound pressure or sound flux in the domain. A raytracing procedure to be coupled on the Boundary Element Method expects intensities of sound sources as loading input data. The required transformation can be done by the Singular Indirect Boundary Element Method [1]. It couples both numerical procedures in an intermediate step between the Boundary Element Method and the raytracing algorithm. This method works well but suffers from the disadvantage needing a defined interface. Here, an alternative way to couple boundary elements and a raytracing procedure is presented. The method of fundamental solutions is used to find intensities of point sources which produce the previously determined sound pressure. The method of fundamental solutions is a meshfree method so it does neither demand the discretization of the domain nor of the boundary. A defined interface is not needed. In addition, an optimization algorithm is implemented to find optimal positions of the sources. The presented hybrid numerical method is applied on outdoor sound propagation problems. [1] S. Langer; S. Hampel: Coupling Boundary Elements to a Raytracing Procedure using the Singular Indirect Method. In: Proceedings in applied mathematics and mechanics (PAMM), Gesellschaft für Angewandte Mathematik und Mechanik, Vol. 5(1), 2005