Testing the accomplishment of the radial integration method with the direct interpolation boundary element technique for solving Helmholtz problems

Abstract

This paper presents the combination of two boundary element techniques whose principal aim is the transformation of domain integrals into boundary integrals: the radial integration method (RIM) and the direct integration boundary element method (DIBEM). RIM performs this transformation using a suitable change of variables. When used in problems with unknown variables, the RIM employs radial basis functions, following a similar procedure to the Dual Reciprocity Method, in which the primal variable is interpolated. DIBEM differentiates itself from other methods by interpolating the whole kernel of the domain integral, including not only the primal variable but also the fundamental solution. Here, the RIM is used to substitute the primitive auxiliary interpolation function employed exclusively to transform the domain integral into boundary integral in the DIBEM approach. Evaluation of the efficacy of the proposed composition is done solving the Helmholtz equation, including the direct frequency response and the eigenvalue problem. The expected advantages are confirmed by numerical tests performed: the computational cost is strongly reduced and an increase in accuracy is observed, particularly if coarser meshes are used.