Efficient field point evaluation by combined direct and hybrid boundary element methods

Abstract

A new procedure for calculating field points with the boundary element method (BEM) is outlined. In the conventional BEM (CBEM) field points are computed as post-processing by recurrently solving the boundary integral equation with known boundary data for every field point of interest. This procedure is very time-consuming. On the other hand, newly developed hybrid boundary element formulations (HBEMs) based on variational principles compute field points from the known boundary solution by simply transforming it to the domain using fundamental solutions as field approximation. The advantage of the HBEM is that the related system matrices are symmetric by construction but the computational effort to obtain the boundary solution is higher than in CBEMs. Thus, if symmetry of the system matrices has no priority, it is advantageous to compute the boundary solution with the CBEM and the field point solution with the HBEM. The additional implementation effort is relatively low, since only one extra matrix has to be computed, which is sparse and has analytical entries.