Eecient Field Point Evaluation by Combined Direct and Hybrid Boundary Element Methods

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