Evaluation of Non-Singular BEM Algorithms for Potential Problems

Two non-singular boundary element method (BEM) algorithms for two-dimensional potential problems have been implemented using isoparametric quadratic, cubic and quartic elements. The first one is based on the self-regular potential boundary integral equation (BIE) and the second on the self-regular flux-BIE. The flux-BIE requires the C-1,C-alpha continuity of the density functions, which is not satisfied by the standard isoparametric elements. This requirement is remedied by adopting the relaxed continuity strategy. The self-regular flux-BIE has presented some poor and oscillatory results, mainly with continuous quadratic elements. This odd behavior has completely disappeared when discontinuous elements, which satisfy the continuity requirement, were applied, and this suggests that the 'relaxed continuity hypothesis' seems to be the main cause of numerical errors in the implementation of the self-regular flux-BIE. On the other side, the potential algorithm has shown very reliable solutions.