A regularized boundary element method for anisotropic potential problems

The presentation is mainly devoted to the research on theregularized BEM formulations for homogeneous anisotropic potential problems.Based on a limit theorem for the transformation from domain integralequations into boundary integral equations (BIEs) and a novel decompositiontechnique to the fundamental solutions, the regularized BIEs with indirectunknowns, which don't involve singular integrals, are established. Comparedwith the existing methods, the presented method can solve theconsidered problems directly instead of transforming them into isotropicones, and for this reason, no inverse transform is required. In addition,this method doesn't require to calculate multiple integral as the Galerkinmethod, but rather evaluate CPV integrals indirectly, and so it is simpleand easy to program. Furthermore, the proposed gradient BIEs are suited forthe computation of \partial u/\partial x_i (i =1,2) on the boundary, not only limited to normal flux \partial u/\partial n. Especially, for the boundary valueproblems with elliptic boundary, an exact element is developed to model itsboundary with almost no error. The convergence and accuracy of the proposedalgorithm are investigated and compared for several numerical examples,demonstrating that a better precision and high computational efficiency canbe achieved.