The domain superposition technique for solving three-dimensional piecewise homogeneous laplace problems. (15th August 2020) - Barbosa, J.P.; Lara, L.O.C.; Loeffler, C.F.
Abstract: Within the context of the Boundary Element Method, the Domain Superposition Technique is a novel alternative to the classical sub-regions approach for solving piecewise homogeneous problems. This new technique was successful in two-dimensional piecewise cases governed by the Laplace Equation and for this reason it is applied in this work to similar three-dimensional problems. Unlike the two-dimensional problems, the modus operandi of the coordinates transformation, the numerical integration procedures and the treatment of singular integrals are not simple and are described herein a proper way. Flat triangular isoparametric elements with linear variation are used for discretization. Considering the absence of analytical solutions, the Finite Element Method was used to generate the reference solutions for adequate performance comparison.