The direct interpolation boundary element method applied to smoothly inhomogeneous Laplace's problems

This paper presents the recent Direct Interpolation Boundary Element Method (DIBEM) addressing problems governed by the inhomogeneous Laplace's Equation, that is, cases in which the constitutive medium property varies smoothly according to a known function. These problems are usually solved by domain numerical techniques. Here, using the DIBEM formulation, one can accurately transform the domain integral generated by the non-homogeneity of the medium into a boundary integral and thus taking advantage of the operational facilities generated by simplification of the discrete model. Four test problems are presented showing the efficacy of the proposed model. In two first the complete domain is inhomogeneous and the rest, the heterogeneity occurs in a restricted sector. Simulations using the Finite Element Method obtained the reference results.