Boundary cloud method: A combined scattered point/boundary integral approach for boundary-only analysis

A boundary cloud method (BCM), for boundary-only analysis of partial differential equations, is presented in this paper for solving potential equations in two dimensions (2-D). The BCM combines a weighted least-squares approach for construction of interpolation functions with a boundary integral formulation for the governing equations. Given a set of scattered points on the surface of an arbitrary object, Hermite-type interpolation functions are constructed by developing a weighted least-squares approach. We also introduce truncated Hermite-type interpolation functions. The boundary integrals are evaluated by using a cell structure. We propose various schemes for evaluating the singular, nearly singular and nonsingular integrals. We also propose a true meshless approach for boundary-only analysis of potential equations. Numerical results, comparing the classical boundary element method and the BCM, are presented for several 2-D potential problems.