Solving the 3D Laplace equation by meshless collocation via harmonic kernels

This paper solves the Laplace equation ∆u = 0 on domains Ω ⊂ R by meshless collocation on scattered points of the boundary ∂Ω. In contrast to the Method of Fundamental Solutions, there are no singularities and no artificial boundaries, since we use new singularity–free positive definite kernels which are harmonic in both arguments. In contrast to many other… (More)