Analysis of the dipole simulation method for two-dimensional Dirichlet problems in Jordan regions with analytic boundaries
The main aim of the paper is to introduce ways in which to arrange the dipole points and collocation points as well as to define the dipole moments in order to guarantee the stability and exponential convergence of the dipole simulation method (DSM). In order to take into account more general domains than the disk the author introduces the notion of peripheral conformal mapping from an annulus to a neighborhood of the domain boundary. Two numerical experiments are carried out. In the first one the domain is a disk and in the second one the domain is the interior simply-connected region surrounded by the curve defined by a polynomial. In each numerical experiment, the author considers two types of boundary data: a harmonic polynomial and a logarithmic potential. The numerical outcomes confirm the convergence theorem.
scientific article; zbMATH DE number 6667568
scientific article