Numerical treatment of a skew-derivative problem for the Laplace equation in the exterior of an open arc

Abstract

The skew-derivative problem for harmonic functions in the exterior of an open arc in a plane is considered. This problem models the electric current in a semiconductor film from an electrode of arbitrary shape in the presence of a magnetic field. A numerical method for solving the problem is proposed. The method is based on a boundary-integral-equation approach. The proposed numerical method is tested. The numerical simulation is presented for different values of the parameters and different shapes of the electrode. Physical effects found in numerical experiments are discussed.