Comparison of several discretization methods of the Steklov–Poincaré operator

Abstract

SUMMARYIn this paper, we present three methods to discretize the Steklov-Poincare´operator. Two of these methods are already well known and commonly used and the third one is new. These methods are based either on the ballooning technique or on the integral theory or on the Calderon equations and we recall the principles of the discretization for each method. Then, we implement these discretization procedures in a code which treats the three-dimensional magnetostatic problem with a mixed and hybrid finite element method. The exterior domain is treated with the Steklov-Poincare´operator discretized using the three procedures. A comparison in terms of precision, performance and ease of implementation is given.