Numerical Foundations, Integral Methods and Applications

Abstract

In this paper the mathematical foundations and the application of various integral formulations based on vector and scalar potentials for the numerical treatment of magnetostatic and eddy current problems with the boundary element method (BEM) are presented. Starting from Maxwell’s equations the basic integral equations are derived by applying Green’s theorem for scalar and vector variables and the definition of the appropriate Green’s functions. In order to apply the BEM the discretization of the boundaries into boundary elements is discussed. This discretization transforms the boundary integral equations into a system of algebraic equations which can be solved by various methods. The boundary element formulations and numerical results of examples for three-dimensional magnetostatic field problems and eddy current problems are presented. It can be seen that there exists a wide range of applications of integral methods and which are alternatives to differential equation methods, e.g. the finite element method.