A new BEM technique for nonlinear 2D magnetostatics
The paper presents a new boundary element technique for the solution of nonlinear 2D magnetostatic problems. It is based on a recurrent formulation of Poisson's equation where the change in material property between the domains is modelled as a single layer along the interfaces. Then the nonhomogeneity appears as a source term. The nonlinear regions are decomposed into subdomains where the material is assumed homogeneous. The underlying principle lies on the transmission-line modelling (TLM) method that is commonly used for electric network analysis. A new numerical scheme is derived where the solution is obtained iteratively without any system of algebraic equations for open boundary problems. This is an important point with respect to the classical FEM and BEM treatment that always require the assembly and the solution of a set of simultaneous algebraic equations. Numerical results show significant reduction in memory requirements for our method due to the absence of any matrix storage.
magnetostatics transmission-line modelling nonlinear problems finite elements