Indirect Coupling of the Cell Method and BEM for Solving 3-D Unbounded Magnetostatic Problems

A novel hybrid approach for solving magnetostatic problems with an unbounded air domain is presented. The basic idea is to use augmented dual grids for interfacing the cell method (CM) and Boundary Element Method by indirect coupling, introducing equivalent surface field sources. The field problem in bounded domains is discretized by the CM in terms of integral variables, i.e., line integrals of the magnetic vector potential. Boundary integral conditions, formulated with the reduced magnetic scalar potential, are applied to avoid the air region meshing. A mixed final symmetric algebraic system, which can be solved by fast iterative solvers, such as Minimal Residual Method or SYMMLQ, is finally obtained. The magnetic field in the air region is then easily reconstructed from the equivalent sources. Numerical tests show that the hybrid method is accurate even by using a collocation approach for discretizing the boundary integral conditions.