Computation of magnetic fields using a 2-D hybrid finite-element/boundary-element algorithm and comparison with analytical solutions

Magnetic field computations using the finite-element (FE) method usually involve large air domains surrounding the conductors to satisfy boundary conditions at infinity. Elimination of these air domains saves computations and simplifies model generation-especially in large problems involving complex geometries like railguns and pulsed power generators, where fields in the air regions are calculated using fields at the air-conductor interface. The air domain can be avoided using the hybrid finite-element/boundary-element (FE/BE) method. A two-dimensional (2-D) hybrid FE/BE algorithm with the fundamental solution of Poisson´s equation as the weighting function is investigated here for applications to electromagnetic launch problems. Two examples with analytical solutions are used: a rectangular conductor carrying uniform current, and a quadrupole coil configuration. Solutions obtained using the hybrid algorithm match analytical solutions favorably in all regions, including geometric corners. The effects of the number of integration nodes in quadrature formulas and coupling schemes between the FE and BE formulations through the normal fluxes at the boundaries are also presented. These 2-D analyses serve as forerunners for three-dimensional investigations.