New formulation of finite-element method with gauge condition for three-dimensional magnetic field analysis

A novel magnetic vector potential formulation for three-dimensional problems is described. In order to establish the boundary conditions of different materials, it is necessary to impose some kind of gauge for three-dimensional magnetic field analysis. The partial differential equation including the gauge is discretized using the Galerkin method, which in turn yields a new formulation. The three components of A are formulated separately. By separating the components, memory size and calculation time are reduced greatly. The calculated results show that the formulation is valid