LAUSR

In the edge element discretization for magnetostatic problems, a gauge scheme, such as tree gauge, Lagrangian multiplier (LM) gauge, and auto gauge, is usually adopted to handle the singular curl–curl equation in terms of the magnetic vector potential. However, tree-gauge and LM-gauge schemes are not very efficient as a nonlinear problem with many increments has to be resolved. In order to overcome those difficulties, a mixed-gauge scheme based on current-splitting is proposed in this article. First, we make an improvement for LM-gauged formulation and adapt it to calculate the initial increment with a specially designed CG solver; then split the discrete source current density into a compatible part and incompatible part based on discrete Helmholtz decomposition; auto gauge cooperates with the compatible part to calculate the following increments. The mixed-gauge scheme combines the advantages of LM-gauge and auto-gauge schemes, which avoids the step to determine the source term, and at the same time, has high computational efficiency. The mixed-gauge scheme is tested in some examples against some other gauge schemes and found to be efficient and robust, where others possibly converge slowly or fail to produce a reliable solution.