Semiexplicit time integration of a reduced magnetic vector potential magneto-quasistatic field formulation

In this article, a reduced vector potential formulation for transient magneto-quasistatic field problems is presented. The finite element method for spatial discretization yields a system of differential algebraic equations (DAE). Applying a generalized Schur complement the DAE system decomposes into a system of ordinary differential equations (ODE) and an algebraic equation. In order to avoid computationally expensive linearization schemes to solve nonlinear eddy current problems the ODE system is integrated in time using a semiexplicit Euler scheme. The vector potential is split into a source vector potential and a reduced vector potential which describes the eddy current and magnetization effects. The reduced formulation is compared with the underlying nonreduced formulation regarding the overall performance. In addition, the proper orthogonal decomposition method is applied to the iterative preconditioned conjugate gradient method to minimize the number of iterations per time step.