Space and Time Adaptive Calculation of Transient 3D Magnetic Fields

Abstract

Transient quasistatic magnetic fields are described by a degenerate parabolic initial-boundary value problems which can be considered as dynamical systems of nonlinear differential-algebraic equations (DAE) of index 1. This DAE structure is retained after the spatial discretization with geometric discretization schemes like the finite element method based on Whitney form functions (WFEM). External transient electric current excitations yield commonly thin layers of eddy currents in electric conductors. Furthermore nonlinear saturation effects have to be taken into account in ferromagnetic materials. A common approach in established simulation tools for solving this problem is the Method of Lines where the space is adaptively discretized at the beginning of the simulation and then kept fixed within the adaptive time integration of the time dependent equation. This approach, however, fails to take into account changes of the solution in the regions of material related to strong local field variation depending on the excitation wave form. This problem is solved by Rothe’s method coupling adaptive strategies in space and time.