Reduced vector potential formulations for FI2TD schemes

Finite integration implicit time domain (FI²TD) schemes for transient magneto-quasistatic problems have so far been developed for a magnetic field description based on a modified vector potential formulation. A reduced vector potential formulation for these schemes is introduced, where the magnetic field is additively decomposed into a source part originating from the exciting coil currents, which thus can be modelled independently of the computational grid, and a part resulting from the presence of eddy currents due to electric conductivity and/or the nonlinear material behaviour. Numerical tests for 3-D transient problems show an improved convergence behaviour of the iterative CG-algorithm with respect to the new formulation.