Reduced vector potential formulation for FI2TD schemes

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