Numerical algorithms for the FDiTD and FDFD simulation of slowly varying electromagnetic fields

The simulation of slowly varying electromagnetic fields is possible for very large, realistic problems with finite-difference implicit time-domain (FDiTD) and frequency-domain (FDFD) formulations on the basis of the consistent Finite-Integration Technique (FIT). Magneto-quasistatic time-domain formulations combined with implicit time marching schemes require the repeated solution of real-valued symmetric systems. The solution of driven frequency domain problems usually consists in the solution of one non-Hermitean system. Preconditioned conjugate gradient-type methods are well-suited for this task. They allow the efficient solution even for consistent singular or near-singular systems, which typically arise from formulations for slowly varying electromagnetic fields using the Maxwell-Grid-Equations of the FI-Method. Numerical results for TEAM workshop 11 benchmark problem and for a large practical problem, a shading ring sensor, show that the presented algorithms are capable of solving realistic problems for large numbers of unknowns in acceptable calculation times on contemporary medium sized workstations. Copyright © 1999 John Wiley & Sons, Ltd.