A hybrid Finite Integration–Finite Volume Scheme

A hybridized scheme for the numerical solution of transient electromagnetic field problems is presented. The scheme combines the Finite Integration Technique (FIT) and the Finite Volume Method (FVM) in order to profit from the computational efficiency of the FIT while taking advantage of the superior dispersive properties of the FVM. The scheme is based on the longitudinal–transverse (LT) splitting of the discrete curl operator. The FIT is employed for discretizing the two-dimensional subproblem while the one-dimensional problem is discretized according to the FVM. The scheme offers benefits for the simulation of multiscale setups, where the size of the computational domain along one preferred direction is electrically much larger than along the others. In such situations, the accumulation of dispersion errors within hundreds of thousands of time steps usually deteriorates the solution accuracy. The hybrid scheme is applied in combination with adaptive mesh refinement, yielding an efficient scheme for multiscale applications.