by C.T. Wu and Y.C. Sun
Numerical instability may exhibit in the extremely late time for hybrid Finite Difference/ Finite Element Time Domain method, although both methods are stable if employed separately. In this paper, a novel piecewise constant basis is applied in place of linear basis in finite element modeling to perfectly comply with the uniform field distribution of FDTD. It is found that the late time instability can be removed by such a choice of basis. As a result, not only can this hybrid method be used to solve most electromagnetic problems with high accuracy, flexibility, and computing efficiency, but also its stability can be guaranteed.
As shown in figure is transient response of a Gaussian pulse into a penetrable dielectric cylinder. Numerical errors will be accumulated to generate instability if the linear FEM basis is employed. Such occurrence will be suppressed thoroughly by employing the novel pulse FEM basis.