A hybrid unconditionally/conditionally stable parallel spectral-element time-domain algorithm for multi-scale computation

This paper proposes a hybrid unconditionally/conditionally stable parallel spectral-element time-domain algorithm for the analysis of multi-scale electromagnetic problems. Usually multi-scale simulation will lead to very small cells and thus making the time step size extremely small. However, when using this method, the time step size is no longer constrained by the CFL condition and it will greatly reduce the computation time. The Newmark-Beta scheme is employed for the small cells with MUMPS solver and central difference is for the large cells with direct solution procedure. Consequently, a relatively large time step size can be adopted. Parallel technique is also applied to achieve a satisfied efficiency with MPI. Finally, numerical results demonstrate the accuracy and effectiveness of the proposed method.