An Iterative CN-Leapfrog Scheme Based Hybrid Implicit–Explicit Discontinuous Galerkin Finite-Element Time-Domain Method for Analysis of Multiscale Problems

摘要

The discontinuous Galerkin finite-element time-domain (DG-FETD) method with the ability to deal with unstructured meshes is well suited to analyze the multiscale system. However the DG-FETD method with explicit integration schemes is constrained by stability conditions that can be very restrictive upon highly fine meshes. The hybrid implicit-explicit Crank-Nicolson (CN) leapfrog scheme is effective in solving this problem; but because of using CN scheme, the inversion of a large sparse matrix must be calculated at each time step in the fine regions. The hybrid implicit- explicit iterative CN leapfrog scheme is introduced to improve the computational efficiency which can form a block diagonal matrix. The leapfrog scheme is employed for electrically coarse regions and iterative CN scheme for electrically fine ones. The numerical examples have demonstrated the validity and efficiency of the method.