Efficient Noniterative Implicit Time-Stepping Scheme Based on E and B Fields for Sequential DG-FETD Systems

The discontinuous Galerkin finite-element time-domain (DG-FETD) method with implicit time integration has an advantage in modeling electrically fine-scale electromagnetic problems. Based on domain decomposition methods, it avoids the direct inversion of a large system matrix as in the conventional FETD method; by employing implicit time integration, it obviates an extremely small time-step interval to maintain stability as in explicit schemes. Based on curl-conforming basis functions for the electric field intensity E field and divergence-conforming basis functions for the magnetic flux density B field, a new noniterative implicit time-stepping scheme is proposed to efficiently solve sequentially ordered systems for electrically fine-scale problems. Compared with the previous EH-based scheme, the new scheme introduces fewer unknowns and, thereby, results in a smaller matrix system. Based on the Crank-Nicholson algorithm for time integration, the matrix system is in a block tridiagonal form. Then, through separating the surface unknowns from the volume unknowns, a block lower-diagonal-upper (LDU) decomposition is implemented, reducing the computational complexity of the original system. The adaptivity of parallel computing in subdomain level during preprocessing further helps shorten the computation time. Numerical results confirm that the proposed LDU scheme presents improved efficiency in terms of memory and CPU time while retaining the same accuracy, compared with the previous implicit block-Thomas method. With respect to the explicit Runge-Kutta method and the standard FDTD, it also shows an advantage in CPU time. The proposed scheme will help improve the performance of DG-FETD in modeling electrically fine-scale problems.