Transient Implicit Solver

The implicit solver is based on the finite element time domain (FETD) method with an implicit time stepping [13-14]. The Implicit Solver is unconditional stable and is not limited by any Courant-Friedrichs-Lewy (CFL) type condition as the Hybrid Solver. Therefore the Implicit Solver can have much larger time step compared to the Hybrid Solver. To satisfy Nyquist sampling theory, the time step for the Implicit Solver is such that resolves the spectral content of the input signal (time-step = 1/(20*fmax)). On the other hand, the implicit solver solves a large sparse system matrix during time stepping. Therefore, each step of the implicit solver takes much longer than that of the hybrid solver. Both the memory usage and simulation time can increase rapidly as the problem size becomes larger. This renders the implicit solver less efficient for solving electrically large problems. Finally, the implicit solver does not support GPU acceleration. A warning message will be shown in the user interface when the GPU is enabled for an implicit simulation.

The hybrid solver is based on the explicit-implicit discontinuous Galerkin time domain method [15]. When the GPU is enabled, only the explicit part of the hybrid solver is running and being accelerated by GPUs. More information about the hybrid solver can be found in Transient Solution Theory.