A Hybrid Spectral-Element / Finite-Element Method with the Implicit-Explicit Runge-Kutta Time Stepping Scheme for Multiscale Computation

摘要

Realistic system level electromagnetic problems such as electronic packaging are often multiscale, where electrically fine structures and electrically coarse structures coexist. Simulating the transient multiscale problems can be very challenging for conventional numerical techniques: the dense mesh/grid for fine structures will lead to a large number of wasted unknowns in the coarse domains. Besides, small cells for fine structures make the size of time steps extremely small, thus lead to an unaffordable number of steps in time integration. Here we propose a hybrid spectralelement / finite-element method (SEM/FEM) combined with the implicit-explicit Runge-Kutta (IMEX-RK) scheme for multiscale electromagnetic computation. This method is flexible in spatial discretization and efficient in time stepping. The basic idea and numerical results are presented in following sections.