Efficient multiscale electromagnetic simulations require several major challenges that need to be addressed, such as flexible and robust geometric modeling schemes, efficient and stable time-stepping methods, etc. Due to the versatile choices of spatial discretization and temporal integration, discontinuous Galerkin time-domain (DGTD) methods can be very promising in simulating transient multiscale problems. This paper provides a comprehensive review of different DGTD schemes, highlighting the fundamental issues arising in each step of constructing a DGTD system. The issues discussed include the selection of governing equations for transient electromagnetic analysis, different basis functions for spatial discretization, as well as the implementation of different time-stepping schemes. Numerical examples demonstrate the advantages of DGTD for multiscale electromagnetic simulations.
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Chen et al. (2012) studied this question.
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