An Adaptive DGTD Algorithm Based on Hierarchical Vector Basis Functions

To accurately obtain the radiation and propagation characteristics of the highly oscillating electromagnetic waves, the p-refinement method which expands the physical quantities by high-order basis functions has been proposed. Nevertheless, since the time-domain electromagnetic simulation is a dynamic process, a static refinement is not applicable. In this paper, an efficient dynamic p-adaptation method based on hierarchical vector basis functions having the property of nesting to facilitate the construction of basis functions has been developed for the discontinuous Galerkin time domain (DGTD) method. In this approach, based on the relationship between the amplitude of the expansion coefficients of hierarchical vector basis functions and the corresponding expansion coefficients of the physical quantities captured by each element in the previous time step, an error estimator is proposed to determine the order of each element in the next time step. In order to reduce the computational overhead, the basis orders of each element can be dynamically adjusted when the pulse passes through or is dissipated. The numerical results demonstrate the accuracy and efficiency of the proposed approach.