A new implicit hybridizable discontinuous Galerkin time-domain method for solving the 3-D electromagnetic problems

摘要

Based on an implicit time scheme, this paper presents a new implicit hybridizable discontinuous Galerkin time-domain (imHDGTD) method for solving the 3-D electromagnetic problems with locally refined meshes. Compared with the classical discontinuous Galerkin (DG) method, the proposed imHDGTD method has a larger suitable time step and the reduction in number of degrees of freedom (DOFs). Besides, we adopt the nodal hierarchical basis functions and further propose a matrix solving technology with an effective p-type multigrid preconditioner, which decreases significantly imHDGTD's matrix factorization time and memory usage. Some numerical results show the accuracy and a higher computational performance of the imHDGTD, which illustrates this method more promising and effective for the complex multiscale electromagnetic problem.

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