A new implicit hybridizable discontinuous Galerkin time-domain method for solving the 3-D electromagnetic problems (Q1739459)

The authors propose a new implicit hybridizable discontinuous Galerkin time-domain method for solving the 3-D Maxwell's equations with locally refined meshes. Compared to the classical discontinuous Galerkin method, the proposed method allows a larger time step and has less degrees of freedom. Furthermore, by using the nodal hierarchical basis functions, the authors propose an effective \(p\)-type multigrid preconditioner to solve the resulting linear system. Numerical results are presented to demonstrate the accuracy and computational efficiency of the proposed method.