Improved local time‐stepping algorithm for leap‐frog discontinuous Galerkin time‐domain method

Abstract

The discontinuous Galerkin time-domain (DGTD) method is now very popular for the solution of Maxwell's equations. Owing to the ability to deal with various types and shapes, and possibly locally refined meshes, it handles easily complicated geometries and remains globally explicit with easy parallelisation and extension to high orders of accuracy. However, the limitation of the stability of the method, related to the smallest elements in the mesh, requires the construction of local time-stepping algorithm. An improved local time-stepping algorithm of the explicit leap-frog DGTD method is proposed. The monostatic and bistatic radar cross section of several typical targets (a dielectric sphere, a perfect electric conductor almond, and a simplified missile) is calculated by the proposed algorithm. The simulated results show that although the entire solution relative error calculated by the proposed method has a slight increase compared with that of the previous scheme, the computational efficiency of the explicit leap-frog DGTD method is greatly improved. Meanwhile, the proposed algorithm does not require any additional storage. Compared to the improvement of the computational efficiency, this slight increase of the relative error can be absolutely acceptable.