Study On The Method Of Non - Continuous Galerkin Time Domain Integral Equations

Since the time domain integral equation has a great advantage in the computation of the wide band electromagnetic scattering problem, it is becoming an important research direction in the field of computational electromagnetism to analyze the electromagnetic scattering by using the time domain integral equation. Marching-On-in-Time (MOT) is one of the time domain integral methods, and usually use RWG basis function to discrete the surface of targets, so it can only deal with the problem which has a conformal discretization. Once the grid is not conformal, the traditional MOT method will be failed. This article will focus on this issue.First, the time domain integral equations for electromagnetic scattering of metal targets are derived, and the form of matrix equations based on the time stepping method is given, and the basic principle of discontinuous Galerkin method (DG) is introduced in detail. Next by combing the DG method and the MOT method a novel time domain integral method is developed which can handle the non-conformal meshing problem. Here it is called DG-TDIE method. To fight against the shortcomings of the time domain surface integral equation which consuming a lot of memory and having low efficiency, plan wave time domain is used in the DG-TDIE method,and the results is that the memory and time is reduced largely.Next, the article introduces a kind of higher order hierarchical vector basis function into the DG-TDIE method, and successfully reduces the memory consumption of the algorithm while ensuring the accuracy. The hybrid order modeling technique based on the non-conformal mesh generation is studied. Different order of higher order basis functions are used in different subdivision area with different mesh size. Different from the traditional hybrid modeling techniques, it allows non-conforming meshing between two discrete faces. As a consequence, it can further improve the generality of higher order hybrid modeling. In the end of the chapter, the correctness and superiority of the high order mixed modeling time domain integral equation method are verified by some numerical examples.