基于DG时域有限元方法的辐射问题分析

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摘要自从麦克斯韦方程被提出以来，电磁场理论的研究和应用就从未停止过。在用理论分析求解复杂电磁问题的时候，理论模型也越来越复杂，若通过经典电磁学的解析方法来求解，解析问题时往往有很大的局限性甚至无法实现。随着计算技术的不断提高和电子计算机软件和硬件技术的不断发展，各项技术与电磁场理论相结合，计算电磁学应运而生。

近几十年，计算电磁学研究者们一直在关注着时域有限元方法。它能够对复杂几何结构与非均匀介质进行精确模拟、获得目标的宽频电磁特性。随着计算规模的增大，对内存的需求也越来越大，与此同时，对计算时间的要求也在变高。传统的时域有限元法在求解时相当的耗时，而不连续迦辽金法可以有效地解决时域有限元法的求解问题。

DG时域有限元方法由时域有限元法与不连续迦辽金法相结合，此方法可以得到具有块对角特性的质量矩阵。在DG时域有限元方法中，区域分界面处的基函数是不连续的，这就需要引入数值通量，强加磁场与电场的切向连续性。本文使用了DG时域有限元方法来分析物体的电磁辐射特性。以电磁辐射问题为例，利用HFSS软件来实现使用DG时域有限元方法对电磁辐射问题的求解，所得结果与传统时域有限元法求解的结果作比对。通过算例验证了DG时域有限元方法的高效性和正确性。42464

关键词时域有限元法，DG时域有限元方法，电磁辐射，HFSS

毕业论文设计说明书外文摘要

Title Analyze electromagnetic issues by DG time-domain finite element method

Abstract

Since the Maxwell equations were proposed, the investigations and implements of electromagnetic field theory has been an important program for scientists. The theoretical model is more complicated when it is applied to analyze or solve the complex electromagnetic issues. When the analytic method of the classical electromagnetism is used to solve such issues, the large limitation of this method, which is hard to overcome, would be a large barrier for solving the electromagnetic issues. With the development of computer technology and the improvement of the computer software and hardware technology, the technologies of computer were implied in electromagnetism and the computer electromagnetism is developed.

During the recent several decades, scientists have been reachingon the time-domain finite-element method-tdfem. The time-domain finite-element method-tdfem achieves the accurate simulation of complex geometric structure and inhomogeneous medium and figure out the broadband and electromagnetic properties of the tested items. However, the larger calculation scale requires a larger internal storage and it also requires a shorter time for calculation. The traditional time-domain finite-element method-tdfem fails to save time while the discontinuous Gakerkin method could solve this limitation effectively.

DG time-domain finite element method is the combination of time-domain finite-element method-tdfem and discontinuous Gakerkin method and the new method could work out the mass matrix with block tridiagonal feature. The basis functions of regional interface is discontinuous when applying the DG time-domain finite element method and the numerical flux is implied to intensify the tangential continuity of electric and magnetic fields. In this paper, the DG time-domain finite element method is used to analyze the electric radiation characteristics of objects. For example, the HFSS software is implied to achieve the implement of DG time-domain finite element method when discussing the electromagnetic radiation and compare the experimental result with the one figured out with traditional time-domain finite-element method-tdfem. Finally the example demonstrated the effectiveness and accuracy of DG time-domain finite element method.