【作者】 华怡；

【导师】 刘其中；

【作者基本信息】 西安电子科技大学 ， 电磁场与微波技术， 2008， 硕士

【摘要】 有限元法特别适合于解决具有非均匀媒质的复杂几何结构的电磁问题。在电磁学领域内,有限元法己广泛用于解决辐射、散射、波导传输及谐振腔等问题。由于对许多目标的电磁现象的辐射及散射分析都涉及到无限区域,有限元方法需要在离开目标物体一段距离的地方设置吸收边界条件,这就自然增加了计算量。而基于积分方程的边界积分方法尽管可以直接分析目标问题,但其不利的一面是产生的矩阵是一个满阵,因此受到计算机内存的限制,只适合于分析电小尺寸问题。为了避开这两种方法的不利一面同时保留其优点,发展了一种混合算法:有限元-边界积分混合方法(FE-BI)。该方法的基本原理是引入一个包围所研究目标的虚构边界,在虚构边界内部用有限元方法来分析,在边界上用边界元来处理。这两个区域中的场在虚构边界上通过场的连续性耦合起来,从而得到一个内部和边界场解的耦合方程组。推导了基于四面体剖分的矢量基函数的有限元公式,编写了有限元程序,并用该程序计算了波导以及传输线内的场,程序计算结果与数值结果吻合良好。根据有限元-边界积分混合方法的原理,推导了有限元-边界积分混合方法的公式,其中内部区域采用基于四面体剖分的矢量基函数,边界部分采用的三角形剖分的RWG基函数。根据这些公式编写了程序,应用该程序计算了三维目标的电磁散射问题,程序计算结果与传统矩量法和有限元法计算结果吻合良好。更多还原

【Abstract】 The finite element method (FEM) suits specially to solve the electromagnetic problems of the structures consisting of an inhomogeneous dielectric body of arbitrary shape. In the electromagnetic domain, the finite element method has widely used in solving problems such as radiation, scattering, wave guide transmission and resonant cavity problem. Since the electromagnetic radiation and scattering analysis of many problems is in open space, the absorbing boundary elements at the outer surface of the meshed region must be employed when the finite element method is used, thus the computation burden is increased out of question. Although the boundary integral method based on the integral equation is very efficient at solving the open radiation problems, the matrix gained by this method is full and requires too much memory. So the boundary integral method is only suitable to solve the problem of the electrically small object. To take advantage the strengths of the both methods and avoid their disadvantages, a hybrid method is presented, viz. the hybrid finite element-boundary integral method. The principle of this hybrid method is that the FEM is employed to handle the interior domain of bodies and the boundary integrate is used to develop surface integrals that relate the field quantities on boundary surfaces with the equivalent surface currents. These integral equations are then coupled to the finite element equations through the continuity of the tangential magnetic fields across the hybrid boundaries.Based on the edge-based vector basis functions defined within tetrahedrons, the finite element formulae are deduced and the program is written to compute the fields within the wave-guide and transmission line. The computed results are in excellent agreement with the exact solutions. Then, based on the principle of the hybrid finite element-boundary integral method, the formulae of this hybrid method are deduced. In the interior region the edge-based vector finite elements are used and on the surface the RWG basis functions are used. Based on these formulae, another program is also written. The electromagnetic scattering programs of the three-dimensional objects are computed using our hybrid method program and the computed results agree well with the results computed by the moment method and the finite element method.更多还原