粗糙面及其与目标复合电磁散射的有限元与边界积分方法研究
发布时间：2019-06-21 06:05
【摘要】：本论文采用有限元方法(Finite Element Method,FEM)与边界积分方法(Boundary Integral Method,BIM)对随机粗糙面及其与上下方目标复合模型的相关电磁散射问题展开了系统研究。通过将BIM与基尔霍夫近似(Kirchhoff Approximation,KA)结合提高了BIM的仿真效率,并将基于完全匹配层(Perfectly Matched Layer,PML)的FEM算法引入到一维粗糙面与二维目标的复合电磁散射问题中,采用FEM与BIM的混合算法对粗糙面与目标的电磁散射问题作了系统讨论,并基于KA对FEM/BIM算法进行了加速,最后通过FEM/MoM对二维粗糙面及三维目标的复合电磁散射问题进行了研究。论文的主要工作如下:1、针对一维介质粗糙面及其下方埋藏目标的复合电磁散射,通过KA对粗糙面的场信息进行近似,并采用BIM对目标区域进行模拟,同时迭代考虑两者之间的耦合,从而提高了复合电磁散射问题的求解效率。2、将FEM/PML引入到随机粗糙面与目标的复合电磁散射问题中,通过PML边界对半开放区域进行截断,截断区域内部采用FEM处理,基于该方法对一维粗糙面及其上下方二维目标、一维多层粗糙面及其下方二维埋藏目标等复合电磁散射问题进行了讨论。3、为了减小粗糙面相关电磁散射问题的求解区域,采用BIM边界对FEM区域进行截断,对FEM/BIM在粗糙面及其与目标复合电磁散射问题中的理论公式进行了详细推导。4、为了提高FEM/BIM算法的求解效率,通过将其与KA进行结合,形成了一种高低频混合方法。通过将粗糙面与目标分区处理,粗糙面区域采用KA近似处理,目标区域通过FEM/BIM求解,两者之间的电磁耦合通过迭代过程考虑。为了改善其仿真精度,基于多区域原则,将粗糙面区域划分为多个子区域,主区域采用BIM处理,辅区域仍采用KA处理。5、基于矢量四面体基函数,三维目标区域通过FEM结合Mo M边界求解,同时结合RWG基函数,二维粗糙面区域采用MoM处理,通过积分边界考虑两区域之间的耦合,从而将FEM/Mo M混合算法引入到二维粗糙面与三维目标的复合电磁散射问题中。
[Abstract]:In this paper, the finite element method (Finite Element Method,FEM) and the boundary integral method (Boundary Integral Method,BIM) are used to systematically study the electromagnetic scattering problems of random rough surfaces and their composite models with upper and lower targets. By combining BIM with Kirchhoff approximation (Kirchhoff Approximation,KA), the simulation efficiency of BIM is improved, and the FEM algorithm based on perfectly matched layer (Perfectly Matched Layer,PML is introduced into the composite electromagnetic scattering problem of one-dimensional rough surface and two-dimensional target. The hybrid algorithm of FEM and BIM is used to systematically discuss the electromagnetic scattering problem between rough surface and target, and the FEM/BIM algorithm is accelerated based on KA. Finally, the composite electromagnetic scattering of two-dimensional rough surface and three-dimensional target is studied by FEM/MoM. The main work of this paper is as follows: 1. Aiming at the composite electromagnetic scattering of one-dimensional dielectric rough surface and its buried target, the field information of rough surface is approximated by KA, and the target region is simulated by BIM, and the coupling between the two is considered iteratively, thus improving the efficiency of solving the composite electromagnetic scattering problem. 2, FEM/PML is introduced into the composite electromagnetic scattering problem of random rough surface and target. The semi-open region is truncated by PML boundary, and FEM is used to deal with the truncated region. Based on this method, the composite electromagnetic scattering problems such as one-dimensional rough surface and its upper and lower two-dimensional targets, one-dimensional multi-layer rough surface and its lower two-dimensional buried target are discussed. 3. In order to reduce the solving region of the rough surface related electromagnetic scattering problem, the BIM boundary is used to truncate the FEM region. The theoretical formula of FEM/BIM in rough surface and its composite electromagnetic scattering problem with target is deduced in detail. 4. In order to improve the efficiency of FEM/BIM algorithm, a high and low frequency hybrid method is formed by combining it with KA. By processing the rough surface and the target partition, the rough surface region is treated by KA approximation, and the target region is solved by FEM/BIM. The electromagnetic coupling between the two is considered by iterative process. In order to improve the simulation accuracy, based on the principle of multi-region, the rough surface region is divided into several subregions, the main region is processed by BIM, and the auxiliary region is still processed by KA. 5. Based on the vector tetrahedral basis function, the 3D target region is solved by FEM combined with MoM boundary, and the two-dimensional rough surface region is processed by MoM, and the coupling between the two regions is considered by integral boundary. Thus, the FEM/Mo M hybrid algorithm is introduced into the composite electromagnetic scattering problem of two-dimensional rough surface and three-dimensional target.
【学位授予单位】：西安电子科技大学
【学位级别】：博士
【学位授予年份】：2016
【分类号】：TN011
，
本文编号：2503848
[Abstract]:In this paper, the finite element method (Finite Element Method,FEM) and the boundary integral method (Boundary Integral Method,BIM) are used to systematically study the electromagnetic scattering problems of random rough surfaces and their composite models with upper and lower targets. By combining BIM with Kirchhoff approximation (Kirchhoff Approximation,KA), the simulation efficiency of BIM is improved, and the FEM algorithm based on perfectly matched layer (Perfectly Matched Layer,PML is introduced into the composite electromagnetic scattering problem of one-dimensional rough surface and two-dimensional target. The hybrid algorithm of FEM and BIM is used to systematically discuss the electromagnetic scattering problem between rough surface and target, and the FEM/BIM algorithm is accelerated based on KA. Finally, the composite electromagnetic scattering of two-dimensional rough surface and three-dimensional target is studied by FEM/MoM. The main work of this paper is as follows: 1. Aiming at the composite electromagnetic scattering of one-dimensional dielectric rough surface and its buried target, the field information of rough surface is approximated by KA, and the target region is simulated by BIM, and the coupling between the two is considered iteratively, thus improving the efficiency of solving the composite electromagnetic scattering problem. 2, FEM/PML is introduced into the composite electromagnetic scattering problem of random rough surface and target. The semi-open region is truncated by PML boundary, and FEM is used to deal with the truncated region. Based on this method, the composite electromagnetic scattering problems such as one-dimensional rough surface and its upper and lower two-dimensional targets, one-dimensional multi-layer rough surface and its lower two-dimensional buried target are discussed. 3. In order to reduce the solving region of the rough surface related electromagnetic scattering problem, the BIM boundary is used to truncate the FEM region. The theoretical formula of FEM/BIM in rough surface and its composite electromagnetic scattering problem with target is deduced in detail. 4. In order to improve the efficiency of FEM/BIM algorithm, a high and low frequency hybrid method is formed by combining it with KA. By processing the rough surface and the target partition, the rough surface region is treated by KA approximation, and the target region is solved by FEM/BIM. The electromagnetic coupling between the two is considered by iterative process. In order to improve the simulation accuracy, based on the principle of multi-region, the rough surface region is divided into several subregions, the main region is processed by BIM, and the auxiliary region is still processed by KA. 5. Based on the vector tetrahedral basis function, the 3D target region is solved by FEM combined with MoM boundary, and the two-dimensional rough surface region is processed by MoM, and the coupling between the two regions is considered by integral boundary. Thus, the FEM/Mo M hybrid algorithm is introduced into the composite electromagnetic scattering problem of two-dimensional rough surface and three-dimensional target.
【学位授予单位】：西安电子科技大学
【学位级别】：博士
【学位授予年份】：2016
【分类号】：TN011
，
本文编号：2503848
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