【摘要】：本論文采用有限元方法(Finite Element Method,FEM)與邊界積分方法(Boundary Integral Method,BIM)對(duì)隨機(jī)粗糙面及其與上下方目標(biāo)復(fù)合模型的相關(guān)電磁散射問(wèn)題展開了系統(tǒng)研究。通過(guò)將BIM與基爾霍夫近似(Kirchhoff Approximation,KA)結(jié)合提高了BIM的仿真效率,并將基于完全匹配層(Perfectly Matched Layer,PML)的FEM算法引入到一維粗糙面與二維目標(biāo)的復(fù)合電磁散射問(wèn)題中,采用FEM與BIM的混合算法對(duì)粗糙面與目標(biāo)的電磁散射問(wèn)題作了系統(tǒng)討論,并基于KA對(duì)FEM/BIM算法進(jìn)行了加速,最后通過(guò)FEM/MoM對(duì)二維粗糙面及三維目標(biāo)的復(fù)合電磁散射問(wèn)題進(jìn)行了研究。論文的主要工作如下:1、針對(duì)一維介質(zhì)粗糙面及其下方埋藏目標(biāo)的復(fù)合電磁散射,通過(guò)KA對(duì)粗糙面的場(chǎng)信息進(jìn)行近似,并采用BIM對(duì)目標(biāo)區(qū)域進(jìn)行模擬,同時(shí)迭代考慮兩者之間的耦合,從而提高了復(fù)合電磁散射問(wèn)題的求解效率。2、將FEM/PML引入到隨機(jī)粗糙面與目標(biāo)的復(fù)合電磁散射問(wèn)題中,通過(guò)PML邊界對(duì)半開放區(qū)域進(jìn)行截?cái)?截?cái)鄥^(qū)域內(nèi)部采用FEM處理,基于該方法對(duì)一維粗糙面及其上下方二維目標(biāo)、一維多層粗糙面及其下方二維埋藏目標(biāo)等復(fù)合電磁散射問(wèn)題進(jìn)行了討論。3、為了減小粗糙面相關(guān)電磁散射問(wèn)題的求解區(qū)域,采用BIM邊界對(duì)FEM區(qū)域進(jìn)行截?cái)?對(duì)FEM/BIM在粗糙面及其與目標(biāo)復(fù)合電磁散射問(wèn)題中的理論公式進(jìn)行了詳細(xì)推導(dǎo)。4、為了提高FEM/BIM算法的求解效率,通過(guò)將其與KA進(jìn)行結(jié)合,形成了一種高低頻混合方法。通過(guò)將粗糙面與目標(biāo)分區(qū)處理,粗糙面區(qū)域采用KA近似處理,目標(biāo)區(qū)域通過(guò)FEM/BIM求解,兩者之間的電磁耦合通過(guò)迭代過(guò)程考慮。為了改善其仿真精度,基于多區(qū)域原則,將粗糙面區(qū)域劃分為多個(gè)子區(qū)域,主區(qū)域采用BIM處理,輔區(qū)域仍采用KA處理。5、基于矢量四面體基函數(shù),三維目標(biāo)區(qū)域通過(guò)FEM結(jié)合Mo M邊界求解,同時(shí)結(jié)合RWG基函數(shù),二維粗糙面區(qū)域采用MoM處理,通過(guò)積分邊界考慮兩區(qū)域之間的耦合,從而將FEM/Mo M混合算法引入到二維粗糙面與三維目標(biāo)的復(fù)合電磁散射問(wèn)題中。
[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.
【學(xué)位授予單位】：西安電子科技大學(xué)
【學(xué)位級(jí)別】：博士
【學(xué)位授予年份】：2016
【分類號(hào)】：TN011
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本文編號(hào)：2503848