本文選題：時域有限差分法　切入點：完全匹配層　出處：《安徽大學(xué)》2017年碩士論文

【摘要】：時域有限差分法(Finite-Difference Time-Domain,FDTD)自提出以來在電磁計算領(lǐng)域得到了廣泛的研究,并已經(jīng)發(fā)展成為一種成熟的數(shù)值計算方法。在實際計算時,通常會遇到半開放和開放區(qū)域的問題,然而計算資源是有限的,因此吸收邊界條件對于FDTD區(qū)域的截斷至關(guān)重要。另外,FDTD算法的時間步長需滿足Courant-Friedrich-Levy(CFL)穩(wěn)定性條件,這使其在一些包含細小結(jié)構(gòu)的仿真模型中的計算效率不高�；谏鲜鰡栴},本文的研究內(nèi)容是圍繞吸收邊界條件的吸收性能的改進以及無條件穩(wěn)定的FDTD算法展開的。首先,本文簡要介紹了一下FDTD算法的基礎(chǔ)知識以及幾種經(jīng)典的完全匹配層(perfect match layer,PML)技術(shù)。接著,針對傳統(tǒng)卷積完全匹配層(CPML)技術(shù)中存在的場值更新時刻不同步問題,提出了一種改進的CPML技術(shù)。與傳統(tǒng)的CPML技術(shù)相比,這種改進的CPML的吸收性能更好,計算效率更高,并且沒有增加CPML算法的復(fù)雜度。其次,對無條件穩(wěn)定的交替方向隱式FDTD(Alternating-Direction-Explicit FDTD,ADI-FDTD)算法、弱條件穩(wěn)定的混合顯隱式FDTD(Hybrid Implicit-Explicit FDTD,HIE-FDTD)算法進行了介紹,詳細推導(dǎo)了兩種算法引入CPML吸收邊界后的時域迭代公式,并給出了公式中場分量的迭代順序,驗證了CPML吸收邊界在ADI-FDTD和HIE-FDTD算法中的正確性和有效性。最后,介紹了一種顯式的無條件穩(wěn)定算法即空間濾波FDTD(Spatially filtered FDTD,SF-FDTD)算法,與隱式的FDTD算法相比,它不需要復(fù)雜的公式推導(dǎo)及矩陣求逆運算,從而降低了無條件穩(wěn)定算法在FDTD方法中應(yīng)用的難度。傳統(tǒng)SF-FDTD的不足之處在于只能應(yīng)用在每個方向網(wǎng)格尺寸相同的區(qū)域中,基于此,本文提出了一種改進的SF-FDTD算法,使其能夠應(yīng)用在各方向網(wǎng)格尺寸不相同的區(qū)域中,擴大了 SF-FDTD算法的應(yīng)用范圍。接著,將SF-FDTD引入到亞網(wǎng)格技術(shù)中,由于SF-FDTD突破了 CFL條件的限制,在細網(wǎng)格區(qū)域可選取與粗網(wǎng)格區(qū)域相同的時間步長,有效地提高了計算效率。
[Abstract]:Finite-Difference Time-Domain FDTD (FDTD) has been widely studied in the field of electromagnetic computation since it was proposed, and has been developed into a mature numerical method.In practical computation, the problem of semi-open and open region is usually encountered. However, the computational resources are limited, so the absorbing boundary condition is very important for the truncation of the FDTD region.In addition, the time step size of FDTD algorithm needs to satisfy the stability condition of Courant-Friedrich-Levyn CFL, which makes it inefficient in some simulation models with small structures.Based on the above problems, this paper focuses on the improvement of the absorption performance of the absorbing boundary condition and the unconditionally stable FDTD algorithm.Firstly, this paper briefly introduces the basic knowledge of FDTD algorithm and several classical perfectly matched match layers.Then, an improved CPML technique is proposed to solve the problem of out-of-sync of field value update time in traditional convolution perfectly matched layer (CPML) technology.Compared with the traditional CPML technique, the improved CPML has better absorption performance and higher computational efficiency, and does not increase the complexity of the CPML algorithm.Secondly, the unconditionally stable alternating direction implicit FDTD(Alternating-Direction-Explicit FDTDU ADI-FDTD algorithm and the weakly conditional stable hybrid explicit implicit FDTD(Hybrid Implicit-Explicit FDTD- HIE-FDTD algorithm are introduced. The time domain iterative formulas of the two algorithms after introducing the CPML absorbing boundary are derived in detail.The iterative order of the field component of the formula is given to verify the correctness and validity of the CPML absorbing boundary in the ADI-FDTD and HIE-FDTD algorithms.Finally, an explicit unconditionally stable algorithm, spatial filtering FDTD(Spatially filtered FDTDX SF-FDTD algorithm, is introduced. Compared with the implicit FDTD algorithm, it does not require complicated formula derivation and matrix inversion.Therefore, the application difficulty of unconditional stability algorithm in FDTD method is reduced.The disadvantage of traditional SF-FDTD is that it can only be used in the same area of grid size in every direction. Based on this, an improved SF-FDTD algorithm is proposed to make it applicable to different areas with different grid sizes in different directions.The application of SF-FDTD algorithm is expanded.Then, SF-FDTD is introduced into subgrid technology. Because SF-FDTD breaks through the restriction of CFL condition, the time step of fine grid region can be chosen the same as that of coarse grid area, and the computational efficiency is improved effectively.
【學(xué)位授予單位】：安徽大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2017
【分類號】：O441

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