boundary integral equation 中文意思是什麼
boundary integral equation
解釋
邊界積分方程-
First, in virtual of identification of flaws is a typical of in - verse problems, proceeding from time - harmonic electromagnetic maxwell ' s equa - tion and helmholtz equation, the uniqueness and existence of direct scattering problems including the numerical algorithms of diverse of boundary conditions is given. second, the uniqueness and existence of inverse scattering problems and the theory of ill - posed integral equation are briefly looked back upon. finally, indicator function method for boundary identification is set up under all kinds of boundary conditions for inverse scattering of homogenous and inhomogenous objects, meanwhile, the proof of possibility for near - field measurements and nu - merical simulation are given
由於缺陷的識別是一類典型的反問題，因而首先從時諧電磁maxwell方程和helmholz方程出發，具體地闡述了求解正散射問題的有關方法，包括各種（夾雜）邊界條件下的數值解法，就解的存在性唯一性給予了肯定的回答；隨后對逆散射問題的理論作了簡短的回顧，包括解的唯一性以及非線性不適定積分方程的處理等；然後對均勻介質和非均勻介質的逆散射問題建立了在各種邊界條件下的邊界識別的指示函數方法，鑒于近場數據獲得的重要性，對近場測試時邊界識別的方法給予了相應的證明，並且實現了數值模擬。 -
Boundary integral equation of electromagnetic field with line current element of external source
存在外源線電流元的電磁場邊界積分方程 -
The stability of cauchy singular integral when the integral curve has a smooth perturbation is discussed in our first partition ; we apply some results of the first partition to the second partition and solve the stability of the solution to the cauchy singular integral equation. finally, on the basis of the stability of the cauchy type integral, we study the stability of the solution to the riemann boundary value problem when the contour perturbs smoothly
在第一部分中，我們主要討論了cauchy奇異積分在積分曲線發生光滑擾動時的穩定性問題；而在第二部分中，我們把第一部分的結果應用到cauchy奇異積分方程，導出了其關于積分曲線攝動的穩定性的研究及其一些結果；最後，在第三部分中，我們在研究cauchy型積分關于積分曲線的穩定性問題的基礎上，探討了riemann邊值問題的穩定性問題。 -
From mathematical models for inverse scattering in two dimensional inho - mogenous media including variable impedance, all kinds of probable mixed variable impedance boundaries and cracks, from interior and exterior trans - mission problems and radiation condition, ill - posed integral equation and indicator function method are formulated for the diverse of boundary iden - tification. it is shown that the kernel of the integral equation characters the boundary of scatterer, which is determined by solving it by virtual of regularity method, meanwhile, some numerical tests are given. 3
在二維非均勻介質逆散射邊界識別的數學模型（包括一般的非均勻介質，正交各向異性介質，變阻抗介質，各種可能的混合變阻抗邊界問題）下，由內透射問題和外透射問題以及輻射條件，推導了上述介質的邊界識別的積分方程和指示函數方法，由於積分方程的核充分表徵了散射物的邊界，由此說明只要利用正則化方法求解該積分方程，就可以確定散射物的邊界。 -
From mathematical models for inverse scattering in two dimensional homoge - nous media including dirichlet, neumann, robin, all kinds of probable mixed boundaries and cracks, direct and inverse scattering are discussed, and ill - posed integral equation and indicator function method are formulated for the diverse of boundary identification. it is shown that the kernel of the integral equation characters the boundary of scatterer, which is determined by solv - ing it by virtual of regularity method, meanwhile, some numerical tests are given. 2
在二維均勻介質逆散射各種邊界識別的數學模型（包括dirichlet ， neumann ， robin ，各種可能的混合邊界問題，裂紋問題）下，分別考慮了正散射問題和逆散射問題，推導了上述各種邊界識別的不適定積分方程以及指示函數方法，由於積分方程的核充分表徵了散射物的邊界，由此說明只要利用正則化方法求解該積分方程，就可以確定散射物的邊界，並給出了一些數值實驗。 -
The radar cross section of grounded open cavities is computed by fem combined with boundary integral equation method. the cavities filled with complex materials are also analyzed. accurate results have been obtained
應用eb - fem結合邊界積分方程對接地腔體的雷達散射面積進行了分析，討論了腔體內復雜介質填充情況對散射特性的影響，得到了比較精確的結果，討論了該混合方法在分析此類問題中的優缺點。 -
Based on the fundamental solution of two perfectly bonded elastic halfspaces, and using the boundary integral equation method and the finite - part integral concepts, the problem is reduced to a hypersingular integral equation in which the unknown function is the crack opening displacement discontinuity
首先根據雙材料空間的彈性力學基本解，使用邊界積分方程方法，在有限部積分的意義下導出了以裂紋面位移間斷為未知函數的超奇異積分方程。 -
In this dissertation, the numerical computation for the acoustic radiation problem ( arp ) is studied deeply and systematically in the theory, method and the application technique, based on analyzing the situation of the home and abroad on the numerical computation for the acoustic radiation problem. the calculation formulas of the boundary element method ( bem ) for the exterior acoustic radiation problem in the full - space and half - space are deduced, based on the wave propagation theorem ; the arising of the non - unique solutions, which is associated with the application of the boundary integral equation ( bie ) in acoustic radiation problem, is analyzed and proofed ; the improved combined helmholtz integral equation formulation ( ichief ) is presented to overcome the non - uniqueness problem more effectively and reliably ; the determination of the singular integral coefficients on various occasions is analyzed ; the properties and treatments of the singular integrals with different orders axe studied ; the computation program of the cubic spline ichief is developed and its ability to overcome the non - uniqueness problem and feasibility to discrete the surface coarsely with the sufficient calculation precision are examined through examples
第二章在聲波動理論基礎上，詳細地推導出對應于無限域和半無限域的外部振動聲輻射問題的邊界積分方程計算公式；根據fredholm積分理論，對利用邊界積分方程計算振動聲輻射問題過程中解的非唯一性的產生進行了分析和證明；改進了chief法以提高其克服解的非唯一性的有效性和可靠性；對不同條件下奇性系數的計算、強奇性積分的收斂性及其在變量替換時與普通積分的差異性、不同階奇性積分的計算、數值求積分等進行了研究；開發了三次樣條改進chief法計算軟體，並通過算例考核了該方法在特徵波數處克服解的非唯一性的有效性和在保證計算精度的前提下實現剖分粗化以提高計算效率的可行性。 -
The boundary integral equation for elasticity is derived through the general green ’ s formula and the corresponding fundamental solution. the paper represents the contact conditions, which are essential for the coupling of the boundary integral equations of the two different elastic contact bodies, in a local coordinate system properly chosen
利用廣義格林公式和基本解得出彈性問題的邊界積分方程，採用循環迭代的方法，通過尋求與接觸條件相協調的接觸邊界位移及面力增量來確定接觸區域的大小。 -
For the boundary nonlinear problems, such as elastic contact problem, the boundary displacements and boundary tractions are just the basic variables of the boundary integral equation, and the contact conditions can be satisfied with higher accuracy in bem ; therefore, the bem can be applied to solve the elastic contact problem more accurately
對于彈性接觸問題等邊界非線性問題而言，由於邊界位移和邊界面力正是邊界積分方程中的基本未知量，邊界元法能以更高精度滿足接觸條件，因此，邊界元法能更精確地求解彈性接觸問題。 -
The calculation of nearly singular integrals about points close to boundary in boundary integral equation
邊界積分方程中近邊界點幾乎奇異積分的計算 -
In this paper, we study the numerical solutions of these problems using galerkin boundary element, especially for the problem with open boundary such as the problems exterior to an open segment or an open curve in the plane. since the equivalent boundary integral equation for two dimensional laplace equation has constraint condition
因為把二維調和方程的邊值問題轉化為等價的邊界積分方程時帶有約束條件，用galerkin邊界元方法求解帶約束條件的變分方程，在數值離散時，我們採用lagrange乘子法處理約束條件。 -
Boundary integral equation
邊界積分方程 -
Local boundary integral equation method ( lbie ) developed recently is a new efficient and flexible numerical method
無網格局部邊界積分方程方法是一種近期發展起來的數值方法。 -
Based on the boundary integral equation method, the system equation of contact problems, including contact conditions, is established
利用邊界積分方程，結合接觸條件，形成接觸問題的系統方程。 -
Based on the analysis of previous work in detail, a scheme of a - posteriori error estimation is introduced into the local boundary integral equation method ( lbiem ), which is constructed with the difference between the raw solutions of lbiem and the post - processing solutions with taylor expansion and moving least square approximation ( mlsa )
通過對無網格演算法在誤差估計方面的工作分析，根據原始解和后處理解的不同，將一種誤差佑計的方案引入到局部邊界積分方程方法中，其中后處理解採用泰勒展開和移動最小二乘近似得到。 -
For these proposes, we chose electromagnetic boundary integral equation ( bie ) theory as the theoretical foundation, method of moments ( mom ) as numerical process and the multilevel fast multipole algorithm ( mlfma ) to accelerate the solving process and reduce memory requirement
為此，我們選擇了電磁場邊界積分方程（ bie ）理論作為理論基礎，以矩量法（ mom ）作為數值求解方法，並使用多層快速多極演算法（ mlfma ）來加速求解過程和降低存儲需求。 -
In this paper, the boundary problem of laplace equation is changed into the variational equation which is equivalent to the boundary integral equation. using linear element, it is solved by galerkin boundary element method
本文把laplace方程的邊值問題轉化為邊界積分方程后，通過與邊界積分方程等價的變分形式，採用線性單元，利用galerkin邊界元方法求解。 -
In this paper, firstly we present some results about of conventional bem, and multiple reciprocity method ( mrm ) for solving dynamics response of viscoelastic thin plate is given the whole plane expression and boundary integral equation for mrm, next we prove that the solution of the boundary integral equation obtained by mrm is the same as the one derived from the conventional fundamental solution of boundary value problem
本文首先給出了常規邊界元方法的一些結果及在laplace變換區域中得到了由重調和運算元基本解序列給出了粘彈性薄板動力響應問題的多重互易法（ mrm方法） 。並對粘彈性薄板的動力響應問題的mrm方法給出了收斂性分析，證明了mrm方法導出的邊界積分方程的解與邊值問題基本解導出的常規邊界方程的解是相同的。 -
This method need fewer computation time than connecting scheme ( cs ) based on boundary integral equation and can be apply more easily and more widely. all the numerical results listed in this dissertation have demonstrated the validity and high efficiency of our research works
該方法比以前用積分方程級聯法求解內部口徑導納矩陣需要更少的計算時間，並且能應用於具有更復雜腔體內部結構的含腔目標。
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