helmholtz equation 中文意思是什麼
helmholtz equation
解釋
亥姆霍茲方程式；黑目合茲方程式-
A class of nonlinear local orthogonal transformations for helmholtz equation
方程的一類非線性局部正交變換 -
A new coupled - mode theory based on scalar modes is presented for the anisotropic waveguide with random disturbance via helmholtz equation and a modified dielectric tensor
摘要從亥姆霍茲方程出發，得到了各向異性光波導在弱導近似下的耦合模理論。 -
It also roundly researched the solution of the helmholtz equation in the circumrotating ellipsoidal coordinates, and discussed how to calculate the solution of the electro - magnetic field in the circumrotating ellipsoidal coordinates using special functions, and researched circumrotating ellipsoidal cavity ’ s latent value and quality parameter using arithmetic simulation, finally we compared the ellipsoidal cavity with the spheriform cavity. the main content of this thesis are as following : 1. calculated the distribution of the electro - magnetic field inside the ellipsoidal cavity based on maxwell equations and boundary conditions, and confirmed the syntonic mode inside the ellipsoidal cavity using arithmetic methods
本文從maxwell方程及其邊界條件求解出橢球腔內的電磁場分佈，較為全面的研究了旋轉橢球坐標系下赫姆霍茲方程的解的問題，討論了用特殊函數來求解旋轉橢球坐標系下電磁場的解，並通過數值模擬研究了旋轉橢球諧振腔的本徵值和品質因數，並和球形諧振腔做了比較，主要內容為: 1 .用maxwell方程及其邊界條件求解出橢球腔內的電磁場分佈，並且分析了橢球腔內的諧振模式。 -
In solving the helmholtz equation in the acoustical waveguides with a curved bottom, slow convergence may occurs when the linear local orthogonal transformation is adopted. in this paper, a class of nonlinear local orthogonal transformations ( nlot ) is proposed. it is an approach to improve the slow convergence mentioned above
本文嘗試通過在深度方向選取非線性局部正交變換，將曲底求解區域化為平坦求解區域，然後求解helmholtz方程的辦法，來改善用線性（深度方向）局部正交變換時，步進求解時會出現的局部收斂慢的問題。 -
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。 -
Base on helmholtz integral equation, the incoherent scattering of plane wave from rough cone - shaped surface is derived with the far field theory and stationary phase method. and the incoherent scattering of plane wave from rough conical surface is also derived with shadowing function when the the radius of principal
最後計算並分析了入射光為= 0 . 48 m時，粗糙錐面的平面波散射特性，考察了入射波和散射波的幾何關系，偏振態以及粗糙面統計參量等對散射強度的影響。 -
The general forms of the transformed new equation and the coefficients are also given. numerical simulations show that it can be efficiently used in solving the helmholtz equation
數值模擬表明，適當地選取某些非線性局部正交變換來求解在曲底區域中的helmholtz方程，確實可以改善數值求解的效率。 -
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。 -
Essential to their utility is the requirement that the evolution of the basic functions through the propagation environment constitutes a simplified problem with an exact or approximate closed form solution to the original wave equation. the evolution of a spatial fourier harmonic through a homogeneous medium is governed by a reduced wave equation, obtained by applying the fourier transform to the helmholtz equation, with a simple and well - known solution - the plane wave
這些方法均採用一組具有全局特性的基本函數對波場進行分解，如占據整個空間的富氏調諧函數或充滿各個方向的dirac函數（點源） ，並通過求解基本函數滿足波動方程的精確解或近似解來達到波場外推的目的。 -
On the base of mathematical domain decomposition method ( ddm ), this paper investigates systematically the quasi - static problems based on laplace equation, the transmission problems in waveguide based helmholtz equation and the three - dimensional scattering and radiation problems based on maxwell equations. the theoretical system is built for the further exploration of ddm in electromagnetic problems
本文在區域分解法已有的數學基礎上，從基於laplace方程的準靜態問題，到基於helmholtz方程的波導傳輸問題以及基於maxwell方程的三維散射輻射問題，系統地探討了該方法在電磁領域中的應用，為進一步擴展應用研究建立了理論體系。 -
First of all, the algorithm base on the boundary problem of helmholtz equation and finite - difference technique, calculate the field in “ cold ” cavity and disperse the helmholtz equation, as a result of the formula : ax = x. secondly, according to the eigenvalue of matrix theory and applied iterative methods, eigenmode adopt a numerical approach which allows the improved chebyshev polynomial iteration which based on the power method to extract the isolated eigenmode in the spectrum. finally, we resolve the problem of compatibility in software and insert the eigenmode module into the chipic which will have the function of eigenmode analysis
具體的說: （ 1 ）首先以電磁理論中的亥姆霍茲方程的邊值問題理論和計算電磁學中的有限差分法為基礎，計算冷腔中的場分佈並離散亥姆霍茲方程，得到標準的本徵值問題: ax = x ; （ 2 ）然後根據矩陣理論中的eigenvalue問題和數值計算中的迭代方法，採用改進后的chebyshev多項式，在power迭代法的基礎上對ax = x進行多項式迭代，實現對頻譜中孤立本徵模的萃取; （ 3 ）最後將用fortran語言編制的eigenmode模塊加入到chipic軟體中，解決了eigenmode模塊與chipic主代碼的兼容問題，從而實現了chipic軟體的模式分析功能。 -
2 ) in order to solve the scattering and diffraction of sound radiation, in this dissertation, based on helmholtz equation and its boundary equations, modeling of three - dimensional fem is given for computing low frequency sound transfer function in small enclosures
2 ）為解決聲音在傳播過程中所發生的散射和衍射現象，本文基於有源helmholtz方程及其邊界條件，建立了求解小尺度封閉空間內低頻聲傳遞函數的三維有限元模型。 -
The fft of helmholtz equation on the regular domain is studied. and the multifrontal algorithm is used to solve the matrix equations in computational electromagnetics. finally, the finite - difference approximate forms of maxwell equations and the despres transmission condition are discussed
為了充分提高演算法的計算效率，研究了規則區域上helmholtz方程的fft快速演算法，以及有效地將多波前演算法引入計算電磁學領域用於求解差分稀疏矩陣方程。 -
A new approach, the multipole theory ( mt ) method, is briefly described for analysis of waveguide eigenvalue problems. the essential concept is to represent the solution of the waveguide partial differential equation by the generalized mt formula of 2 - d helmholtz equation. the applied rules and the procedure of the mt method are also introduced. by calculating and analyzing some engineering problems, it is shown that the mt method is an effective approach for analysis of waveguide eigenvalue problems
本文利用多極理論分析波導本徵值問題.給出用多極理論分析波導本徵值問題的使用規則和實施方法.實例計算結果表明，用多極理論分析波導本徵值問題，不僅具有較高的計算精度，而且可以很方便地應用於波導工程問題的設計與計算，多極理論是一種有效的波導本徵值分析方法 -
The solving steps are as follows : the field is divided into three regions by the cylindrical surface of the finite - length cylinder and the location of the delta - coils. because " the surface current source is placed at the interface, the non - homogenous restricted equation on the magnetic vector potential is transformed into the homogenous helmholtz equation. by using the method of separation of variables to solve equation and according to the interface conditions and the condition at infinity to determine the unknown constants, the expressions for the magnetic vector potential of the three regions are solved out
在求解過程中，假定放置式圓柱線圈是由無窮多個對稱圓環線圈密饒而成，首先求解含有有限長磁芯的通電對稱圓環線圈的電磁場：以有限長圓柱磁芯的側面和圓環線圈所在圓柱面為分界面將場域劃分為三個小區域，由於場源放置在內邊界面上，使得關于矢量磁位的非齊次約束方程轉化成齊次亥姆霍茲方程，利用分離變量法求解，根據分界面鄭州大學碩十研究生畢業論文摘要條件以及無限遠條件確定待定常數，從而得到各場區矢量磁位的表達式。
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