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1 
A TV regularization method for the convectiondominated diffusion equations. / CUHK electronic theses & dissertations collectionJanuary 2013 (has links)
對流佔優擴散問題一直是一個俱有挑戰性的問題。眾所週知，解可能在邊界或者內部表現出局部斷層。傳統的數值解法在解決對流佔優擴散問題時不夠穩定和精確。因此有很多空間穩定技巧被提出和學習。 / 在這篇論文中，我們設計了一個全變分規則化方法來解對流佔優擴散方程。首先，選取一個較小的測試函數空間構造一個欠定模型。然後，通過附加條件最小化全變分來計算唯一解。這個想法是基於離散化解雙曲形偏微分方程的全變分遞減原理。為了實現這個全變分規則化方法，我們需要找出相應的拉格郎日方程的最優條件，並當做時間依賴方程進行求解。論文中涉及了三個運算符拆分方法，PeacemanRachford方法，DouglasRachford方法和Theta方法。數值實驗證明我們的方法可以準確的描繪出對流佔優擴散問題的邊界和內部斷層現象，因此可以在擴散系數很小的時候提供可靠的數值結果。 / The convectiondominated diffusion problem has been a challenge problem for a long time. It is well known that the solution may exhibit localized layer on the boundary or in the interior. Conventional numerical schemes for the convectiondominated diffusion problem are lacking in both stability and accuracy. Therefore many spatial stabilization techniques have been proposed and studied. / In this thesis, we devise a TV regularization method for solving convectiondominated diffusion equations. First, we form an underdetermined system by choosing a small test function space. Then, we find the unique solution by minimizing the total variation. The idea is based on the fact that total variation diminishing (TVD) is a property of certain discretization schemes used to solve hyperbolic partial differential equation. To implement this TV regularization approach, we find the optimality condition of the corresponding Lagrange function for the minimization problem, and then solve it as a time dependent problem. Three operator splitting methods, the PeacemanRachford method, the DouglasRachford method and the Theta scheme are studied. The numerical experiments demonstrate that our scheme can accurately capture the boundary and internal layer for the convectiondominated problem, and therefore provide reliable numerical result for small diffusivity. / Detailed summary in vernacular field only. / Detailed summary in vernacular field only. / Zhang, Qi. / Thesis (M.Phil.)Chinese University of Hong Kong, 2013. / Includes bibliographical references (leaves 56[58]). / Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Abstracts also in Chinese. / Chapter 1  Introduction  p.6 / Chapter 2  TV scheme  p.9 / Chapter 2.1  TV regularization  p.9 / Chapter 2.1.1  The underdetermined system  p.10 / Chapter 2.1.2  The minimization problem  p.10 / Chapter 2.2  The optimality conditions  p.11 / Chapter 2.3  Discrete version  p.14 / Chapter 3  Numerical schemes  p.17 / Chapter 3.1  PeachmentRachford method  p.17 / Chapter 3.2  DouglasRachford method  p.18 / Chapter 3.3  Theta scheme  p.19 / Chapter 3.4  Two systems  p.22 / Chapter 3.4.1  System 1  p.23 / Chapter 3.4.2  System 2  p.25 / Chapter 3.5  Matrix representation  p.26 / Chapter 4  Numerical examples  p.29 / Chapter 4.1  Scenario  p.30 / Chapter 4.1.1  Initial condition  p.30 / Chapter 4.1.2  Notation  p.30 / Chapter 4.1.3  Parameter  p.31 / Chapter 4.2  Experiment 1  p.32 / Chapter 4.3  Experiment 2  p.38 / Chapter 4.4  Experiment 3  p.42 / Chapter 4.5  Experiment 4  p.48 / Chapter 5  Conclusion  p.55

2 
Projective solution of differential equations.Csendes, Zoltan Joseph. January 1972 (has links)
No description available.

3 
Asymptotic behavior of solutions to x'(t)+p(t)x(t)=0Holland, Charles Jordan 08 1900 (has links)
No description available.

4 
The existence and structure of the solution of y ́= Aya + BxbBuchanan, Angela Marie. January 1973 (has links)
No description available.

5 
Projective solution of differential equations.Csendes, Zoltan Joseph. January 1972 (has links)
No description available.

6 
The existence and structure of the solution of y ́= Aya + BxbBuchanan, Angela Marie. January 1973 (has links)
No description available.

7 
Numerical solution of integral equation of the second kind.January 1998 (has links)
by ChiFai Chan. / Thesis (M.Phil.)Chinese University of Hong Kong, 1998. / Includes bibliographical references (leaves 5354). / Abstract also in Chinese. / Chapter Chapter 1  INTRODUCTION  p.1 / Chapter §1.1  Polynomial Interpolation  p.1 / Chapter §1.2  Conjugate Gradient Type Methods  p.6 / Chapter §1.3  Outline of the Thesis  p.10 / Chapter Chapter 2  INTEGRAL EQUATIONS  p.11 / Chapter §2.1  Integral Equations  p.11 / Chapter §2.2  Numerical Treatments of Second Kind Integral Equations  p.15 / Chapter Chapter 3  FAST ALGORITHM FOR SECOND KIND INTEGRAL EQUATIONS  p.20 / Chapter §3.1  Introduction  p.20 / Chapter §3.2  The Approximation  p.24 / Chapter §3.3  Error Analysis  p.35 / Chapter §3.4  Numerical Examples  p.40 / Chapter §3.5  Concluding Remarks  p.51 / References  p.53

8 
Computation of the stresses on a rigid body in exterior stokes and oseen flowsSchuster, Markus 11 June 1998 (has links)
This paper is about the computation of the stresses on a rigid body from a knowledge
of the far field velocities in exterior Stokes and Oseen flows. The surface of the
body is assumed to be bounded and smooth, and the body is assumed to move with
constant velocity. We give fundamental solutions and derive boundary integral equations
for the stresses. As it turns out, these integral equations are singular, and their
null space is spanned by the normal to the body. We then discretize the problem by
replacing the body by an approximating polyhedron with triangular faces. Using a
collocation method, each integral equation delivers a linear system. Since its matrix
approximates a singular integral operator, the matrix is illconditioned, and the solution
is unstable. However, since we know that the problem is uniquely solvable in
the hyperspace orthogonal to the normal, we use regularization methods to get stable
solutions and project them in the normal direction onto the hyperspace. / Graduation date: 1999

9 
A computer subroutine for the numerical solution of nonlinear Fredholm equationsTieman, Henry William 25 April 1991 (has links)
Graduation date: 1991

10 
Small prime solutions of some ternary equations蕭偉泉, Siu, Waichuen. January 1995 (has links)
published_or_final_version / Mathematics / Master / Master of Philosophy

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