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Title of Thesis

Application of Sobolev Gradients to Poisson-Boltzmann Systems

Author(s)

Abdul Majid

Institute/University/Department Details
Department Of Mathematics / Lahore University of Management Science, Lahore
Session
2010
Subject
Mathematics
Number of Pages
135
Keywords (Extracted from title, table of contents and abstract of thesis)
Application, Sobolev, Gradients, Poisson, Boltzmann, Systems

Abstract
Available

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S. No. Chapter Title of the Chapters Page Size (KB)
1 0 CONTENTS

 

1
166 KB
2

1

POISSON-BOLTZMANN SYSTEM

1.1 PBE
1.2 Derivation
1.3 Energy functional

13
285 KB
3 2 SOBOLEV GRADIENT

2.1 Sobolevgradient Approach
2.2 Sobolev Spaces
2.3 Minimization Problem
2.4 Weak Derivatives And Gradients
2.5 Preconditioner And Condition Number
2.6 Finited Difference
2.7 Finite Element

21
376 KB
4 3 NUMERICAL METHODS

3.1 LU Decomposition (Crout factorization)
3.2 Conjugate Gradient Method
3.3 Steepest Descent
3.4 Newton's Method
3.5 Nonlinear Multigrid FAS
3.6 Numerical Setting And Implementation
3.7 Computing

41
321 KB
5 4 APPLICATION TO LINEAR PBE

4.1 A Test Problem
4.2 Finite Difference
4.3 Finite Element

59
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6

5

APPLICATION TO NONLINEAR PBE

5.1 A Test Problem
5.2 Finite Difference
5.3 Finite Element

71
412 KB
7

6

CONCLUSION AND FUTURE WORK

6.1 Conclusion
6.2 Future Work

91
191 KB
8

7

APPENDICES & BIBLIOGRAPHY

 

95
246 KB