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Graduate School
Adaptive Systems Advanced
Hideyuki AZEGAMI Professor
Department: Graduate School of Information Science
Class Time:  2013 Spring Friday 
Recommended for:  Informatics students majoring in complex system science 
Course Overview
Course Aims
This course focuses on adapting phenomena of distributed parameter systems (systems with an infinite degree of freedom) such as elastic continua and flow fields which are modeled as boundary value problems of partial differential equations. Optimization problems of domains in which boundary value problems are defined become mathematical representations of adapting phenomena. We aim to understand the mathematical theories and methods to solve numerically the optimization problems.
Key Features
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Syllabus
Course Objectives
Understanding the methods for changing phenomena obtained in numerical analysis into desired outcome by using mathematics.
Lesson Outline
Each chapter consists of two halves. The first half consists of lectures using slides. The second half sets aside some time to solve exercise problems. The problems will be reviewed after that.
Course Requirements
Basic foreknowledge on analytics and linear algebra is recommended.
Related Resources
Arora, J. S. : Introduction to optimum design, McGrawHill, 1989.
Rao, S. S.: Engineering optimization: theory and practice, 3rd ed., John Wiley & Sons, 1996.
Haftka, R. T. and Gürdal, Z.: Elements of structural optimization, 3rd ed., Kluwer Academic, 1992.
Brezis Haim, Analyse Fonctionnelle –Theorie et Applicationes, Dunod, 2002
Yosida, K. : Functional analysis, 6th ed, Springer, (1980)
Cea, J. : Numerical methods of shape optimal design, Edited by Haug, E. J. and Cea, J., Optimization of Distributed Parameter Structures, Vol. 2, Sijthoff & Noordhoff, Alphen aan den Rijn, (1981), pp. 10491088.
Pironneau, O.: Optimal Shape Design for Elliptic Systems, SpringerVerlag, New York, (1984).
Armijo, L.: Minimization of functions having Lipschitzcontinuous first partial derivatives, Pacific Journal of Mathematics, 16, (1966), pp. 13.
Y. C. Juan (Translation by Y .Ohashi, S. Murakami, N. Kamiya)::Kotai no Rikigaku/Riron, BaifuuKan, 1970
Hughes,T.J.R : The Finite element method : Linear static and dynamic finite element analysis, PrenticeHall, (1987)
Ciarlet, P. G. : Handbook of Numerical Analysis, Vol. 2, Finite Element Methods (Part1), edited by Ciarlet, P. G. and Lions, J. L., NorthHolland, (1991).
Kardestuncer, H. editorinchief : Finite element handbook, McGrawHill, (1987)
Pironneau, O.: Optimal Shape Design for Elliptic Systems, SpringerVerlag, New York, (1984).
Strang, Gilbert and Fix, George J. : An Analysis of the Finite Element Method, PrenticeHall, Englewood Cliffs, New Jersey, (1973)
Zienkiewicz, O. C. and Taylor, R. L. : The Finite Element Method  Fourth Edition , Volumes 1 and 2, McGrawHill, London, (1989)
Hughes, Thomas J. R. : The Finite Element Method, PrenticeHall, Englewood Cliffs, New Jersey, (1987)
Sneddon, Ian N. : Fourier Transforms, McGrowHill, New York, (1951).
Cea, J., Numerical methods of shape optimal design, Optimization of Distributed Parameter Structures, edited by Haug, E. J. and Cea, J., Sijthoff & Noordhoff, Alphen aan den Rijn, volume 2, 1981, pp. 10491088.
Zolésio, J. P., Domain variational formulation for free boundary problems , ibid, pp. 11521194.
Sokolowski, J. and Zolésio, J. P., Introduction to Shape Optimization: Shape Sensitivity Analysis, SpringerVerlag, New York, 1991.
Haug E. J., Choi, K. K. and Komkov, V. : Design Sensitivity Analysis of Structural Systems, Academic Press, Orland, (1986).
Pironneau, O.: Optimal Shape Design for Elliptic Systems, SpringerVerlag, New York, (1984).
Cea, J. : Numerical methods of shape optimal design, Edited by Haug, E. J. and Cea, J., Optimization of Distributed Parameter Structures, Vol. 2, Sijthoff & Noordhoff, Alphen aan den Rijn, (1981), pp. 10491088.
Zolésio, J. P. : The material derivative (or speed) method for shape optimization, ibid., pp. 10891151.
Azegami, H., Shimoda, M., Katamine, E. and Wu, Z. Q. : A domain optimization technique for elliptic boundary value problems, Computer Aided Optimization Design of Structures IV, Structural Optimization, edited by Hernandez, S. and ElSayed, S. and Brebbia, C. A., Computational Mechanics Publications, Southampton (1995), pp. 5158.
Azegami, H., Kaizu, S., Shimoda, M. and Katamine, E. : Irregularity of shape optimization problems and an improvement technique, Computer Aided Optimization Design of Structures V, edited by Hernandez, S. and Brebbia, C. A., Computational Mechanics Publications, Southampton (1997), pp. 309326.
Azegami, H. : Solution to boundary shape identification problems in elliptic boundary value problems using shape derivatives, Inverse Problems in Engineering Mechanics II, edited by Tanaka, M. and Dulikravich, G. S., Elsevier, Tokyo, (2000), pp. 277284.
Azegami, H., Yokoyama, S. and Katamine, E. : Solution to shape optimization problems of continua on thermal elastic deformation, Inverse Problems in Engineering Mechanics III, edited by Tanaka, M. and Dulikravich, G. S., Elsevier, Tokyo, (2002), pp. 6166
Course Schedule
Session  Contents 

1  Guidance 
2  Chapter 1: the Basics of Nonlinear Optimization Theory  Lagrange Multiplier Method  Kuhn Tucker Condition  The Duality Theorem 
3  
4  Chapter 2: the Basics of Optimum Design  the State Equation  Gâteaux derivative, Fréchet derivative  Gradient  the Ajoint Variable method 
5  Chapter 3: Nonlinear Programming Method  the Gradient Method  Newton Method  the Sequential Quadratic Programming Method 
6  Chapter 4: Variational Principle and the Basics of Functional Analysis  Variational Principle  Linear space, Banach space, Hilbert Space  the Dual space  Riesz representation theorem 
7  
8  Chapter 5: The Boundary Value Problem of the Partial Differential Equation  Poisson Problem  the Abstract Variational Problem  LaxMilgram Theory  the Minimum Variational Problem  the Linear Elastic Problem  Stokes Problem  the Saddle Point Variational Problem  the Dynamic Linear Elastic Problem  NavierStokes Problem 
9  
10  Chapter 6: the Finite Element Method  Galerkin Method  the Finite Element Method  the Isoparametric Element  Gaussian Quadrature Rule  the Error Estimation 
11  
12  Chapter 7: Shape Optimization Problem  the Abstract Optimization Problem  the Abstract Gradient Method  the Optimum Shape Variation Problem  the Shape Derivative  the H1 Gradient Method  the Linear Elastic Problem  Stokes Problem  the Dynamic Linear Elastic Problem  NavierStokes Problem 
13  
14  Chapter 8: Topology Optimization Problem  the Optimum Density Variation Problem  the Linear Density Problem  the H1 Gradient Method 
15  Practice with a 3dimensional input device 
Grading
Grading will be based on the final examination.
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Class Materials
Lecture Handouts
Note: All files are in Japanese.
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Page last updated February 11, 2009
The class contents were most recently updated on the date indicated. Please be aware that there may be some changes between the most recent year and the current page.