Introduction to Shape Optimization: Theory, Approximation and Computation (Advances in Design and Control v. 7)
By: R.A.E. Makinen (author), J. Haslinger (author), Ralph Smith (series_editor)Paperback
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The efficiency and reliability of manufactured products depend on, among other things, geometrical aspects; it is therefore not surprising that optimal shape design problems have attracted the interest of applied mathematicians and engineers. This self-contained, elementary introduction to the mathematical and computational aspects of sizing and shape optimization enables readers to gain a firm understanding of the theoretical and practical aspects so they may confidently enter this field.
J. Haslinger is a Professor in the Department of Physics of Metals at Charles University in Prague. He is the author or co-author of five monographs and over 110 publications in scientific journals. His research interests include the approximation of elliptic equations and inequalities, contact mechanics, nonsmooth analysis, approximation of differentialinclusions, and shape and material optimization. R. A. E. Makinen is a Professor in the Department of Mathematical Information Technology at the University of Jyvaskyla in Finland. He has also acted as a modeling specialist at Numerola Oy (Inc.). Professor Makinen is the author or co-author of over 50 publications in scientific journals and conference proceedings. His research interests include structural optimization, especially shape optimization; numerical solution of partial differential equations; and numerical software.
Preface; Notation; Introduction; Part I. Mathematical aspects of sizing and shape optimization. 1. Why the mathematical analysis is important; 2. A mathematical introduction to sizing and shape optimization; Part II. Computational aspects of sizing and shape optimization. 3. Sensitivity analysis; 4. Numerical minimization methods; 5. On automatic differentiation of computer programs; 6. Fictitious domain methods in shape optimization; Part III. Applications. 7. Applications in elasticity; 8. Fluid mechanical and multidisciplinary applications; Appendix A. Weak formulations and approximations of elliptic equations and inequalities; Appendix B. On parametrizations of shapes and mesh generation; Bibliography; Index.
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- ID: 9780898715361
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