Finite Element Approximation for Optimal Shape Design: Theory and ApplicationsExplains how to speed the optimal shape design process using a computer. Outlines the problems inherent in optimal shape design and discusses methods of their solution. Concentrates on finite element approximation and describes numerical realization of optimization techniques. Treats optimal design problems via the optimal control theory when the state systems are governed by variational inequalities. Provides useful background information, followed by numerous approaches to optimal shape design, all supported by illustrative examples. Appendices provide algorithms and numerous examples and their calculations are included. |
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Page 91
... solving optimal shape design prob- lems by applying nonlinear programming software Most of the general purpose codes ... solve ( 5.39 ) using the " black - box " optimization code ( which we call OPTIMIZER ) we need the following modules ...
... solving optimal shape design prob- lems by applying nonlinear programming software Most of the general purpose codes ... solve ( 5.39 ) using the " black - box " optimization code ( which we call OPTIMIZER ) we need the following modules ...
Page 273
... solve elasticity problems by using SSOR2 instead of SSOR ( resulting method CG - SSOR2 ( DP2 ) ) . It should be possible to extend the method to solve ( DP3 ) also . AI.4 . Numerical examples We consider four numerical examples of ...
... solve elasticity problems by using SSOR2 instead of SSOR ( resulting method CG - SSOR2 ( DP2 ) ) . It should be possible to extend the method to solve ( DP3 ) also . AI.4 . Numerical examples We consider four numerical examples of ...
Page
... solve them , the authors place emphasis on problems governed by elliptic variational inequalities and on the finite element method . The appendices contain algorithms which readers may find useful . This book will be of particular ...
... solve them , the authors place emphasis on problems governed by elliptic variational inequalities and on the finite element method . The appendices contain algorithms which readers may find useful . This book will be of particular ...
Contents
Preliminaries | 1 |
Abstract setting of optimal shape design problem and | 28 |
Optimal shape design of systems governed by a unilateral | 53 |
Copyright | |
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Common terms and phrases
algorithm Appendix applied approximation boundary value problem C₁ Céa Computer constraints contact problems convex convex set cost functional defined denote design sensitivity analysis differentiable discrete domain elastic element method exist a subsequence Figure Find finite element finite element method follows formula given Glowinski Gm(a H¹(Î Haslinger Haug Hlaváček Ir(an ITERATION jEJk ji Eli Komkov Lagrange multipliers Lemma lim inf lim sup linear Lipschitz continuous lower semicontinuous matrix minimization Nečas Neittaanmäki nodes nonlinear programming nonsmooth Numerical results obtain optimal control optimal design optimal pair optimal shape design parameter Pironneau Proof results for Example Section sequence shape design problems Shape optimization Sokolowski solves P(a structural design structural optimization subgradient subset T(Un T₁ Theorem triangulation un(an variational inequality vector w₁ Zolesio г₁