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 viii
... appendices in this book . Appendix I is devoted to the numerical algorithms for solving unilateral boundary value problems . We make a comparison of efficiency between different algorithms . In Appendix II the differentiation of ...
... appendices in this book . Appendix I is devoted to the numerical algorithms for solving unilateral boundary value problems . We make a comparison of efficiency between different algorithms . In Appendix II the differentiation of ...
Page xi
... Appendix I. Algorithms for FEM 268 AI.1 . Introduction 268 AI.2 . Iterative methods for solving ( DP1 ) ..269 AI.2.1 . SOR - method ... 269 AI.2.2 . Conjugate gradient and preconditioning ... 270 AI.2.3 . Multigrid method ... ..271 AI.3 ...
... Appendix I. Algorithms for FEM 268 AI.1 . Introduction 268 AI.2 . Iterative methods for solving ( DP1 ) ..269 AI.2.1 . SOR - method ... 269 AI.2.2 . Conjugate gradient and preconditioning ... 270 AI.2.3 . Multigrid method ... ..271 AI.3 ...
Page 94
... ( Appendix IV ) or subgradient method ( Appendix III ) has been applied as an optimizer . Nonlinear constraints , if they appear , are linearized in the usual manner . FUN . This module computes the value of I and its gradient at point a ...
... ( Appendix IV ) or subgradient method ( Appendix III ) has been applied as an optimizer . Nonlinear constraints , if they appear , are linearized in the usual manner . FUN . This module computes the value of I and its gradient at point a ...
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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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