Titlebook: Optimal Shape Design for Elliptic Systems; Olivier Pironneau Book 1984 Springer-Verlag New York Inc. 1984 Design.Diskretisation.Elliptisch

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Elliptic Partial Differential Equations,In this chapter we review the main tools used to study elliptic partial differential equations (PDE): Sobolev spaces, variational formulations, and continuous dependence on the data.

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Problem Statement,In this chapter we.Concurrently, we introduce some concrete examples of optimal shape design problems, and we give some indication of the likely future developments of this field in industry.

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Optimization Methods,In this chapter we review the classical algorithms of optimization which are used in the numerical solution of shape design problems. For unconstrained minimization problems, the most widely used algorithm is the conjugate gradient method; however, it is best to begin with the method of steepest descent and Newton’s method.

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Other Methods,0], [61] and the method of characteristic functions [18], [63]. These methods lead naturally to numerical algorithms using the finite difference method. Thus, finite difference solutions of shape design problems as studied in [18], [48], [35] are also presented here. Finally, we also analyze the feasibility of the boundary element method.