Level Set Methods for Optimization Problems Involving Geometry and Constraints I. Frequencies of a Two-Density Inhomogeneous Drum

Stanley J. Osher, Fadil Santosa

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474 Scopus citations

Abstract

Many problems in engineering design involve optimizing the geometry to maximize a certain design objective. Geometrical constraints are often imposed. In this paper, we use the level set method devised in (Osher and Sethian, J. Comput. Phys. 79, 12 (1988)), the variational level set calculus presented in (Zhao et al., J. Comput. Phys. 127, 179 (1996)), and the projected gradient method, as in (Rudin et al., Physica D. 60, 259 (1992)), to construct a simple numerical approach for problems of this type. We apply this technique to a model problem involving a vibrating system whose resonant frequency or whose spectral gap is to be optimized subject to constraints on geometry. Our numerical results are quite promising. We expect to use this approach to deal with a wide class of optimal design problems in the future.

Original languageEnglish (US)
Pages (from-to)272-288
Number of pages17
JournalJournal of Computational Physics
Volume171
Issue number1
DOIs
StatePublished - Jul 20 2001

Bibliographical note

Funding Information:
1 The research of SJO is supported in part by DARPA/NSF VIP Grant NSF DMS9615854, NSF DMS0074735 and ARO DAAG 55-98-1-0323. The research of FS is supported in part by an AFOSR/MURI Grant to the University of Delaware.

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