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A boundary‐perturbation finite element approach for shape optimization
Author(s) -
Givoli Dan,
Demchenko Tatyana
Publication year - 2000
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/(sici)1097-0207(20000210)47:4<801::aid-nme798>3.0.co;2-p
Subject(s) - shape optimization , finite element method , perturbation (astronomy) , boundary knot method , mathematical optimization , boundary value problem , mixed finite element method , extended finite element method , mathematics , partial differential equation , boundary (topology) , obstacle problem , boundary element method , method of fundamental solutions , optimization problem , mathematical analysis , computer science , physics , engineering , structural engineering , quantum mechanics
A numerical method is proposed for the efficient solution of shape optimization problems, which combines the boundary perturbation technique and finite element analysis. The method is computationally efficient in that it requires a number of finite element analyses with a fixed geometry , as opposed to standard shape optimization which requires re‐analysis with varying geometry. The application of the method to general shape optimization is considered. In addition, a special optimization scheme is devised for a class of problems governed by linear partial differential equations. The performance of the method is illustrated via an example which involves acoustic wave scattering from an obstacle. Copyright © 2000 John Wiley & Sons, Ltd.