Abstract
This paper is concerned with a second-order numerical method for shape optimization problems. The first variation and the second variation of the objective functional are derived. These variations are discretized by introducing a set of boundary-value problems in order to derive the second-order numerical method. The boundary-value problems are solved by the conventional finite-element method.
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Communicated by N. V. Banichuk
The authors would like to express their thanks to Mr. T. Masanao, who was an undergraduate student, for his cooperation and comments. They also thank Professor Y. Sakawa of Osaka University for his encouragement.
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Goto, Y., Fujii, N. Second-order numerical method for domain optimization problems. J Optim Theory Appl 67, 533–550 (1990). https://doi.org/10.1007/BF00939648
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DOI: https://doi.org/10.1007/BF00939648