PDE CONSTRAINED GEOMETRY OPTIMIZATION WITH RANDOM DATA

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NEHRANI A.; KEYANPOUR M.

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Paper Information

Journal: Journal of Operational Research in its Applications Year:2015 | Volume:12 | Issue:2 (45) Page(s): 37-59

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Information Journal Paper

Title

PDE CONSTRAINED GEOMETRY OPTIMIZATION WITH RANDOM DATA

Author(s)

NEHRANI A. | KEYANPOUR M. | Issue Writer Certificate

Keywords

GEOMETRY OPTIMIZATIONQ2

STOCHASTIC PDEQ2

UNCERTAINTY QUANTIFICATIONQ2

OPTIMAL CONTROLQ2

Abstract

The present paper considers geometric shape optimization of structures that are modelled by PDEs with random data. Random data appears in inputs and parameters of the PDE. Theoretical bases are presented, and the perturbation of the identity method is applied for transforming the shape optimization problem into a fixed domain and then formulated as a stochastic OPTIMAL CONTROL problem. Random data is taken as random fields that are approximated by Karhunen-Loeve expansion. UNCERTAINTY QUANTIFICATION is performed by applying non-intrusive techniques e.g., stochastic collocation method. Gradient method is applied for optimization. Numerical result is represented in order to illustrate the applicability of the proposed method.

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APA: Copy

NEHRANI, A., & KEYANPOUR, M.. (2015). PDE CONSTRAINED GEOMETRY OPTIMIZATION WITH RANDOM DATA. JOURNAL OF OPERATIONAL RESEARCH AND ITS APPLICATIONS (JOURNAL OF APPLIED MATHEMATICS), 12(2 (45)), 37-59. SID. https://sid.ir/paper/164657/en

Vancouver: Copy

NEHRANI A., KEYANPOUR M.. PDE CONSTRAINED GEOMETRY OPTIMIZATION WITH RANDOM DATA. JOURNAL OF OPERATIONAL RESEARCH AND ITS APPLICATIONS (JOURNAL OF APPLIED MATHEMATICS)[Internet]. 2015;12(2 (45)):37-59. Available from: https://sid.ir/paper/164657/en

IEEE: Copy

A. NEHRANI, and M. KEYANPOUR, “PDE CONSTRAINED GEOMETRY OPTIMIZATION WITH RANDOM DATA,” JOURNAL OF OPERATIONAL RESEARCH AND ITS APPLICATIONS (JOURNAL OF APPLIED MATHEMATICS), vol. 12, no. 2 (45), pp. 37–59, 2015, [Online]. Available: https://sid.ir/paper/164657/en

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