Acceleration of shape optimization analysis using model order reduction by Karhunen-Loève expansion

This paper presents a method to reduce the computational time required to solve shape optimization problems. A volume minimization problem under the mean compliance constraint is chosen as an example of the shape optimization problem. To solve this problem, an iterative algorithm based on the H 1 gr...

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Bibliographic Details
Published in:Japan journal of industrial and applied mathematics 2022, Vol.39 (1), p.385-401
Main Authors: Tango, Shuichi, Azegami, Hideyuki
Format: Article
Language:English
Subjects:
Applications of Mathematics
Computational Mathematics and Numerical Analysis
Computing time
Connecting rods
Eigenvalues
Eigenvectors
Elastic bodies
Iterative algorithms
Iterative methods
Mathematics
Mathematics and Statistics
Model reduction
Modulus of elasticity
Optimization
Original Paper
Random variables
Shape optimization
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Summary:This paper presents a method to reduce the computational time required to solve shape optimization problems. A volume minimization problem under the mean compliance constraint is chosen as an example of the shape optimization problem. To solve this problem, an iterative algorithm based on the H 1 gradient method is considered as a conventional approach. In this study, we attempt to use a method of model order reduction for solving the linear elasticity problem based on the idea by Karhunen-Loève expansion (KLE). We consider the displacements obtained by the conventional method to be sampling data of a random variable; the orthonormal bases of KLE are defined as eigenfunctions of the eigenvalue problem obtained as the optimality condition of the variance maximization problem for the random variable. The feasibility of the proposed method is illustrated by testing the numerical scheme to a linear elastic body of the connecting rod type.
ISSN:0916-7005
1868-937X
DOI:10.1007/s13160-021-00489-5