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GPU-Enabled Isogometric Topology Optimization with Bėzier Element Stiffness Mapping

by Xuesong Li1, Shuting Wang1,2, Nianmeng Luo1,*, Aodi Yang1, Xing Yuan1, Xianda Xie2,*

1 School of Mechanical Science and Engineering, Huazhong University of Science and Technology, Wuhan, 430074, China
2 School of Advanced Manufacturing, Nanchang University, Nanchang, 330031, China

* Corresponding Authors: Nianmeng Luo. Email: email; Xianda Xie. Email: email

Computer Modeling in Engineering & Sciences 2025, 142(2), 1481-1514. https://doi.org/10.32604/cmes.2024.058798

Abstract

Due to the high-order B-spline basis functions utilized in isogeometric analysis (IGA) and the repeatedly updating global stiffness matrix of topology optimization, Isogeometric topology optimization (ITO) intrinsically suffers from the computationally demanding process. In this work, we address the efficiency problem existing in the assembling stiffness matrix and sensitivity analysis using Bėzier element stiffness mapping. The Element-wise and Interaction-wise parallel computing frameworks for updating the global stiffness matrix are proposed for ITO with Bėzier element stiffness mapping, which differs from these ones with the traditional Gaussian integrals utilized. Since the explicit stiffness computation formula derived from Bėzier element stiffness mapping possesses a typical parallel structure, the presented GPU-enabled ITO method can greatly accelerate the computation speed while maintaining its high memory efficiency unaltered. Numerical examples demonstrate threefold speedup: 1) the assembling stiffness matrix is accelerated by 10× maximumly with the proposed GPU strategy; 2) the solution efficiency of a sparse linear system is enhanced by up to 30× with Eigen replaced by AMGCL; 3) the efficiency of sensitivity analysis is promoted by 100× with GPU applied. Therefore, the proposed method is a promising way to enhance the numerical efficiency of ITO for both single-patch and multiple-patch design problems.

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APA Style
Li, X., Wang, S., Luo, N., Yang, A., Yuan, X. et al. (2025). Gpu-enabled isogometric topology optimization with bėzier element stiffness mapping. Computer Modeling in Engineering & Sciences, 142(2), 1481–1514. https://doi.org/10.32604/cmes.2024.058798
Vancouver Style
Li X, Wang S, Luo N, Yang A, Yuan X, Xie X. Gpu-enabled isogometric topology optimization with bėzier element stiffness mapping. Comput Model Eng Sci. 2025;142(2):1481–1514. https://doi.org/10.32604/cmes.2024.058798
IEEE Style
X. Li, S. Wang, N. Luo, A. Yang, X. Yuan, and X. Xie, “GPU-Enabled Isogometric Topology Optimization with Bėzier Element Stiffness Mapping,” Comput. Model. Eng. Sci., vol. 142, no. 2, pp. 1481–1514, 2025. https://doi.org/10.32604/cmes.2024.058798



cc Copyright © 2025 The Author(s). Published by Tech Science Press.
This work is licensed under a Creative Commons Attribution 4.0 International License , which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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