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An optimized, easy-to-use, open-source GPU solver for large-scale inverse homogenization problems

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Abstract

We propose a high-performance GPU solver for inverse homogenization problems to design high-resolution 3D microstructures. Central to our solver is a favorable combination of data structures and algorithms, making full use of the parallel computation power of today’s GPUs through a software-level design technology exploration. This solver is demonstrated to optimize homogenized stiffness tensors, such as bulk modulus, shear modulus, and Poisson’s ratio, under the constraint of bounded material volume. Practical high-resolution examples with \(512^3 \approx 134.2\) million finite elements run in less than 40 s per iteration with a peak GPU memory of 9 GB on an NVIDIA GeForce GTX 1080Ti GPU. Besides, our GPU implementation is equipped with an easy-to-use framework with less than 20 lines of code to support various objective functions defined by the homogenized stiffness tensors. Our open-source high-performance implementation is publicly accessible at https://github.com/lavenklau/homo3d.

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Acknowledgements

The authors would like to acknowledge the financial support from the Provincial Natural Science Foundation of Anhui (2208085QA01), the Fundamental Research Funds for the Central Universities (WK0010000075), the National Natural Science Foundation of China (61972368 and 62025207).

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Authors and Affiliations

  1. School of Mathematical Sciences, University of Science and Technology of China, Hefei, China

    Di Zhang, Xiaoya Zhai, Ligang Liu & Xiao-Ming Fu

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  1. Di Zhang
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  2. Xiaoya Zhai
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  3. Ligang Liu
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  4. Xiao-Ming Fu
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Correspondence to Xiaoya Zhai.

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Replication of results

Important details for replication of results have been described in the manuscript. Code for this paper is at https://github.com/lavenklau/homo3d.

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Responsible Editor: Ole Sigmund.

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Zhang, D., Zhai, X., Liu, L. et al. An optimized, easy-to-use, open-source GPU solver for large-scale inverse homogenization problems. Struct Multidisc Optim 66, 207 (2023). https://doi.org/10.1007/s00158-023-03657-y

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