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Highly efficient density-based topology optimization using DCT-based digital image compression

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Abstract

In this brief note we show that the number of design variables in density-based topology optimization can be phenomenally reduced using discrete cosine transform (DCT), which is one of the most frequently used transforms in digital image compression. Only quite a few nonzero DCT coefficients corresponding to low frequency components are needed to generate optimized topology with high resolution. Through two examples, one for compliance minimization and the other for heat conduction, we show that the density method can be surprisingly efficient than people have thought. Moreover, there is no need to use additional density filter or sensitivity filter since high frequency components are inherently filtered by the DCT-based compression.

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Fig. 1
Fig. 2

Notes

  1. Equation (3) is called DCT while (4) is called IDCT.

  2. There are a lot of fast algorithms for DCT. However, the most convenient one is to use dct, dctmtx or dct2 in MATLAB.

  3. NAG is a commercial numerical library, cf. https://www.nag.com for more information.

  4. The statistics are obtained using the profile provided within MATLAB.

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Acknowledgements

The research is supported by NSFC (11772170, 11372154) which is gratefully acknowledged by the authors. The authors would also like to thank Mr. Daniel White with whom the helpful discussions during WCSMO12 at Braunschweig, Germany inspires the first author to come up with the basic idea of this paper.

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Authors and Affiliations

  1. Department of Automotive Engineering, Tsinghua University, Beijing, People’s Republic of China

    Pingzhang Zhou & Zhenhua Lü

  2. School of Aerospace Engineering, Tsinghua University, Beijing, People’s Republic of China

    Jianbin Du

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  1. Pingzhang Zhou
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  2. Jianbin Du
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  3. Zhenhua Lü
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Correspondence to Jianbin Du.

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Zhou, P., Du, J. & Lü, Z. Highly efficient density-based topology optimization using DCT-based digital image compression. Struct Multidisc Optim 57, 463–467 (2018). https://doi.org/10.1007/s00158-017-1840-z

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  • DOI: https://doi.org/10.1007/s00158-017-1840-z

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