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Erschienen in: Structural and Multidisciplinary Optimization 1/2018

07.11.2017 | BRIEF NOTE

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

verfasst von: Pingzhang Zhou, Jianbin Du, Zhenhua Lü

Erschienen in: Structural and Multidisciplinary Optimization | Ausgabe 1/2018

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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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Fußnoten
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.
 
Literatur
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Metadaten
Titel
Highly efficient density-based topology optimization using DCT-based digital image compression
verfasst von
Pingzhang Zhou
Jianbin Du
Zhenhua Lü
Publikationsdatum
07.11.2017
Verlag
Springer Berlin Heidelberg
Erschienen in
Structural and Multidisciplinary Optimization / Ausgabe 1/2018
Print ISSN: 1615-147X
Elektronische ISSN: 1615-1488
DOI
https://doi.org/10.1007/s00158-017-1840-z

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