Efficient topology optimization in MATLAB using 88 lines of code. The paper presents an efficient 88 line MATLAB code for topology optimization. It has been developed using the 99 line code presented by {it O. Sigmund} [ibid. 21, No. 2, 120--127 (2001)] as a starting point. The original code has been extended by a density filter, and a considerable improvement in efficiency has been achieved, mainly by preallocating arrays and vectorizing loops. A speed improvement with a factor of 100 is obtained for a benchmark example with 7,500 elements. Moreover, the length of the code has been reduced to a mere 88 lines. These improvements have been accomplished without sacrificing the readability of the code. The 88 line code can therefore be considered as a valuable successor to the 99 line code, providing a practical instrument that may help to ease the learning curve for those entering the field of topology optimization. The paper also discusses simple extensions of the basic code to include recent PDE-based and black-and-white projection filtering methods. The complete 88 line code is included as an appendix and can be downloaded from the web site url{}.

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  1. Alacoque, Lee; Watkins, Ryan T.; Tamijani, Ali Y.: Stress-based and robust topology optimization for thermoelastic multi-material periodic microstructures (2021)
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  6. Yano, Masayuki; Huang, Tianci; Zahr, Matthew J.: A globally convergent method to accelerate topology optimization using on-the-fly model reduction (2021)
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  8. Zambrano, Miguel; Serrano, Sintya; Lazarov, Boyan S.; Galvis, Juan: Fast multiscale contrast independent preconditioners for linear elastic topology optimization problems (2021)
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  10. Brune, Alexander; Kočvara, Michal: On barrier and modified barrier multigrid methods for three-dimensional topology optimization (2020)
  11. Deng, Hao; To, Albert C.: Topology optimization based on deep representation learning (DRL) for compliance and stress-constrained design (2020)
  12. De, Subhayan; Maute, Kurt; Doostan, Alireza: Bi-fidelity stochastic gradient descent for structural optimization under uncertainty (2020)
  13. Fernández, Eduardo; Yang, Kai-ke; Koppen, Stijn; Alarcón, Pablo; Bauduin, Simon; Duysinx, Pierre: Imposing minimum and maximum member size, minimum cavity size, and minimum separation distance between solid members in topology optimization (2020)
  14. Gao, Wenjun; Wang, Fengwen; Sigmund, Ole: Systematic design of high-(Q) prestressed micro membrane resonators (2020)
  15. Kanno, Yoshihiro: Exploiting Lagrange duality for topology optimization with frictionless unilateral contact (2020)
  16. Li, Xiang; Ning, Shaowu; Liu, Zhanli; Yan, Ziming; Luo, Chengcheng; Zhuang, Zhuo: Designing phononic crystal with anticipated band gap through a deep learning based data-driven method (2020)
  17. Luo, Yangjun; Xing, Jian; Kang, Zhan: Topology optimization using material-field series expansion and Kriging-based algorithm: an effective non-gradient method (2020)
  18. Zhang, Hui-Kai; Wu, Wen-Jun; Kang, Zhan; Feng, Xi-Qiao: Topology optimization method for the design of bioinspired self-similar hierarchical microstructures (2020)
  19. Zheng, Yongfeng; Da, Daicong; Li, Hao; Xiao, Mi; Gao, Liang: Robust topology optimization for multi-material structures under interval uncertainty (2020)
  20. Burman, Erik; Elfverson, Daniel; Hansbo, Peter; Larson, Mats G.; Larsson, Karl: Cut topology optimization for linear elasticity with coupling to parametric nondesign domain regions (2019)

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