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. Deng, Hao; Vulimiri, Praveen S.; To, Albert C.: CAD-integrated topology optimization method with dynamic extrusion feature evolution for multi-axis machining (2022)
  2. Høghøj, Lukas C.; Träff, Erik A.: An advection-diffusion based filter for machinable designs in topology optimization (2022)
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  5. Álvarez Hostos, Juan C.; Fachinotti, Víctor D.; Peralta, Ignacio: Computational design of thermo-mechanical metadevices using topology optimization (2021)
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  7. Chu, Sheng; Xiao, Mi; Gao, Liang; Zhang, Yan; Zhang, Jinhao: Robust topology optimization for fiber-reinforced composite structures under loading uncertainty (2021)
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  10. Kumar, Tej; Sridhara, Saketh; Prabhune, Bhagyashree; Suresh, Krishnan: Spectral decomposition for graded multi-scale topology optimization (2021)
  11. Liu, Yang; Yang, Cheng; Wei, Peng; Zhou, Pingzhang; Du, Jianbin: An ODE-driven level-set density method for topology optimization (2021)
  12. Salas, Ruben Andres; Silva, Andre Luis Ferreira da; Silva, Emílio Carlos Nelli: HYIMFO: hybrid method for optimizing fiber orientation angles in laminated piezocomposite actuators (2021)
  13. Smith, Hollis; Norato, Julián A.: Topology optimization with discrete geometric components made of composite materials (2021)
  14. Wang, Rixin; Zhang, Xianmin; Zhu, Benliang: A projective transformation-based topology optimization using moving morphable components (2021)
  15. Yano, Masayuki; Huang, Tianci; Zahr, Matthew J.: A globally convergent method to accelerate topology optimization using on-the-fly model reduction (2021)
  16. Ypsilantis, Konstantinos-Iason; Kazakis, George; Lagaros, Nikos D.: An efficient 3D homogenization-based topology optimization methodology (2021)
  17. Zambrano, Miguel; Serrano, Sintya; Lazarov, Boyan S.; Galvis, Juan: Fast multiscale contrast independent preconditioners for linear elastic topology optimization problems (2021)
  18. Zhang, Xiaojia Shelly; Chi, Heng; Zhao, Zhi: Topology optimization of hyperelastic structures with anisotropic fiber reinforcement under large deformations (2021)
  19. Zhang, Zeyu; Li, Yu; Zhou, Weien; Chen, Xiaoqian; Yao, Wen; Zhao, Yong: TONR: an exploration for a novel way combining neural network with topology optimization (2021)
  20. Brune, Alexander; Kočvara, Michal: On barrier and modified barrier multigrid methods for three-dimensional topology optimization (2020)

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