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. Brune, Alexander; Kočvara, Michal: On barrier and modified barrier multigrid methods for three-dimensional topology optimization (2020)
  2. Deng, Hao; To, Albert C.: Topology optimization based on deep representation learning (DRL) for compliance and stress-constrained design (2020)
  3. Gao, Wenjun; Wang, Fengwen; Sigmund, Ole: Systematic design of high-(Q) prestressed micro membrane resonators (2020)
  4. Kanno, Yoshihiro: Exploiting Lagrange duality for topology optimization with frictionless unilateral contact (2020)
  5. 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)
  6. Luo, Yangjun; Xing, Jian; Kang, Zhan: Topology optimization using material-field series expansion and Kriging-based algorithm: an effective non-gradient method (2020)
  7. Zheng, Yongfeng; Da, Daicong; Li, Hao; Xiao, Mi; Gao, Liang: Robust topology optimization for multi-material structures under interval uncertainty (2020)
  8. 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)
  9. Chakraborty, Souvik; Goswami, Somdatta; Rabczuk, Timon: A surrogate assisted adaptive framework for robust topology optimization (2019)
  10. Chu, Sheng; Xiao, Mi; Gao, Liang; Li, Hao; Zhang, Jinhao; Zhang, Xiaoyu: Topology optimization of multi-material structures with graded interfaces (2019)
  11. Dapogny, Charles; Estevez, Rafael; Faure, Alexis; Michailidis, Georgios: Shape and topology optimization considering anisotropic features induced by additive manufacturing processes (2019)
  12. Du, Zongliang; Zhang, Weisheng; Zhang, Yupeng; Xue, Riye; Guo, Xu: Structural topology optimization involving bi-modulus materials with asymmetric properties in tension and compression (2019)
  13. He, Linwei; Gilbert, Matthew; Johnson, Thomas; Pritchard, Tom: Conceptual design of AM components using layout and geometry optimization (2019)
  14. Lagaros, Nikos D.; Vasileiou, Nikos; Kazakis, Georgios: A C# code for solving 3D topology optimization problems using SAP2000 (2019)
  15. Liang, Yuan; Cheng, Gengdong: Topology optimization via sequential integer programming and canonical relaxation algorithm (2019)
  16. O’Sullivan, S.; Bird, R. E.; Coombs, W. M.; Giani, Stefano: Rapid non-linear finite element analysis of continuous and discontinuous Galerkin methods in MATLAB (2019)
  17. Perry, Daniel J.; Kirby, Robert M.; Narayan, Akil; Whitaker, Ross T.: Allocation strategies for high fidelity models in the multifidelity regime (2019)
  18. Sosnovik, Ivan; Oseledets, Ivan: Neural networks for topology optimization (2019)
  19. Vishwanathan, Aditya; Vio, Gareth A.: Efficient quantification of material uncertainties in reliability-based topology optimization using random matrices (2019)
  20. Xiao, Mi; Chu, Sheng; Gao, Liang; Li, Hao: A hybrid method for density-related topology optimization (2019)

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