MATLAB function topopt_multi: Multimaterial topology optimization by volume constrained Allen-Cahn system and regularized projected steepest descent method. A new computational algorithm is introduced in the present study to solve multimaterial topology optimization problems. It is based on the penalization of the objective functional by the multiphase volume constrained Ginzburg-Landau energy functional. The update procedure is based on the gradient flow of the objective functional by a fractional step projected steepest descent method. In the first step, the new design is found based on the projected steepest descent method to ensure the reduction in the objective functional, simultaneously satisfying the control constraints. In the second step, regularization step, an $H^1$ regularity of the solution is ensured while keeping the feasibility of solution with respect to the set of control constraints. The presented algorithm could be accounted as a constrained $H^1$ optimization algorithm, which, according to our knowledge, has not been reported to solve such kind of problems yet. The success and efficiency of the presented method are shown through several test problems. Numerical results show that the presented algorithm ends with a near 0--1 topology and its computational cost scales sub-linearly by the number of phases. For the sake of reader convenience and the ease of further extension, the MATLAB implementation of the presented algorithm is included in the appendix.

References in zbMATH (referenced in 23 articles , 1 standard article )

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  1. López, Jorge; Valizadeh, Navid; Rabczuk, Timon: An isogeometric phase-field based shape and topology optimization for flexoelectric structures (2022)
  2. Xue, Liang; Wen, Guilin; Wang, Hongxin; Liu, Jie: Eigenvectors-guided topology optimization to control the mode shape and suppress the vibration of the multi-material plate (2022)
  3. Jeong, Darae; Li, Yibao; Choi, Yongho; Lee, Chaeyoung; Yang, Junxiang; Kim, Junseok: A practical adaptive grid method for the Allen-Cahn equation (2021)
  4. Sha, Wei; Xiao, Mi; Gao, Liang; Zhang, Yan: A new level set based multi-material topology optimization method using alternating active-phase algorithm (2021)
  5. Xu, Shuzhi; Liu, Jikai; Zou, Bin; Li, Quhao; Ma, Yongsheng: Stress constrained multi-material topology optimization with the ordered SIMP method (2021)
  6. Yu, Qian; Wang, Kunyang; Xia, Binhu; Li, Yibao: First and second order unconditionally energy stable schemes for topology optimization based on phase field method (2021)
  7. Zheng, Yongfeng; Da, Daicong; Li, Hao; Xiao, Mi; Gao, Liang: Robust topology optimization for multi-material structures under interval uncertainty (2020)
  8. Liu, Yisi; Wang, Xiaojun; Wang, Lei; Liu, Dongliang: A modified leaky ReLU scheme (MLRS) for topology optimization with multiple materials (2019)
  9. Xia, Qi; Shi, Tielin: Generalized hole nucleation through BESO for the level set based topology optimization of multi-material structures (2019)
  10. Liu, Jikai; Ma, Yongsheng: A new multi-material level set topology optimization method with the length scale control capability (2018)
  11. Regazzoni, F.; Parolini, N.; Verani, M.: Topology optimization of multiple anisotropic materials, with application to self-assembling diblock copolymers (2018)
  12. Sanders, Emily D.; Aguiló, Miguel A.; Paulino, Glaucio H.: Multi-material continuum topology optimization with arbitrary volume and mass constraints (2018)
  13. Shen, Yadong; Feng, Jianhu: Parametric level set-based multimaterial topology optimization of heat conduction structures (2018)
  14. Wang, Yaguang; Kang, Zhan: A level set method for shape and topology optimization of coated structures (2018)
  15. Ivvan Valdez, S.; Botello, Salvador; Ochoa, Miguel A.; Marroquín, José L.; Cardoso, Victor: Topology optimization benchmarks in 2D: results for minimum compliance and minimum volume in planar stress problems (2017)
  16. Lieu, Qui X.; Lee, Jaehong: A multi-resolution approach for multi-material topology optimization based on isogeometric analysis (2017)
  17. Pandey, Anmol; Datta, Rituparna; Bhattacharya, Bishakh: Topology optimization of compliant structures and mechanisms using constructive solid geometry for 2-d and 3-d applications (2017)
  18. Tavakoli, Rouhollah: On the coupled continuous knapsack problems: projection onto the volume constrained Gibbs (N)-simplex (2016)
  19. Tavakoli, Rouhollah: Unconditionally energy stable time stepping scheme for Cahn-Morral equation: application to multi-component spinodal decomposition and optimal space tiling (2016)
  20. Tavakoli, Rouhollah: Optimal design of multiphase composites under elastodynamic loading (2016)

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