topopt_multi swMATH ID: 25723 Software Authors: Tavakoli, Rouhollah Description: 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. Homepage: http://www.optimization-online.org/DB_FILE/2013/11/4116.pdf Dependencies: Matlab Keywords: gradient projection; MATLAB code; multiphase Allen-Cahn; multiphase Cahn-Hilliard; multiphase topology optimization; Sobolev gradient Related Software: top.m; Matlab; top88.m; PetIGA; PETSc; PolyTop; CONLIN; UMFPACK; Python; ToPy; ABAQUS; Mosek Cited in: 23 Publications Standard Articles 1 Publication describing the Software, including 1 Publication in zbMATH Year Multimaterial topology optimization by volume constrained Allen-Cahn system and regularized projected steepest descent method. Zbl 1423.74764Tavakoli, Rouhollah 2014 all top 5 Cited by 57 Authors 5 Tavakoli, Rouhollah 2 Gao, Liang 2 Kang, Zhan 2 Li, Yibao 2 Liu, Jikai 2 Ma, Yongsheng 2 Xiao, Mi 1 Aguilo, Miguel A. 1 Bhattacharya, Bishakh 1 Botello, Salvador 1 Cardoso, Victor 1 Choi, Yongho 1 Da, Daicong 1 Datta, Rituparna 1 Feng, Jianhu 1 Jeong, Darae 1 Kim, Junseok 1 Lee, Chaeyoung 1 Lee, Jaehong 1 Li, Hao 1 Li, Quhao 1 Lieu, Qui X. 1 Liu, Dongliang 1 Liu, Jie 1 Liu, Yisi 1 Luo, Zhen 1 Marroquin, Jose Luis 1 Ochoa, Miguel A. 1 Pandey, Anmol 1 Parolini, Nicola 1 Paulino, Glaucio H. 1 Rabczuk, Timon 1 Regazzoni, Francesco 1 Sanders, Emily D. 1 Sha, Wei 1 Shen, Yadong 1 Shi, Tielin 1 Valdez, S. Ivvan 1 Valizadeh, Navid 1 Verani, Marco 1 Wang, Hongxin 1 Wang, Kunyang 1 Wang, Lei 1 Wang, Xiaojun 1 Wang, Yaguang 1 Wang, Yiqiang 1 Wen, Guilin 1 Xia, Binhu 1 Xia, Qi 1 Xu, Shuzhi 1 Xue, Liang 1 Yang, Junxiang 1 Yu, Qian 1 Zhang, Nong 1 Zhang, Yan 1 Zheng, Yongfeng 1 Zou, Bin all top 5 Cited in 9 Serials 13 Computer Methods in Applied Mechanics and Engineering 2 Journal of Computational Physics 2 Applied Mathematics and Computation 1 Physica A 1 Applied Mathematical Modelling 1 Mathematical Problems in Engineering 1 Soft Computing 1 Archives of Computational Methods in Engineering 1 Optimization Letters all top 5 Cited in 9 Fields 17 Mechanics of deformable solids (74-XX) 7 Calculus of variations and optimal control; optimization (49-XX) 7 Numerical analysis (65-XX) 3 Partial differential equations (35-XX) 3 Operations research, mathematical programming (90-XX) 2 Statistical mechanics, structure of matter (82-XX) 1 Computer science (68-XX) 1 Classical thermodynamics, heat transfer (80-XX) 1 Game theory, economics, finance, and other social and behavioral sciences (91-XX) Citations by Year