TY - JOUR
T1 - A closer look at consistent operator splitting and its extensions for topology optimization
AU - Talischi, Cameron
AU - Paulino, Glaucio H.
N1 - Funding Information:
The authors acknowledge the support by the Department of Energy Computational Science Graduate Fellowship Program of the Office of Science and National Nuclear Security Administration in the Department of Energy under contract DE-FG02-97ER25308 , and the National Science Foundation (NSF) through grants # 1234243 and # 1321661 (Civil, Mechanical and Manufacturing Innovation Division). The information presented in this paper is the sole opinion of the authors and does not necessarily reflect the views of the sponsoring agencies.
Publisher Copyright:
© 2014 Elsevier B.V.
PY - 2015
Y1 - 2015
N2 - In this work, we explore the use of operator splitting algorithms for solving regularized structural topology optimization problems. The context is a classical structural design problem (e.g., compliance minimization and compliant mechanism design), parametrized by means of density functions, whose ill-posedness is addressed by introducing a Tikhonov regularization term. The proposed forward-backward splitting algorithm treats the constituent terms of the cost functional separately, which allows for suitable approximations of the structural objective. We will show that one such approximation, inspired by the reciprocal expansions underlying the optimality criteria method, improves the convergence characteristics and leads to an update scheme resembling the heuristic sensitivity filtering method. We also discuss a two-metric variant of the splitting algorithm that removes the computational overhead associated with bound constraints on the density field without compromising convergence and quality of optimal solutions. We present several numerical results and investigate the influence of various algorithmic parameters.
AB - In this work, we explore the use of operator splitting algorithms for solving regularized structural topology optimization problems. The context is a classical structural design problem (e.g., compliance minimization and compliant mechanism design), parametrized by means of density functions, whose ill-posedness is addressed by introducing a Tikhonov regularization term. The proposed forward-backward splitting algorithm treats the constituent terms of the cost functional separately, which allows for suitable approximations of the structural objective. We will show that one such approximation, inspired by the reciprocal expansions underlying the optimality criteria method, improves the convergence characteristics and leads to an update scheme resembling the heuristic sensitivity filtering method. We also discuss a two-metric variant of the splitting algorithm that removes the computational overhead associated with bound constraints on the density field without compromising convergence and quality of optimal solutions. We present several numerical results and investigate the influence of various algorithmic parameters.
KW - Forward-backward splitting
KW - Optimality criteria method
KW - Tikhonov regularization
KW - Topology optimization
KW - Two-metric projection
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U2 - 10.1016/j.cma.2014.07.005
DO - 10.1016/j.cma.2014.07.005
M3 - Article
AN - SCOPUS:84910091552
SN - 0045-7825
VL - 283
SP - 573
EP - 598
JO - Computer Methods in Applied Mechanics and Engineering
JF - Computer Methods in Applied Mechanics and Engineering
ER -