Abstract Practical engineering designs typically involve many load cases. For topology optimization with many deterministic load cases, a large number of linear systems of equations must be solved at each optimization step, leading to an enormous computational cost. To address this challenge, we propose a mirror descent stochastic approximation (MD-SA) framework with various step size strategies to solve topology optimization problems with many load cases. We reformulate the deterministic objective function and gradient into stochastic ones through randomization, derive the MD-SA update, and develop algorithmic strategies. The proposed MD-SA algorithm requires only low accuracy in the stochastic gradient and thus uses only a single sample per optimization step (i.e., the sample size is always one). As a result, we reduce the number of linear systems to solve per step from hundreds to one, which drastically reduces the total computational cost, while maintaining a similar design quality. For example, for one of the design problems, the total number of linear systems to solve and wall clock time are reduced by factors of 223 and 22, respectively.
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Convergence acceleration of Monte Carlo many-body perturbation methods by using many control variates
- NSF-PAR ID:
- 10190217
- Publisher / Repository:
- American Institute of Physics
- Date Published:
- Journal Name:
- The Journal of Chemical Physics
- Volume:
- 153
- Issue:
- 9
- ISSN:
- 0021-9606
- Page Range / eLocation ID:
- Article No. 094108
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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