Journal article
Computing multiple solutions of topology optimization problems
- Abstract:
- Topology optimization problems often support multiple local minima due to a lack of convexity. Typically, gradient-based techniques combined with continuation in model parameters are used to promote convergence to more optimal solutions; however, these methods can fail even in the simplest cases. In this paper, we present an algorithm to perform a systematic exploratory search for the solutions of the optimization problem via second-order methods without a good initial guess. The algorithm combines the techniques of deflation, barrier methods and primal-dual active set solvers in a novel way. We demonstrate this approach on several numerical examples, observe mesh-independence in certain cases and show that multiple distinct local minima can be recovered.
- Publication status:
- Published
- Peer review status:
- Peer reviewed
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- Files:
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(Preview, Accepted manuscript, 3.1MB, Terms of use)
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- Publisher copy:
- 10.1137/20M1326209
Authors
- Publisher:
- Society for Industrial and Applied Mathematics
- Journal:
- SIAM Journal on Scientific Computing More from this journal
- Volume:
- 43
- Issue:
- 3
- Pages:
- A1555–A1582
- Publication date:
- 2021-05-06
- Acceptance date:
- 2021-01-11
- DOI:
- EISSN:
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1095-7197
- ISSN:
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1064-8275
- Language:
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English
- Keywords:
- Pubs id:
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1154021
- Local pid:
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pubs:1154021
- Deposit date:
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2021-01-12
Terms of use
- Copyright holder:
- Society for Industrial and Applied Mathematics
- Copyright date:
- 2021
- Rights statement:
- © 2021, Society for Industrial and Applied Mathematics
- Notes:
- This is the accepted manuscript version of the article. The final version will be available is available from Society for Industrial and Applied Mathematics at: https://doi.org/10.1137/20M1326209
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