Quasi-Newton Methods for Topology Optimization Using a Level-Set Method
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arXiv
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| Format: | Preprint |
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2023
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| _version_ | 1866914088049704960 |
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| author | Blauth, Sebastian Sturm, Kevin |
| author_facet | Blauth, Sebastian Sturm, Kevin |
| contents | The ability to efficiently solve topology optimization problems is of great importance for many practical applications. Hence, there is a demand for efficient solution algorithms. In this paper, we propose novel quasi-Newton methods for solving PDE-constrained topology optimization problems. Our approach is based on and extends the popular solution algorithm of Amstutz and Andrä (A new algorithm for topology optimization using a level-set method, Journal of Computational Physics, 216, 2006). To do so, we introduce a new perspective on the commonly used evolution equation for the level-set method, which allows us to derive our quasi-Newton methods for topology optimization. We investigate the performance of the proposed methods numerically for the following examples: Inverse topology optimization problems constrained by linear and semilinear elliptic Poisson problems, compliance minimization in linear elasticity, and the optimization of fluids in Navier-Stokes flow, where we compare them to current state-of-the-art methods. Our results show that the proposed solution algorithms significantly outperform the other considered methods: They require substantially less iterations to find a optimizer while demanding only slightly more resources per iteration. This shows that our proposed methods are highly attractive solution methods in the field of topology optimization. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2303_15070 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Quasi-Newton Methods for Topology Optimization Using a Level-Set Method Blauth, Sebastian Sturm, Kevin Optimization and Control The ability to efficiently solve topology optimization problems is of great importance for many practical applications. Hence, there is a demand for efficient solution algorithms. In this paper, we propose novel quasi-Newton methods for solving PDE-constrained topology optimization problems. Our approach is based on and extends the popular solution algorithm of Amstutz and Andrä (A new algorithm for topology optimization using a level-set method, Journal of Computational Physics, 216, 2006). To do so, we introduce a new perspective on the commonly used evolution equation for the level-set method, which allows us to derive our quasi-Newton methods for topology optimization. We investigate the performance of the proposed methods numerically for the following examples: Inverse topology optimization problems constrained by linear and semilinear elliptic Poisson problems, compliance minimization in linear elasticity, and the optimization of fluids in Navier-Stokes flow, where we compare them to current state-of-the-art methods. Our results show that the proposed solution algorithms significantly outperform the other considered methods: They require substantially less iterations to find a optimizer while demanding only slightly more resources per iteration. This shows that our proposed methods are highly attractive solution methods in the field of topology optimization. |
| title | Quasi-Newton Methods for Topology Optimization Using a Level-Set Method |
| topic | Optimization and Control |
| url | https://arxiv.org/abs/2303.15070 |