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Topology optimization problems usually feature multiple local minimizers. To guarantee convergence to local minimizers that perform best globally or to find local solutions that are desirable for practical applications due to easy manufacturability or aesthetic designs, it is important to compute multiple local minimizers of topology optimization problems. Existing methods typically rely on Newton-type solvers during the optimization process, which makes them unsuitable for sensitivity-based topology optimization. In this paper, we introduce a novel deflation approach to systematically find multiple local minimizers of general topology optimization problems. The approach is based on a penalization of previously found local solutions in the objective. We validate our approach on the so-called two-pipes five-holes example. Finally, we introduce a model for the topology optimization of bipolar plates of hydrogen electrolysis cells and demonstrate that our deflation approach enables the discovery of novel designs for such plates.
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In this paper we consider the topology optimization for a bipolar plate of a hydrogen electrolysis cell. We use the Borvall-Petersson model to describe the fluid flow and derive a criterion for a uniform flow distribution in the bipolar plate. Furthermore, we introduce a novel deflation approach to compute multiple local minimizers of topology optimization problems. The approach is based on a penalty method that discourages convergence towards previously found solutions. Finally, we demonstrate this technique on the topology optimization for bipolar plates and show that multiple distinct local solutions can be found.
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@Article{Baeck2024Novel,
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@Misc{Baeck2024Computing,
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author = {Leon Baeck and Sebastian Blauth and Christian Leithäuser and René Pinnau and Kevin Sturm},
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title = {{A Novel Deflation Approach for Topology Optimization and Application for Optimization of Bipolar Plates of Electrolysis Cells}},
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title = {{Computing Multiple Local Minimizers for the Topology Optimization of Bipolar Plates in Electrolysis Cells}},
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year = {2024},
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archiveprefix = {arXiv},
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doi = {10.48550/arXiv.2406.17491},
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eprint = {2406.17491},
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doi = {10.48550/arXiv.2401.09230},
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eprint = {2401.09230},
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primaryclass = {math.OC},
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}
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.. tab-item:: Plain text citation
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.. code-block:: text
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A Novel Deflation Approach for Topology Optimization and Application for Optimization of Bipolar Plates of Electrolysis Cells
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Computing Multiple Local Minimizers for the Topology Optimization of Bipolar Plates in Electrolysis Cells
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Leon Baeck, Sebastian Blauth, Christian Leithäuser, René Pinnau, and Kevin Sturm
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Preprint on arXiv, 2024
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https://arxiv.org/abs/2406.17491
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https://arxiv.org/abs/2401.09230
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#. | **Computing Multiple Local Minimizers for the Topology Optimization of Bipolar Plates in Electrolysis Cells**
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|*with Leon Baeck, Christian Leithäuser, René Pinnau, Kevin Sturm*
In this paper we consider the topology optimization for a bipolar plate of a hydrogen electrolysis cell. We use the Borvall-Petersson model to describe the fluid flow and derive a criterion for a uniform flow distribution in the bipolar plate. Furthermore, we introduce a novel deflation approach to compute multiple local minimizers of topology optimization problems. The approach is based on a penalty method that discourages convergence towards previously found solutions. Finally, we demonstrate this technique on the topology optimization for bipolar plates and show that multiple distinct local solutions can be found.
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Topology optimization problems usually feature multiple local minimizers. To guarantee convergence to local minimizers that perform best globally or to find local solutions that are desirable for practical applications due to easy manufacturability or aesthetic designs, it is important to compute multiple local minimizers of topology optimization problems. Existing methods typically rely on Newton-type solvers during the optimization process, which makes them unsuitable for sensitivity-based topology optimization. In this paper, we introduce a novel deflation approach to systematically find multiple local minimizers of general topology optimization problems. The approach is based on a penalization of previously found local solutions in the objective. We validate our approach on the so-called two-pipes five-holes example. Finally, we introduce a model for the topology optimization of bipolar plates of hydrogen electrolysis cells and demonstrate that our deflation approach enables the discovery of novel designs for such plates.
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.. tab-item:: BibTeX citation
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.. code-block:: bibtex
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@Misc{Baeck2024Computing,
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author = {Leon Baeck and Sebastian Blauth and Christian Leithäuser and René Pinnau and Kevin Sturm},
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title = {{Computing Multiple Local Minimizers for the Topology Optimization of Bipolar Plates in Electrolysis Cells}},
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year = {2024},
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archiveprefix = {arXiv},
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doi = {10.48550/arXiv.2401.09230},
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eprint = {2401.09230},
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primaryclass = {math.OC},
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@Article{Baeck2025Novel,
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author = {Baeck, Leon and Blauth, Sebastian and Leith\"{a}user, Christian and Pinnau, Ren\'{e} and Sturm, Kevin},
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journal = {SIAM Journal on Scientific Computing},
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title = {A Novel Deflation Approach for Topology Optimization and Application for Optimization of Bipolar Plates of Electrolysis Cells},
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year = {2025},
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number = {6},
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pages = {B1369-B1399},
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volume = {47},
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doi = {10.1137/24M1670913},
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}
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.. tab-item:: Plain text citation
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.. code-block:: text
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Computing Multiple Local Minimizers for the Topology Optimization of Bipolar Plates in Electrolysis Cells
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A Novel Deflation Approach for Topology Optimization and Application for Optimization of Bipolar Plates of Electrolysis Cells
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Leon Baeck, Sebastian Blauth, Christian Leithäuser, René Pinnau, and Kevin Sturm
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Preprint on arXiv, 2024
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https://arxiv.org/abs/2401.09230
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SIAM Journal on Scientific Computing 47(6), 2025
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https://doi.org/10.1137/24M1670913
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Articles in Peer-Reviewed Journals
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#. | **Enforcing Mesh Quality Constraints in Shape Optimization with a Gradient Projection Method**
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|*with Christian Leithäuser*
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|Computer Methods in Applied Mechanics and Engineering 448, 2026
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