Comparison of FETI-based domain decomposition methods for topology optimization problems
We critically assess the performance of several variants of dual and dual-primal domain decomposition strategies in problems with fixed subdomain partitioning and high heterogeneity in stiffness coefficients typically arising in topology optimization of modular structures. Our study considers Total...
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| Language: | English |
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Czech Technical University in Prague
2022-03-01
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| Series: | Acta Polytechnica CTU Proceedings |
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| Online Access: | https://ojs.cvut.cz/ojs/index.php/APP/article/view/8107 |
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| author | Tomáš Medřický Martin Doškář Ivana Pultarová Jan Zeman |
| author_facet | Tomáš Medřický Martin Doškář Ivana Pultarová Jan Zeman |
| author_sort | Tomáš Medřický |
| collection | DOAJ |
| description | We critically assess the performance of several variants of dual and dual-primal domain decomposition strategies in problems with fixed subdomain partitioning and high heterogeneity in stiffness coefficients typically arising in topology optimization of modular structures. Our study considers Total FETI and FETI Dual-Primal methods along with three enhancements: k-scaling, full orthogonalization of the search directions, and considering multiple search-direction at once, which gives us twelve variants in total. We test these variants both on academic examples and snapshots of topology optimization iterations. Based on the results, we conclude that (i) the original methods exhibit very slow convergence in the presence of severe heterogeneity in stiffness coefficients, which makes them practically useless, (ii) the full orthogonalization enhancement helps only for mild heterogeneity, and (iii) the only robust method is FETI Dual-Primal with multiple search direction and k-scaling. |
| format | Article |
| id | doaj-art-75bd3a1ba7254fcd8c8b6eda820f796d |
| institution | Kabale University |
| issn | 2336-5382 |
| language | English |
| publishDate | 2022-03-01 |
| publisher | Czech Technical University in Prague |
| record_format | Article |
| series | Acta Polytechnica CTU Proceedings |
| spelling | doaj-art-75bd3a1ba7254fcd8c8b6eda820f796d2025-08-20T03:57:08ZengCzech Technical University in PragueActa Polytechnica CTU Proceedings2336-53822022-03-013443–4943–4910.14311/APP.2022.34.00435347Comparison of FETI-based domain decomposition methods for topology optimization problemsTomáš Medřický0Martin Doškář1Ivana Pultarová2Jan Zeman3Czech Technical University in Prague, Faculty of Civil Engineering, Department of Mechanics, Thákurova 7, 166 29 Prague, Czech RepublicCzech Technical University in Prague, Faculty of Civil Engineering, Department of Mechanics, Thákurova 7, 166 29 Prague, Czech RepublicCzech Technical University in Prague, Faculty of Civil Engineering, Department of Mathematics, Thákurova 7, 166 29 Prague, Czech RepublicCzech Technical University in Prague, Faculty of Civil Engineering, Department of Mechanics, Thákurova 7, 166 29 Prague, Czech RepublicWe critically assess the performance of several variants of dual and dual-primal domain decomposition strategies in problems with fixed subdomain partitioning and high heterogeneity in stiffness coefficients typically arising in topology optimization of modular structures. Our study considers Total FETI and FETI Dual-Primal methods along with three enhancements: k-scaling, full orthogonalization of the search directions, and considering multiple search-direction at once, which gives us twelve variants in total. We test these variants both on academic examples and snapshots of topology optimization iterations. Based on the results, we conclude that (i) the original methods exhibit very slow convergence in the presence of severe heterogeneity in stiffness coefficients, which makes them practically useless, (ii) the full orthogonalization enhancement helps only for mild heterogeneity, and (iii) the only robust method is FETI Dual-Primal with multiple search direction and k-scaling.https://ojs.cvut.cz/ojs/index.php/APP/article/view/8107total feti, feti dual-primaltopology optimizationoptimizationheterogeneous problemsk-scalingsimultaneous feti |
| spellingShingle | Tomáš Medřický Martin Doškář Ivana Pultarová Jan Zeman Comparison of FETI-based domain decomposition methods for topology optimization problems Acta Polytechnica CTU Proceedings total feti, feti dual-primal topology optimization optimization heterogeneous problems k-scaling simultaneous feti |
| title | Comparison of FETI-based domain decomposition methods for topology optimization problems |
| title_full | Comparison of FETI-based domain decomposition methods for topology optimization problems |
| title_fullStr | Comparison of FETI-based domain decomposition methods for topology optimization problems |
| title_full_unstemmed | Comparison of FETI-based domain decomposition methods for topology optimization problems |
| title_short | Comparison of FETI-based domain decomposition methods for topology optimization problems |
| title_sort | comparison of feti based domain decomposition methods for topology optimization problems |
| topic | total feti, feti dual-primal topology optimization optimization heterogeneous problems k-scaling simultaneous feti |
| url | https://ojs.cvut.cz/ojs/index.php/APP/article/view/8107 |
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