%0 Conference Paper %1 Buchfink2020a %A Buchfink, P. %A Haasdonk, B. %A Rave, S. %B Proceedings of the Conference Algoritmy 2020 %D 2020 %E Frolkovič, P. %E Mikula, K. %E Ševčovič, D. %I Vydavateľstvo SPEKTRUM %K EXC2075 from:patrickbuchfink peerReviewed pn5 %P 151--160 %T PSD-Greedy Basis Generation for Structure-Preserving Model Order Reduction of Hamiltonian Systems %U http://www.iam.fmph.uniba.sk/amuc/ojs/index.php/algoritmy/article/view/1577/829 %X Hamiltonian systems are central in the formulation of non-dissipative physical systems. They are characterized by a phase-space, a symplectic form and a Hamiltonian function. In numerical simulations of Hamiltonian systems, algorithms show improved accuracy when the symplectic structure is preserved 10. For structure-preserving model order reduction (MOR) of Hamiltonian systems, symplectic MOR 17, 14, 11, 3, 16 can be used. It is based on a reduced-order basis that is symplectic, which requires symplectic basis generation techniques. In our work, we discuss greedy algorithms for symplectic basis generation. We complement the procedure presented in 14 with ideas of the POD-greedy 9, which results in a new greedy symplectic basis generation technique, the PSD-greedy. Inspired by POD-greedy, we use compression techniques in the greedy iterations to enrich the basis iteratively. We prove that this algorithm computes a symplectic basis when symplectic techniques are used for compression. In the numerical experiments, we compare the discussed methods for a linear elasticity problem. The results show that improvements of up to one order of magnitude in the relative reduction error are achievable with the new basis generation technique compared to the existing greedy approach from 14. %@ 978-80-227-5032-5

@inproceedings{Buchfink2020a, abstract = {Hamiltonian systems are central in the formulation of non-dissipative physical systems. They are characterized by a phase-space, a symplectic form and a Hamiltonian function. In numerical simulations of Hamiltonian systems, algorithms show improved accuracy when the symplectic structure is preserved [10]. For structure-preserving model order reduction (MOR) of Hamiltonian systems, symplectic MOR [17, 14, 11, 3, 16] can be used. It is based on a reduced-order basis that is symplectic, which requires symplectic basis generation techniques. In our work, we discuss greedy algorithms for symplectic basis generation. We complement the procedure presented in [14] with ideas of the POD-greedy [9], which results in a new greedy symplectic basis generation technique, the PSD-greedy. Inspired by POD-greedy, we use compression techniques in the greedy iterations to enrich the basis iteratively. We prove that this algorithm computes a symplectic basis when symplectic techniques are used for compression. In the numerical experiments, we compare the discussed methods for a linear elasticity problem. The results show that improvements of up to one order of magnitude in the relative reduction error are achievable with the new basis generation technique compared to the existing greedy approach from [14].}, added-at = {2021-12-08T17:10:08.000+0100}, author = {Buchfink, P. and Haasdonk, B. and Rave, S.}, biburl = {https://puma.ub.uni-stuttgart.de/bibtex/26fef2e6e9cead13f2f46aeb7b8f89235/katharinafuchs}, booktitle = {Proceedings of the Conference Algoritmy 2020}, editor = {Frolkovič, P. and Mikula, K. and Ševčovič, D.}, interhash = {4494b4778a67c602c28cdd64edcf7921}, intrahash = {6fef2e6e9cead13f2f46aeb7b8f89235}, isbn = {978-80-227-5032-5}, keywords = {EXC2075 from:patrickbuchfink peerReviewed pn5}, month = {08}, pages = {151--160}, publisher = {Vydavateľstvo SPEKTRUM}, timestamp = {2021-12-08T16:10:08.000+0100}, title = {PSD-Greedy Basis Generation for Structure-Preserving Model Order Reduction of Hamiltonian Systems}, url = {http://www.iam.fmph.uniba.sk/amuc/ojs/index.php/algoritmy/article/view/1577/829}, year = 2020 }