Optimal order multigrid preconditioners for the distributed control of parabolic equations with coarsening in space and time
| dc.contributor.author | Drăgănescu, Andrei | |
| dc.contributor.author | Hajghassem, Mona | |
| dc.date.accessioned | 2022-03-18T15:20:28Z | |
| dc.date.available | 2022-03-18T15:20:28Z | |
| dc.date.issued | 2022-02-17 | |
| dc.description.abstract | We devise multigrid preconditioners for linear-quadratic space-time distributed parabolic optimal control problems. While our method is rooted in earlier work on elliptic control, the temporal dimension presents new challenges in terms of algorithm design and quality. Our primary focus is on the cG(s)dG(r) discretizations which are based on functions that are continuous in space and discontinuous in time, but our technique is applicable to various other space-time finite element discretizations. We construct and analyse two kinds of multigrid preconditioners: the first is based on full coarsening in space and time, while the second is based on semi-coarsening in space only. Our analysis, in conjunction with numerical experiments, shows that both preconditioners are of optimal order with respect to the discretization in case of cG(1)dG(r) for r = 0; 1, and exhibits a suboptimal behavior in time for Crank-Nicolson. We also show that, under certain conditions, the pre- conditioner using full space-time coarsening is more efficient than the one involving semi-coarsening in space, a phenomenon that has not been observed previously. Our numerical results confi rm the theoretical fi ndings. | en_US |
| dc.description.sponsorship | This material is based upon work supported by the U.S. Department of Energy Office of Science, Office of Advanced Scientific Computing Research, Applied Mathematics program under Award Number DE-SC0005455, and by the National Science Foundation under award DMS-1913201. | en_US |
| dc.description.uri | https://www.tandfonline.com/doi/abs/10.1080/10556788.2021.2022145 | en_US |
| dc.format.extent | 35 pages | en_US |
| dc.genre | journal articles | en_US |
| dc.genre | postprints | en_US |
| dc.identifier | doi:10.13016/m2ilzu-go3v | |
| dc.identifier.citation | Andrei Drăgănescu & Mona Hajghassem (2022) Optimal order multigrid preconditioners for the distributed control of parabolic equations with coarsening in space and time, Optimization Methods and Software, DOI: 10.1080/10556788.2021.2022145 | en_US |
| dc.identifier.uri | https://doi.org/10.1080/10556788.2021.2022145 | |
| dc.identifier.uri | http://hdl.handle.net/11603/24407 | |
| dc.language.iso | en_US | en_US |
| dc.publisher | Taylor & Francis | en_US |
| dc.relation.isAvailableAt | The University of Maryland, Baltimore County (UMBC) | |
| dc.relation.ispartof | UMBC Mathematics Department Collection | |
| dc.relation.ispartof | UMBC Faculty Collection | |
| dc.rights | This is an Accepted Manuscript of an article published by Taylor & Francis in Optimization Methods and Software on February 17, 2022, available online: http://www.tandfonline.com/10.1080/10556788.2021.2022145. | en_US |
| dc.rights | Access to this item will begin on 2-17-2023 | |
| dc.title | Optimal order multigrid preconditioners for the distributed control of parabolic equations with coarsening in space and time | en_US |
| dc.type | Text | en_US |