Nested BDDC for a saddle-point problem
| dc.contributor.author | Sousedík, Bedřich | |
| dc.date.accessioned | 2021-10-27T16:55:18Z | |
| dc.date.available | 2021-10-27T16:55:18Z | |
| dc.date.issued | 2013-03-16 | |
| dc.description.abstract | We propose a Nested BDDC for a class of saddle-point problems. The method solves for both flux and pressure variables. The fluxes are resolved in three-steps: the coarse solve is followed by subdomain solves, and last we look for a divergence-free flux correction and pressure variables using conjugate gradients with a Multilevel BDDC preconditioner. Because the coarse solve in the first step has the same structure as the original problem, we can use this procedure recursively and solve (a hierarchy of) coarse problems only approximately, utilizing the coarse problems known from the BDDC. The resulting algorithm thus first performs several upscaling steps, and then solves a hierarchy of problems that have the same structure but increase in size while sweeping down the levels, using the same components in the first and in the third step on each level, and also reusing the components from the higher levels. Because the coarsening can be quite aggressive, the number of levels can be kept small and the additional computational cost is significantly reduced due to the reuse of the components. We also provide the condition number bound and numerical experiments confirming the theory. | en_US |
| dc.description.sponsorship | Supported in part by the National Science Foundation under grant DMS-0713876, and by the Grant Agency of the Czech Republic GA CR 106/08/0403. Support from DOE/ASCR ˇ is also gratefully acknowledged. | en_US |
| dc.description.uri | https://link.springer.com/article/10.1007/s00211-013-0548-2 | en_US |
| dc.format.extent | 23 pages | en_US |
| dc.genre | journal articles | en_US |
| dc.genre | preprints | en_US |
| dc.identifier | doi:10.13016/m2eeyi-9i2e | |
| dc.identifier.citation | Sousedík, Bedřich; Nested BDDC for a saddle-point problem; Numerische Mathematik, volume 125, pages761–783, 16 March, 2013; https://doi.org/10.1007/s00211-013-0548-2 | en_US |
| dc.identifier.uri | https://doi.org/10.1007/s00211-013-0548-2 | |
| dc.identifier.uri | http://hdl.handle.net/11603/23162 | |
| dc.language.iso | en_US | en_US |
| dc.publisher | Springer Nature | en_US |
| dc.relation.isAvailableAt | The University of Maryland, Baltimore County (UMBC) | |
| dc.relation.ispartof | UMBC Mathematics Department Collection | |
| dc.rights | This item is likely protected under Title 17 of the U.S. Copyright Law. Unless on a Creative Commons license, for uses protected by Copyright Law, contact the copyright holder or the author. | en_US |
| dc.title | Nested BDDC for a saddle-point problem | en_US |
| dc.type | Text | en_US |
| dcterms.creator | https://orcid.org/0000-0002-8053-8956 | en_US |