Coarse spaces over the ages
| dc.contributor.author | Mandel, Jan | |
| dc.contributor.author | Sousedık, Bedrich | |
| dc.date.accessioned | 2021-11-18T13:38:19Z | |
| dc.date.available | 2021-11-18T13:38:19Z | |
| dc.date.issued | 2010 | |
| dc.description.abstract | The objective of this paper is to explain the principles of the design of a coarse space in a simplified way and by pictures. The focus is on ideas rather than on a more historically complete presentation. That can be found, e.g., in Widlund [2008]. Also, space limitation does not allow us to even the mention many important methods and papers that should be rightfully included. The coarse space facilitates a global exchange of information in multigrid and domain decomposition methods for elliptic problems. This exchange is necessary, because the solution is non-local: its value at any point depends on the right-hand-side at any other point. Both multigrid and domain decomposition combine a global correction in coarse space with local corrections, called smoothing in multigrid and subdomain solves in domain decomposition. In multigrid the coarse space is large (typically, the mesh ratio is 2 or 3 at most) and the local solvers are not very powerful (usually, relaxation). In domain decomposition, the coarse space is small (just one or a few degrees of freedom per subdomain), and the local solvers are powerful (direct solvers on subdomain). But the mathematics is more or less the same. | en_US |
| dc.description.uri | https://arxiv.org/abs/0911.5725 | en_US |
| dc.format.extent | 8 pages | en_US |
| dc.genre | conference papers and proceedings postprints | en_US |
| dc.identifier | doi:10.13016/m2a47k-mdxz | |
| dc.identifier.uri | http://hdl.handle.net/11603/23371 | |
| dc.language.iso | en_US | 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 | Coarse spaces over the ages | en_US |
| dc.type | Text | en_US |
| dcterms.creator | https://orcid.org/0000-0002-8053-8956 | en_US |