Name
Abstract | ||
|---|---|---|
We design and analyze optimal additive and multiplicative multilevel methods for solving H 1 problems on graded grids obtained by bisection. We deal with economical local smoothers: after a global smoothing in the finest mesh, local smoothing for each added node during the refinement needs to be performed only for three vertices - the new vertex and its two parent vertices. We show that our methods lead to optimal complexity for any dimensions and polynomial degree. The theory hinges on a new decomposition of bisection grids in any dimension, which is of independent interest and yields a corresponding decomposition of spaces. We use the latter to bridge the gap between graded and quasi-uniform grids, for which the multilevel theory is well-established. |
Year | DOI | Venue |
|---|---|---|
2012 | 10.1007/s00211-011-0401-4 | Numerische Mathematik |
Keywords | Field | DocType |
optimal multilevel method,multilevel theory,new vertex,multiplicative multilevel method,global smoothing,graded grid,economical local smoothers,corresponding decomposition,graded bisection grid,new decomposition,local smoothing,bisection grid,bisection method | Discrete mathematics,Mathematical optimization,Bisection,Vertex (geometry),Multiplicative function,Degree of a polynomial,Smoothing,Hinge,Mathematics | Journal |
Volume | Issue | ISSN |
120 | 1 | 0945-3245 |
Citations | PageRank | References |
2 | 0.39 | 25 |
Authors | ||
3 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Long Chen | 1 | 62 | 11.85 |
| Ricardo H. Nochetto | 2 | 907 | 110.08 |
| Jinchao Xu | 3 | 1478 | 238.14 |