Name
Abstract | ||
|---|---|---|
In this paper, we consider a classical algebraic multigrid (AMG) form of optimal interpolation that directly minimizes the two-grid convergence rate and compare it with a so-called ideal interpolation that minimizes a weak approximation property of the coarse space. We study compatible relaxation type estimates for the quality of the coarse grid and derive a new sharp measure using optimal interpolation that provides a guaranteed lower bound on the convergence rate of the resulting two-grid method for a given grid. In addition, we design a generalized bootstrap AMG setup algorithm that computes a sparse approximation to the optimal interpolation matrix. We demonstrate numerically that the bootstrap AMG method with sparse interpolation matrix (and spanning multiple levels) converges faster than the two-grid method with the standard ideal interpolation (a dense matrix) for various scalar diffusion problems with highly varying diffusion coefficient. |
Year | DOI | Venue |
|---|---|---|
2018 | 10.1137/17M1123456 | SIAM JOURNAL ON SCIENTIFIC COMPUTING |
Keywords | Field | DocType |
algebraic multigrid,compatible relaxation,optimal interpolation,two-grid theory,sharp estimates,convergence | Nearest-neighbor interpolation,Mathematical optimization,Spline interpolation,Polynomial interpolation,Mathematical analysis,Interpolation,Linear interpolation,Trilinear interpolation,Mathematics,Inverse quadratic interpolation,Bilinear interpolation | Journal |
Volume | Issue | ISSN |
40 | 3 | 1064-8275 |
Citations | PageRank | References |
1 | 0.37 | 4 |
Authors | ||
5 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| James J. Brannick | 1 | 33 | 2.74 |
| Fei Cao | 2 | 1 | 0.37 |
| Karsten Kahl | 3 | 15 | 4.39 |
| Robert D. Falgout | 4 | 642 | 70.59 |
| Xiaozhe Hu | 5 | 47 | 16.68 |