Name
Abstract | ||
|---|---|---|
In papers by Arnold, Falk, and Winther, and by Hiptmair, novel multigrid methods for discrete H(curl; Ω)-elliptic boundary value problems have been proposed. Such problems frequently occur in computational electromagnetism, particularly in the context of eddy current simulation.This paper focuses on the analysis of those nodal multilevel decompositions of the spaces of edge finite elements that form the foundation of the multigrid methods. It provides a significant extension of the existing theory to the case of locally vanishing coefficients and nonconvex domains. In particular, asymptotically uniform convergence of the multigrid method with respect to the number of refinement levels can be established under assumptions that are satisfied in realistic settings for eddy current problems.The principal idea is to use approximate Helmholtz-decompositions of the function space H(curl; Ω) into an H1 (Ω)-regular subspace and gradients. The main results of standard multilevel theory for H1 (Ω)-elliptic problems can then be applied to both subspaces. This yields preliminary decompositions still outside the edge element spaces. Judicious alterations can cure this. |
Year | DOI | Venue |
|---|---|---|
2003 | 10.1090/S0025-5718-02-01468-0 | Math. Comput. |
Keywords | Field | DocType |
stable bpx-type splittings,multigrid method,multilevel methods,edge element space,novel multigrid method,edge finite element,discrete h,multi- grid in curl,helmholtz-decomposition. this work was supported by dfg as part of sfb 382.,. edge elements,multilevel method,eddy current simulation,elliptic boundary value problem,existing theory,elliptic problem,eddy current problem,uniform convergence,function space,ω,eddy current | Mathematical optimization,Function space,Mathematical analysis,Uniform convergence,Finite element method,Linear subspace,Numerical analysis,Partial differential equation,Curl (mathematics),Mathematics,Multigrid method | Journal |
Volume | Issue | ISSN |
72 | 243 | 0025-5718 |
Citations | PageRank | References |
4 | 0.73 | 12 |
Authors | ||
1 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| R. Hiptmair | 1 | 199 | 38.97 |