Abstract
We discuss the efficient implementation of powerful domain decomposition smoothers for multigrid methods for high-order discontinuous Galerkin (DG) finite element methods. In particular, we study the inversion of matrices associated to mesh cells and to the patches around a vertex, respectively, in order to obtain fast local solvers for additive and multiplicative subspace correction methods. The effort of inverting local matrices for tensor product polynomials of degree k is reduced from (k 3 d) {mathcal{O}(k{3d})} to (d k d + 1) {mathcal{O}(dk{d+1})} by exploiting the separability of the differential operator and resulting low rank representation of its inverse as a prototype for more general low rank representations in space dimension d.
| Original language | English |
|---|---|
| Pages (from-to) | 709-728 |
| Number of pages | 20 |
| Journal | Computational Methods in Applied Mathematics |
| Volume | 21 |
| Issue number | 3 |
| DOIs | |
| State | Published - Jul 1 2021 |
Funding
This manuscript has been authored by UT-Battelle, LLC under Contract No. DE-AC05-00OR22725 with the U.S. Department of Energy. The United States Government retains and the publisher, by accepting the article for publication, acknowledges that the United States Government retains a non-exclusive, paid-up, irrevocable, worldwide license to publish or reproduce the published form of this manuscript, or allow others to do so, for United States Government purposes. The Department of Energy will provide public access to these results of federally sponsored research in accordance with the DOE Public Access Plan (http://energy.gov/downloads/doe-public-access-plan). The implementation is based on the deal.II library [].
| Funders | Funder number |
|---|---|
| U.S. Department of Energy |
Keywords
- Discontinuous Galerkin Finite Element
- Domain Decomposition
- Fast Diagonalization
- Geometric Multigrid