Name
Abstract | ||
|---|---|---|
AbstractWe construct quasi-optimal elimination trees for 2D finite element meshes with singularities. These trees minimize the complexity of the solution of the discrete system. The computational cost estimates of the elimination process model the execution of the multifrontal algorithms in serial and in parallel shared-memory executions. Since the meshes considered are a subspace of all possible mesh partitions, we call these minimizers quasi-optimal. We minimize the cost functionals using dynamic programming. Finding these minimizers is more computationally expensive than solving the original algebraic system. Nevertheless, from the insights provided by the analysis of the dynamic programming minima, we propose a heuristic construction of the elimination trees that has cost O(Ne log(Ne)), where Ne is the number of elements in the mesh. We show that this heuristic ordering has similar computational cost to the quasi-optimal elimination trees found with dynamic programming and outperforms state-of-the-art alternatives in our numerical experiments. |
Year | DOI | Venue |
|---|---|---|
2015 | 10.1155/2015/303024 | Periodicals |
Field | DocType | Volume |
Dynamic programming,Mathematical optimization,Heuristic,Algebraic number,Polygon mesh,Subspace topology,Computer science,Algorithm,Maxima and minima,Process of elimination,Discrete system | Journal | 2015 |
Issue | ISSN | Citations |
1 | 1058-9244 | 4 |
PageRank | References | Authors |
0.50 | 20 | 12 |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Anna Paszyńska | 1 | 125 | 17.77 |
| Maciej Paszynski | 2 | 193 | 36.89 |
| Konrad Jopek | 3 | 25 | 4.44 |
| M. Wozniak | 4 | 27 | 7.48 |
| Damian Goik | 5 | 18 | 2.27 |
| Piotr Gurgul | 6 | 25 | 4.95 |
| Hassan AbouEisha | 7 | 16 | 3.87 |
| Mikhail Ju. Moshkov | 8 | 335 | 60.44 |
| Victor M. Calo | 9 | 191 | 38.14 |
| Andrew Lenharth | 10 | 456 | 19.94 |
| Donald Nguyen | 11 | 419 | 17.94 |
| Keshav Pingali | 12 | 3056 | 256.64 |