Quasi-Optimal Elimination Trees for 2D Grids with Singularities
Joint Authors
Paszyńska, A.
Paszyński, M.
Jopek, K.
Woźniak, M.
Goik, D.
Gurgul, P.
AbouEisha, H.
Moshkov, M.
Calo, V. M.
Lenharth, A.
Nguyen, D.
Pingali, K.
Source
Issue
Vol. 2015, Issue 2015 (31 Dec. 2015), pp.1-18, 18 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2015-03-10
Country of Publication
Egypt
No. of Pages
18
Main Subjects
Abstract EN
We 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 ONelogNe, 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.
American Psychological Association (APA)
Paszyńska, A.& Paszyński, M.& Jopek, K.& Woźniak, M.& Goik, D.& Gurgul, P.…[et al.]. 2015. Quasi-Optimal Elimination Trees for 2D Grids with Singularities. Scientific Programming،Vol. 2015, no. 2015, pp.1-18.
https://search.emarefa.net/detail/BIM-1076525
Modern Language Association (MLA)
Paszyńska, A.…[et al.]. Quasi-Optimal Elimination Trees for 2D Grids with Singularities. Scientific Programming No. 2015 (2015), pp.1-18.
https://search.emarefa.net/detail/BIM-1076525
American Medical Association (AMA)
Paszyńska, A.& Paszyński, M.& Jopek, K.& Woźniak, M.& Goik, D.& Gurgul, P.…[et al.]. Quasi-Optimal Elimination Trees for 2D Grids with Singularities. Scientific Programming. 2015. Vol. 2015, no. 2015, pp.1-18.
https://search.emarefa.net/detail/BIM-1076525
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1076525