TY - JOUR

T1 - Quasi-Optimal Elimination Trees for 2D Grids with Singularities

AU - Paszyńska, A.

AU - Paszyński, M.

AU - Jopek, K.

AU - Woźniak, M.

AU - Goik, D.

AU - Gurgul, P.

AU - AbouEisha, Hassan M.

AU - Moshkov, Mikhail

AU - Calo, Victor M.

AU - Lenharth, A.

AU - Nguyen, D.

AU - Pingali, K.

N1 - KAUST Repository Item: Exported on 2020-10-01

PY - 2015/3/10

Y1 - 2015/3/10

N2 - 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 O(log(Ne log(Ne)), where N e 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.

AB - 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 O(log(Ne log(Ne)), where N e 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.

UR - http://hdl.handle.net/10754/550467

UR - http://www.hindawi.com/journals/sp/2015/303024/

UR - http://www.scopus.com/inward/record.url?scp=84925582843&partnerID=8YFLogxK

U2 - 10.1155/2015/303024

DO - 10.1155/2015/303024

M3 - Article

SN - 1058-9244

VL - 2015

SP - 1

EP - 18

JO - Scientific Programming

JF - Scientific Programming

ER -