AbouEisha, Hassan M.
Calo, Victor M.
KAUST DepartmentApplied Mathematics and Computational Science Program
Computer Science Program
Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
Earth Science and Engineering Program
Extensions of Dynamic Programming, Machine Learning and Discrete Optimization Research Group
Numerical Porous Media SRI Center (NumPor)
Physical Science and Engineering (PSE) Division
Online Publication Date2015-03-10
Print Publication Date2015
Permanent link to this recordhttp://hdl.handle.net/10754/550467
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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(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.
CitationQuasi-Optimal Elimination Trees for 2D Grids with Singularities 2015, 2015:1 Scientific Programming