Dynamic Programming Algorithm for Generation of Optimal Elimination Trees for Multi-frontal Direct Solver Over H-refined Grids
AuthorsAbouEisha, Hassan M.
Calo, Victor M.
KAUST DepartmentComputer Science Program
Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
Physical Sciences and Engineering (PSE) Division
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AbstractIn this paper we present a dynamic programming algorithm for finding optimal elimination trees for computational grids refined towards point or edge singularities. The elimination tree is utilized to guide the multi-frontal direct solver algorithm. Thus, the criterion for the optimization of the elimination tree is the computational cost associated with the multi-frontal solver algorithm executed over such tree. We illustrate the paper with several examples of optimal trees found for grids with point, isotropic edge and anisotropic edge mixed with point singularity. We show the comparison of the execution time of the multi-frontal solver algorithm with results of MUMPS solver with METIS library, implementing the nested dissection algorithm.
CitationDynamic Programming Algorithm for Generation of Optimal Elimination Trees for Multi-frontal Direct Solver Over H-refined Grids 2014, 29:947 Procedia Computer Science
JournalProcedia Computer Science
Conference/Event name14th Annual International Conference on Computational Science, ICCS 2014