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dc.contributor.authorAbouEisha, Hassan M.
dc.contributor.authorJopek, Konrad
dc.contributor.authorMedygrał, Bartłomiej
dc.contributor.authorMoshkov, Mikhail
dc.contributor.authorNosek, Szymon
dc.contributor.authorPaszyńska, Anna
dc.contributor.authorPaszyński, Maciej
dc.contributor.authorPingali, Keshav
dc.identifier.citationAbouEisha H, Jopek K, Medygrał B, Moshkov M, Nosek S, et al. (2016) Hybrid Direct and Iterative Solver with Library of Multi-criteria Optimal Orderings for h Adaptive Finite Element Method Computations. Procedia Computer Science 80: 865–874. Available:
dc.description.abstractIn this paper we present a multi-criteria optimization of element partition trees and resulting orderings for multi-frontal solver algorithms executed for two dimensional h adaptive finite element method. In particular, the problem of optimal ordering of elimination of rows in the sparse matrices resulting from adaptive finite element method computations is reduced to the problem of finding of optimal element partition trees. Given a two dimensional h refined mesh, we find all optimal element partition trees by using the dynamic programming approach. An element partition tree defines a prescribed order of elimination of degrees of freedom over the mesh. We utilize three different metrics to estimate the quality of the element partition tree. As the first criterion we consider the number of floating point operations(FLOPs) performed by the multi-frontal solver. As the second criterion we consider the number of memory transfers (MEMOPS) performed by the multi-frontal solver algorithm. As the third criterion we consider memory usage (NONZEROS) of the multi-frontal direct solver. We show the optimization results for FLOPs vs MEMOPS as well as for the execution time estimated as FLOPs+100MEMOPS vs NONZEROS. We obtain Pareto fronts with multiple optimal trees, for each mesh, and for each refinement level. We generate a library of optimal elimination trees for small grids with local singularities. We also propose an algorithm that for a given large mesh with identified local sub-grids, each one with local singularity. We compute Schur complements over the sub-grids using the optimal trees from the library, and we submit the sequence of Schur complements into the iterative solver ILUPCG.
dc.description.sponsorshipThe work presented in this paper has been supported by National Science Centre, Poland grant no. DEC-2015/17/B/ST6/01867 and by King Abdullah University of Science and Technology (KAUST).
dc.publisherElsevier BV
dc.rightsUnder a Creative Commons license
dc.subjectElement partition tree
dc.subjectFinite element method
dc.subjectH adaptivity
dc.subjectMulti-frontal direct solver
dc.subjectOrdering algorithms
dc.titleHybrid Direct and Iterative Solver with Library of Multi-criteria Optimal Orderings for h Adaptive Finite Element Method Computations
dc.contributor.departmentApplied Mathematics and Computational Science Program
dc.contributor.departmentComputer Science Program
dc.contributor.departmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
dc.identifier.journalProcedia Computer Science
dc.conference.date2016-06-06 to 2016-06-08
dc.conference.nameInternational Conference on Computational Science, ICCS 2016
dc.conference.locationSan Diego, CA, USA
dc.eprint.versionPublisher's Version/PDF
dc.contributor.institutionDepartment of Computer Science, AGH University of Science and Technology, Kraków, Poland
dc.contributor.institutionFaculty of Physics, Astronomy and Applied Computer Science, Jagiellonian University, Kraków, Poland
dc.contributor.institutionInstitute for Computational and Engineering Sciences, University of Texas, Austin, United States
kaust.personAbouEisha, Hassan M.
kaust.personMoshkov, Mikhail

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