Element Partition Trees For H-Refined Meshes to Optimize Direct Solver Performance. Part I: Dynamic Programming

Abstract
We consider a class of two-and three-dimensional h-refined meshes generated by an adaptive finite element method. We introduce an element partition tree, which controls the execution of the multi-frontal solver algorithm over these refined grids. We propose and study algorithms with polynomial computational cost for the optimization of these element partition trees. The trees provide an ordering for the elimination of unknowns. The algorithms automatically optimize the element partition trees using extensions of dynamic programming. The construction of the trees by the dynamic programming approach is expensive. These generated trees cannot be used in practice, but rather utilized as a learning tool to propose fast heuristic algorithms. In this first part of our paper we focus on the dynamic programming approach, and draw a sketch of the heuristic algorithm. The second part will be devoted to a more detailed analysis of the heuristic algorithm extended for the case of hp-adaptive

Citation
Aboueisha H, Calo VM, Jopek K, Moshkov M, Paszyńka A, et al. (2017) Element Partition Trees For H-Refined Meshes to Optimize Direct Solver Performance. Part I: Dynamic Programming. International Journal of Applied Mathematics and Computer Science 27. Available: http://dx.doi.org/10.1515/amcs-2017-0025.

Acknowledgements
The work was partially supported by the Center for Numerical Porous Media, King Abdullah University of Science and Technology (KAUST), and by the National Science Centre, Poland, grant no. DEC-2012/06/M/ST1/00363. This publication also was made possible by a National Priorities Research Program grant 7-1482-1-278 from the Qatar National Research Fund (a member of The Qatar Foundation). This work was partially supported by the European Union's Horizon 2020 research and an innovation program under the Marie Sklodowska-Curie grant agreement no. 644602. The J. Tinsley Oden Faculty Fellowship Research Program at the Institute for Computational Engineering and Sciences (ICES) of the University of Texas at Austin partially supported the visits of Victor Manuel Calo to the ICES.

Publisher
Walter de Gruyter GmbH

Journal
International Journal of Applied Mathematics and Computer Science

DOI
10.1515/amcs-2017-0025

Additional Links
https://www.degruyter.com/view/j/amcs.2017.27.issue-2/amcs-2017-0025/amcs-2017-0025.xml

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