Element Partition Trees For H-Refined Meshes to Optimize Direct Solver Performance. Part I: Dynamic Programming
Author:
Aboueisha Hassan1, Calo Victor Manuel2, Jopek Konrad3, Moshkov Mikhail1, Paszyńka Anna4, Paszyński Maciej3, Skotniczny Marcin3
Affiliation:
1. Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) King Abdullah University of Science and Technology, Bld. 1 (Al-khawarizmi) 4128-WS03, Thuwal , 23955-6900, Kingdom of Saudi Arabia 2. Faculty of Science and Engineering, Western Australian School of Mines Curtin University, Kent Street, Perth , WA 6102, Australia 3. Faculty of Computer Science, Electronics and Telecommunications AGH University of Science and Technology, al. Mickiewicza 30, 30-059 Kraków , Poland 4. Faculty of Physics, Astronomy and Applied Computer Science Jagiellonian University, ul. Łojasiewicza 11, 30-348 Kraków , Poland
Abstract
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 grids.
Publisher
Walter de Gruyter GmbH
Subject
Applied Mathematics,Engineering (miscellaneous),Computer Science (miscellaneous)
Reference31 articles.
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