Bisections-Weighted-by-Element-Size-and-Order Algorithm to Optimize Direct Solver Performance on 3D hp-adaptive Grids

H. AbouEisha, Victor Calo, K. Jopek, M. Moshkov, A. Paszyńska, M. Paszyński*

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

1 Scopus citations


The hp-adaptive Finite Element Method (hp-FEM) generates a sequence of adaptive grids with different polynomial orders of approximation and element sizes. The hp-FEM delivers exponential convergence of the numerical error with respect to the mesh size. In this paper, we propose a heuristic algorithm to construct element partition trees. The trees can be transformed directly into the orderings, which control the execution of the multi-frontal direct solvers during the hp refined finite element method. In particular, the orderings determine the number of floating point operations performed by the solver. Thus, the quality of the orderings obtained from the element partition trees is important for good performance of the solver. Our heuristic algorithm has been implemented in 3D and tested on a sequence of hp-refined meshes. We compare the quality of the orderings found by the heuristic algorithm to those generated by alternative state-of-the-art algorithms. We show 50% reduction in flops number and execution time.

Original languageEnglish (US)
Title of host publicationComputational Science – ICCS 2018 - 18th International Conference, Proceedings
EditorsValeria V. Krzhizhanovskaya, Michael Harold Lees, Peter M. Sloot, Jack Dongarra, Yong Shi, Yingjie Tian, Haohuan Fu
PublisherSpringer Verlag
Number of pages13
ISBN (Print)9783319937007
StatePublished - 2018
Event18th International Conference on Computational Science, ICCS 2018 - Wuxi, China
Duration: Jun 11 2018Jun 13 2018

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume10861 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349


Conference18th International Conference on Computational Science, ICCS 2018


  • Heuristic algorithms
  • Multi-frontal direct solvers
  • Nested-dissections
  • Ordering
  • hp adaptive finite element method

ASJC Scopus subject areas

  • Theoretical Computer Science
  • General Computer Science


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