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

• H. AbouEisha
• V. M. Calo
• K. Jopek
• M. Moshkov
• A. Paszyńska
• M. Paszyński
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10861)

## Abstract

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.

## Keywords

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

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## Authors and Affiliations

• H. AbouEisha
• 1
• V. M. Calo
• 2
• 3
• 4
• K. Jopek
• 5
• M. Moshkov
• 1
• A. Paszyńska
• 6
• M. Paszyński
• 5
1. 1.King Abdullah University of Science and TechnologyThuwalSaudi Arabia
2. 2.Chair in Computational Geoscience, Applied Geology Department, Western Australian School of Mines, Faculty of Science and EngineeringCurtin UniversityPerthAustralia
3. 3.Mineral ResourcesCommonwealth Scientific and Industrial Research Organization (CSIRO)KensingtonAustralia
4. 4.Curtin Institute for ComputationCurtin UniversityPerthAustralia
5. 5.Faculty of Computer Science, Electronics and TelecommunicationsAGH University of Science and TechnologyKrakowPoland
6. 6.Faculty of Physics, Astronomy and Applied Computer ScienceJagiellonian UniversityKrakowPoland