<abstract xmlns="http://www.w3.org/1999/xhtml"><p> 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.</p></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.

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

International Journal of Applied Mathematics and Computer Science

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

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,...

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

Data publikacji: 08 lip 2017

Zakres stron: 351 - 365

Otrzymano: 11 wrz 2016

Przyjęty: 05 lut 2017

DOI: https://doi.org/10.1515/amcs-2017-0025

Słowa kluczowe
h-adaptive finite element method, ordering, element partition tree, extensions of dynamic programming, multifrontal direct solvers

© by Maciej Paszyński

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

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

Data publikacji: 08 lip 2017

Zakres stron: 351 - 365

Otrzymano: 11 wrz 2016

Przyjęty: 05 lut 2017

DOI: https://doi.org/10.1515/amcs-2017-0025

Słowa kluczoweh-adaptive finite element method, ordering, element partition tree, extensions of dynamic programming, multifrontal direct solvers

© by Maciej Paszyński

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Słowa kluczowe
h-adaptive finite element method, ordering, element partition tree, extensions of dynamic programming, multifrontal direct solvers