Bisections-Weighted-by-Element-Size-and-Order Algorithm to Optimize Direct Solver Performance on 3D hp-adaptive Grids
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...
| Main Authors: | , , , , , |
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| Format: | Conference Paper |
| Published: |
2018
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| Online Access: | http://hdl.handle.net/20.500.11937/69673 |
| _version_ | 1848762103554375680 |
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| author | AbouEisha, H. Calo, Victor Jopek, K. Moshkov, M. Paszynska, A. Paszynski, M. |
| author_facet | AbouEisha, H. Calo, Victor Jopek, K. Moshkov, M. Paszynska, A. Paszynski, M. |
| author_sort | AbouEisha, H. |
| building | Curtin Institutional Repository |
| collection | Online Access |
| description | 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. |
| first_indexed | 2025-11-14T10:42:15Z |
| format | Conference Paper |
| id | curtin-20.500.11937-69673 |
| institution | Curtin University Malaysia |
| institution_category | Local University |
| last_indexed | 2025-11-14T10:42:15Z |
| publishDate | 2018 |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | curtin-20.500.11937-696732018-09-06T02:03:36Z Bisections-Weighted-by-Element-Size-and-Order Algorithm to Optimize Direct Solver Performance on 3D hp-adaptive Grids AbouEisha, H. Calo, Victor Jopek, K. Moshkov, M. Paszynska, A. Paszynski, M. 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. 2018 Conference Paper http://hdl.handle.net/20.500.11937/69673 10.1007/978-3-319-93701-4_60 restricted |
| spellingShingle | AbouEisha, H. Calo, Victor Jopek, K. Moshkov, M. Paszynska, A. Paszynski, M. Bisections-Weighted-by-Element-Size-and-Order Algorithm to Optimize Direct Solver Performance on 3D hp-adaptive Grids |
| title | Bisections-Weighted-by-Element-Size-and-Order Algorithm to Optimize Direct Solver Performance on 3D hp-adaptive Grids |
| title_full | Bisections-Weighted-by-Element-Size-and-Order Algorithm to Optimize Direct Solver Performance on 3D hp-adaptive Grids |
| title_fullStr | Bisections-Weighted-by-Element-Size-and-Order Algorithm to Optimize Direct Solver Performance on 3D hp-adaptive Grids |
| title_full_unstemmed | Bisections-Weighted-by-Element-Size-and-Order Algorithm to Optimize Direct Solver Performance on 3D hp-adaptive Grids |
| title_short | Bisections-Weighted-by-Element-Size-and-Order Algorithm to Optimize Direct Solver Performance on 3D hp-adaptive Grids |
| title_sort | bisections-weighted-by-element-size-and-order algorithm to optimize direct solver performance on 3d hp-adaptive grids |
| url | http://hdl.handle.net/20.500.11937/69673 |