Fast Methods for Solving High Accuracy Surface Modeling
High accuracy surface modeling (HASM) is a novel surface modeling method. The well known preconditioned conjugate gradient (PCG) method is used to solve the equations produced by HASM. In this paper, in order to improve the convergence rate of PCG, we use two preconditioners: incomplete Cholesky dec...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
SAGE Publishing
2013-06-01
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| Series: | Journal of Algorithms & Computational Technology |
| Online Access: | https://doi.org/10.1260/1748-3018.7.2.187 |
| _version_ | 1818454668987072512 |
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| author | Na Zhao Tian Xiang Yue |
| author_facet | Na Zhao Tian Xiang Yue |
| author_sort | Na Zhao |
| collection | DOAJ |
| description | High accuracy surface modeling (HASM) is a novel surface modeling method. The well known preconditioned conjugate gradient (PCG) method is used to solve the equations produced by HASM. In this paper, in order to improve the convergence rate of PCG, we use two preconditioners: incomplete Cholesky decomposition conjugate gradient method (ICCG) and symmetric successive over relaxation-preconditioned conjugate gradient method (SSORCG), which have not previously been available for use with HASM. Furthermore, we give adequate storage scheme of the large sparse matrix and optimize the performance of sparse matrix-vector multiplication. We test the proposed method on a Dell OP990 machine. Numerical tests show that ICCG has the fastest convergence rate of HASM. We also find that both ICCG and SSORCG have much faster convergence rates than some available solvers. |
| first_indexed | 2024-12-14T21:58:33Z |
| format | Article |
| id | doaj.art-52b30ac6c5cd43f7b91bfa62bafaf4e9 |
| institution | Directory Open Access Journal |
| issn | 1748-3018 1748-3026 |
| language | English |
| last_indexed | 2024-12-14T21:58:33Z |
| publishDate | 2013-06-01 |
| publisher | SAGE Publishing |
| record_format | Article |
| series | Journal of Algorithms & Computational Technology |
| spelling | doaj.art-52b30ac6c5cd43f7b91bfa62bafaf4e92022-12-21T22:46:03ZengSAGE PublishingJournal of Algorithms & Computational Technology1748-30181748-30262013-06-01710.1260/1748-3018.7.2.187Fast Methods for Solving High Accuracy Surface ModelingNa ZhaoTian Xiang Yue0 Institute of Geographical Sciences and Natural Resources Research, Chinese Academy of Sciences, Beijing 100101High accuracy surface modeling (HASM) is a novel surface modeling method. The well known preconditioned conjugate gradient (PCG) method is used to solve the equations produced by HASM. In this paper, in order to improve the convergence rate of PCG, we use two preconditioners: incomplete Cholesky decomposition conjugate gradient method (ICCG) and symmetric successive over relaxation-preconditioned conjugate gradient method (SSORCG), which have not previously been available for use with HASM. Furthermore, we give adequate storage scheme of the large sparse matrix and optimize the performance of sparse matrix-vector multiplication. We test the proposed method on a Dell OP990 machine. Numerical tests show that ICCG has the fastest convergence rate of HASM. We also find that both ICCG and SSORCG have much faster convergence rates than some available solvers.https://doi.org/10.1260/1748-3018.7.2.187 |
| spellingShingle | Na Zhao Tian Xiang Yue Fast Methods for Solving High Accuracy Surface Modeling Journal of Algorithms & Computational Technology |
| title | Fast Methods for Solving High Accuracy Surface Modeling |
| title_full | Fast Methods for Solving High Accuracy Surface Modeling |
| title_fullStr | Fast Methods for Solving High Accuracy Surface Modeling |
| title_full_unstemmed | Fast Methods for Solving High Accuracy Surface Modeling |
| title_short | Fast Methods for Solving High Accuracy Surface Modeling |
| title_sort | fast methods for solving high accuracy surface modeling |
| url | https://doi.org/10.1260/1748-3018.7.2.187 |
| work_keys_str_mv | AT nazhao fastmethodsforsolvinghighaccuracysurfacemodeling AT tianxiangyue fastmethodsforsolvinghighaccuracysurfacemodeling |