| Accurate Parallel Algorithm for Adini Nonconforming Finite Element |
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| 作者姓名： | 罗平 周爱辉 |
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| 作者单位： | Department of Computer Science and Technology，Tsinghua University，Beijing 100084，China，Institute of Computational Mathematics and Scientific Engineering Computing，Academy of Mathematics and System Sciences，Chinese Academy of Sciences，Beijing 100080，China |
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| 基金项目： | Supported by the National Natural Science Foundation of China(No.19971050) |
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| 摘 要： | Multi-parameter asymptotic expansions are interesting since they justify the use of multi-parameter extrapolation which can be implemented in parallel and are well studied in many papers for the conforming finite element methods. For the nonconforming finite element methods, however, the work of the multi-parameter asymptotic expansions and extrapolation have seldom been found in the literature. This paper considers the solution of the biharmonic equation using Adini nonconforming finite elements and reports new results for the multi-parameter asymptotic expansions and extrapolation. The Adini nonconforming finite element solution of the biharmonic equation is shown to have a multi-parameter asymptotic error expansion and extrapolation. This expansion and a multi-parameter extrapolation technique were used to develop an accurate approximation parallel algorithm for the biharmonic equation. Finally, numerical results have verified the extrapolation theory.
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Accurate Parallel Algorithm for Adini Nonconforming Finite Element |
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| LUO Ping,ZHOU Aihui.Accurate Parallel Algorithm for Adini Nonconforming Finite Element[J].Tsinghua Science and Technology,2003,8(2). |
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| Authors: | LUO Ping ZHOU Aihui |
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| Institution: | LUO Ping,ZHOU Aihui
Department of Computer Science and Technology,Tsinghua University,Beijing 100084,China,
Institute of Computational Mathematics and Scientific Engineering Computing,Academy of Mathematics and System Sciences,Chinese Academy of Sciences,Beijing 100080,China |
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| Abstract: | Multi-parameter asymptotic expansions are interesting since they justify the use of multi-parameter extrapolation which can be implemented in parallel and are well studied in many papers for the conforming finite element methods. For the nonconforming finite element methods, however, the work of the multi-parameter asymptotic expansions and extrapolation have seldom been found in the literature. This paper considers the solution of the biharmonic equation using Adini nonconforming finite elements and reports new results for the multi-parameter asymptotic expansions and extrapolation. The Adini nonconforming finite element solution of the biharmonic equation is shown to have a multi-parameter asymptotic error expansion and extrapolation. This expansion and a multi-parameter extrapolation technique were used to develop an accurate approximation parallel algorithm for the biharmonic equation. Finally, numerical results have verified the extrapolation theory. |
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| Keywords: | Adini nonconforming element parallel algorithm domain decomposition error expansion |
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