| 固体中短波传播的单位分解有限元法 |
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| 引用本文： | 李锡夔,周浩洋. 固体中短波传播的单位分解有限元法[J]. 应用数学和力学, 2005, 26(8): 965-971 |
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| 作者姓名： | 李锡夔 周浩洋 |
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| 作者单位： | 大连理工大学 工业装备结构分析国家重点实验室, 大连 116024 |
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| 基金项目： | 国家自然科学基资助金项目(50278012;10272027;19832010);国家九七三基金资助项目(2002CB412709) |
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| 摘 要： | 提出了固体中短波传播数值模拟的单位分解有限元法．有限元空间由形成单位分解的标准等参有限元形函数乘以定义为局部子空间基函数的特殊形函数构成．特殊形函数使试空间中包含了关于波动方程的已有知识，因而在单个单元内能近似地再现高度振荡性质．数值例题显示了所提出单位分解有限元在计算精度和效率上的良好性能．
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| 关 键 词： | 短波传播 固体介质 单位分解有限元法 |
| 文章编号： | 1000-0887(2005)08-0965-07 |
| 收稿时间： | 2003-06-04 |
| 修稿时间： | 2003-06-04 |
Partition of Unity Finite Element Method for Short Wave Propagation in Solids |
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| LI Xi-kui,ZHOU Hao-yang. Partition of Unity Finite Element Method for Short Wave Propagation in Solids[J]. Applied Mathematics and Mechanics, 2005, 26(8): 965-971 |
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| Authors: | LI Xi-kui ZHOU Hao-yang |
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| Affiliation: | State Key Laboratory for Structural Analysis of Industrial Equipment, Dalian University of Technology, Dalian 116024, P. R. China |
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| Abstract: | A partition of unity finite element method for numerical simulation of short wave propagation in solids is presented. The finite element spaces were constructed by multiplying the standard isoparametric finite element shape functions, which form a partition of unity, with the local subspaces defined on the corresponding shape functions, which include a priori knowledge about the wave motion equation in trial spaces and approximately reproduce the highly oscillatory properties within a single element. Numerical examples demonstrate the performance of the proposed partition of unity finite element in both computational accuracy and efficiency. |
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