| 张量积形式的三维延拓 Kantorovich 法 |
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| 引用本文： | 林永静, 袁驷. 张量积形式的三维延拓 Kantorovich 法[J]. 工程力学, 2012, 29(5): 8-12. |
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| 作者姓名： | 林永静 袁驷 |
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| 作者单位： | 1.温州职业技术学院建筑工程系, 温州 325035;;2.清华大学土木工程系, 北京 100084 |
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| 基金项目： | 国家杰出青年科学基金项目(59525813);温州职业技术学院重点课题项目(WZY2010009) |
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| 摘 要： | 该文采用张量积的试函数逼近形式,即u(x,y,z)={X(x)}T[Z(z)]{Y(y)},成功地建立了三维延拓Kantorovich 法的算法方程式,克服了简单试函数逼近形式的迭代不收敛的数值困难。三维Poisson 方程的数值算例显示了该算法的迭代收敛性以及高精度和高效率。
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| 关 键 词： | 延拓Kantorovich法 张量积 函数逼近形式 迭代 三维Poisson 方程 |
| 收稿时间： | 2012-05-09 |
| 修稿时间： | 2012-05-09 |
THREE-DIMENSIONAL EXTENDED KANTOROVICH METHOD OF TENSOR PRODUCT FORM |
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| LIN Yong-jing, YUAN Si. THREE-DIMENSIONAL EXTENDED KANTOROVICH METHOD OF TENSOR PRODUCT FORM[J]. Engineering Mechanics, 2012, 29(5): 8-12. |
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| Authors: | LIN Yong-jing YUAN Si |
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| Affiliation: | 1.Department of Architectural Engineering, Wenzhou Vocational Technical College, Wenzhou 325035;;2.Department of Civil Engineering, Tsinghua University, Beijing 100084 |
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| Abstract: | Using the function approximation of tensor product,the extended Kantorovich method was successfully applied to three-dimensional problems in the paper and the non-convergence of the iteration procedure using simple function approximation was overcame.Furthermore,the iteration convergence was displayed and high accuracy and efficiency were demonstrated by numerical examples of the three-dimensional Poisson equation. |
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| Keywords: | extended Kantorovich method tensor product function approximation iteration three-dimensional Poisson equation |
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