Signorini问题的无网格投影迭代法

王延冲

doi:10.13718/j.cnki.xsxb.2014.09.012

西南师范大学学报(自然科学版)

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Signorini问题的无网格投影迭代法

王延冲. Signorini问题的无网格投影迭代法[J]. 西南师范大学学报(自然科学版), 2014, 39(9). doi: 10.13718/j.cnki.xsxb.2014.09.012

引用本文:

王延冲. Signorini问题的无网格投影迭代法[J]. 西南师范大学学报(自然科学版), 2014, 39(9). doi: 10.13718/j.cnki.xsxb.2014.09.012

WANG Yan-chong. On a Meshless Projection Iterative Method for Signorini Problems[J]. Journal of Southwest China Normal University(Natural Science Edition), 2014, 39(9). doi: 10.13718/j.cnki.xsxb.2014.09.012

Citation:

WANG Yan-chong. On a Meshless Projection Iterative Method for Signorini Problems[J]. Journal of Southwest China Normal University(Natural Science Edition), 2014, 39(9). doi: 10.13718/j.cnki.xsxb.2014.09.012

Signorini问题的无网格投影迭代法

王延冲

重庆师范大学数学学院,重庆,401331

On a Meshless Projection Iterative Method for Signorini Problems

WANG Yan-chong

摘要: Signorini问题是一类重要的数学物理问题，该问题的Signorini互补条件位于边界上，特别适合用边界型方法求解。利用投影算子，首先将Signorini边界条件转化为不动点方程，得到Signorini问题的迭代格式，然后用无网格边界点方法求解。此种算法的优点在于只须在原有的无网格边界点程序中做少量的改进，且迭代效率高，计算误差小。数值结果表明，该算法较边界元方法更有效。
- 无网格方法 /
- Signorini问题 /
- 投影迭代算法 /
- 边界点方法 /
- 移动最小二乘近似
Abstract: Signorini problem is an important partial differential boundary value problem .Since the Signorini complementary conditions lie on the boundary of the region ,it is suitable for boundary type method .Ac-cording to a projection operator ,the Signorini boundary conditions have been transformed into a fixed point equation .T hen ,projection iterative scheme of Signorini problem based on the fixed point equation has been established .The meshless boundary node method (BNM ) is introduced for solving Signorini problem in the iterative scheme .T he presented algorithm is easy to be implied .It only needs the minimal change of the BNM programming .The numerical results show that the algorithm is more effective than the boundary element method .
- meshless method，Signorini problem，projection iterative algorithm，boundary node method，moving least square /

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Signorini问题的无网格投影迭代法

王延冲

重庆师范大学数学学院,重庆,401331

关键词:

摘要: Signorini问题是一类重要的数学物理问题，该问题的Signorini互补条件位于边界上，特别适合用边界型方法求解。利用投影算子，首先将Signorini边界条件转化为不动点方程，得到Signorini问题的迭代格式，然后用无网格边界点方法求解。此种算法的优点在于只须在原有的无网格边界点程序中做少量的改进，且迭代效率高，计算误差小。数值结果表明，该算法较边界元方法更有效。

English Abstract

On a Meshless Projection Iterative Method for Signorini Problems

重庆师范大学数学学院,重庆,401331

Keywords:

Abstract: Signorini problem is an important partial differential boundary value problem .Since the Signorini complementary conditions lie on the boundary of the region ,it is suitable for boundary type method .Ac-cording to a projection operator ,the Signorini boundary conditions have been transformed into a fixed point equation .T hen ,projection iterative scheme of Signorini problem based on the fixed point equation has been established .The meshless boundary node method (BNM ) is introduced for solving Signorini problem in the iterative scheme .T he presented algorithm is easy to be implied .It only needs the minimal change of the BNM programming .The numerical results show that the algorithm is more effective than the boundary element method .