| 利用插值型无单元Galerkin方法求解KdV-B方程 |
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| 引用本文： | 裴凯燕,郭龙飞,任红萍. 利用插值型无单元Galerkin方法求解KdV-B方程[J]. 西南民族大学学报(自然科学版), 2015, 41(6): 748-753 |
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| 作者姓名： | 裴凯燕 郭龙飞 任红萍 |
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| 作者单位： | 太原科技大学应用科学学院,太原科技大学应用科学学院,太原科技大学应用科学学院 |
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| 基金项目： | 山西省自然科学基金项目(2014011006-2)；太原科技大学博士研究基金项目(No. 20102024)；太原科技大学研究生科技创新项目(No.20145010). |
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| 摘 要： | 首先讨论移动最小二乘插值法,并利用移动最小二乘插值法建立形函数,结合KdV-B方程的Galerkin积分弱形式,提出求KdV-B方程数值解的插值型无单元Galerkin方法(IEFG),并推导其相应的公式,跟无单元Galerkin方法相比,利用插值型无单元Galerkin方法计算时,本质边界条件可直接施加,从而可提高计算效率,并给出算例说明了该方法的有效性.
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| 关 键 词： | 无网格方法 移动最小二乘插值法 形函数 插值型无单元Galerkin方法(IEFG) KdV-B方程 |
| 收稿时间： | 2015-03-15 |
| 修稿时间： | 2015-10-27 |
Interpolating element-free Galerkin method for the compound KdV-B equation |
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| PEI Kaiyan,GUO Longfei and REN Hongping. Interpolating element-free Galerkin method for the compound KdV-B equation[J]. Journal of Southwest Minzu University (Natural Science Edition), 2015, 41(6): 748-753 |
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| Authors: | PEI Kaiyan GUO Longfei REN Hongping |
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| Affiliation: | School of Applied Science,Taiyuan University of Science and Technology,School of Applied Science,Taiyuan University of Science and Technology,School of Applied Science,Taiyuan University of Science and Technology |
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| Abstract: | An interpolating moving least squares method is discussed first. Combining the shape function constructed by the IMLS method and Galerkin weak form for the compound KdV-B equation, the interpolating element-free Galerkin (IEFG) method for the compound KdV-B equation is put forward, and the corresponding formulae are obtained. Compared with the conventional EFG method, in the IEFG method, the boundary conditions can be directly applied . Numerical results show that it not only has high computational accuracy, but also enhances computational efficiency greatly. |
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| Keywords: | meshless method interpolating moving least squares method shape function interpolating element-free Galerkin (IEFG) method KdV-B equation |
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