中北大学学报（自然科学版）2025，Vol.46Issue(1)：91-97,7.DOI:10.62756/jnuc.issn.1673-3193.2023.09.0010
杂交无单元Galerkin方法施加Dirichlet边界条件研究
Research on Application of the Dirichlet Boundary Condition Using Hybrid Element-Free Galerkin Method
摘要
Abstract
The Lagrange multiplier method and the penalty method are the common methods when apply-ing essential boundary conditions in meshless method.In order to compare the advantage and the disadvan-tage of two methods,the hybrid element-free Galerkin(HEFG)method was presented for analyzing 3D Helmholtz equation.By introducing the dimensional split method,the governing equation could be split into a few 2D forms,for every 2D problem,the Lagrange multiplier method and the penalty method were used to apply the boundary conditions,and the equivalent functional could be established,thus the corre-sponding integral weak forms could be derived.By introducing the improved moving least squares(IMLS)approximation to establish shape functions,the discrete equation of 2D forms could be obtained.In dimensional split direction,the finite difference method was selected to couple these 2D equations,thus the final discrete equation of 3D Helmholtz equation was obtained.In numerical examples,by comparing the computational accuracy and computational time of numerical results,the advantages and disadvantages of two methods for applying boundary conditions were analyzed,respectively.It is shown that the penalty method is better than the Lagrange multiplier method when applying essential boundary conditions.关键词
Lagrange乘子法/罚函数法/Helmholtz方程/杂交无单元Galerkin方法Key words
Lagrange multiplier method/penalty method/Helmholtz equation/hybrid element-free Galerkin method分类
数理科学引用本文复制引用
刘燕,程珩,王韦博..杂交无单元Galerkin方法施加Dirichlet边界条件研究[J].中北大学学报（自然科学版）,2025,46(1):91-97,7.基金项目
山西省青年基金资助项目(20210302124388) （20210302124388）
山西省创新训练项目(20230712) （20230712）
