Meshless or mesh-free (or shorten as MFree) methods have been proposed and achieved remarkable progress over the past few years. The idea of combining MFree methods with other existing numerical techniques such as t...Meshless or mesh-free (or shorten as MFree) methods have been proposed and achieved remarkable progress over the past few years. The idea of combining MFree methods with other existing numerical techniques such as the finite element method (FEM) and the boundary element method (BEM), is naturally of great interest in many practical applications. However, the shape functions used in some MFree methods do not have the Kronecker delta function property. In order to satisfy the combined conditions of displacement compatibility, two numerical techniques, using the hybrid displacement shape function and the modified variational form, are developed and discussed in this paper. In the first technique, the original MFree shape functions are modified to the hybrid forms that possess the Kronecker delta function property. In the second technique, the displacement compatibility is satisfied via a modified variational form based on the Lagrange multiplier method. Formulations of several coupled methods are presented. Numerical exam- ples are presented to demonstrate the effectiveness of the present coupling methods.展开更多
基于A,φ-A法和库伦规范,推导了导体区域和非导体区域的有限元方程及自由空间的边界元方程,通过引入交界面条件,实现了将边界元矩阵等效为有限元矩阵求解的有限元-边界元耦合法(finite element and boundary element coupling method,FE...基于A,φ-A法和库伦规范,推导了导体区域和非导体区域的有限元方程及自由空间的边界元方程,通过引入交界面条件,实现了将边界元矩阵等效为有限元矩阵求解的有限元-边界元耦合法(finite element and boundary element coupling method,FE-BECM)。将FE-BECM应用于TEAM-7问题的计算,验证了该方法处理开域涡流问题的有效性。当FE-BECM应用于运动导体涡流场(moving conductor eddy current,MCEC)问题时,用有限元离散源电流区域和运动部件,用边界元离散自由空间并关联相互独立的有限元区域。该方法克服了常规有限元法使用1套网格处理运动问题所遇到的麻烦。使用有限元-边界元耦合法对单级线圈炮问题进行了计算,验证了算法处理运动导体涡流场问题的有效性。展开更多
In this paper, based on the natural boundary reduction advanced by Feng and Yu, we couple the finite elementapproach with the natural boundary element method to study theweak solvability and Galerkin approximation of ...In this paper, based on the natural boundary reduction advanced by Feng and Yu, we couple the finite elementapproach with the natural boundary element method to study theweak solvability and Galerkin approximation of a class ofnonlinear exterior boundary value problems. The analysis is mainlybased on the variational formulation with constraints.We provethe error estimate of the finite element solution and obtain theasymptotic rate of convergence. Finally, we also give anumerical example.展开更多
A domain decomposition algorithm coupling the finite element and the boundary element was presented. It essentially involves subdivision of the analyzed domain into sub-regions being independently modeled by two metho...A domain decomposition algorithm coupling the finite element and the boundary element was presented. It essentially involves subdivision of the analyzed domain into sub-regions being independently modeled by two methods, i.e., the finite element method （FEM） and the boundary element method （BEM）. The original problem was restored with continuity and equilibrium conditions being satisfied on the interface of the two sub-regions using an iterative algorithm. To speed up the convergence rate of the iterative algorithm, a dynamically changing relaxation parameter during iteration was introduced. An advantage of the proposed algorithm is that the locations of the nodes on the interface of the two sub-domains can be inconsistent. The validity of the algorithm is demonstrated by the consistence of the results of a numerical example obtained by the proposed method and those by the FEM, the BEM and a present finite element-boundary element （FE-BE） coupling method.展开更多
In this paper, some V-cycle multigrid algorithms are presented for the coupling system arising from the discretization of the Dirichlet exterior problem by coupling the natural boundary element method and finite eleme...In this paper, some V-cycle multigrid algorithms are presented for the coupling system arising from the discretization of the Dirichlet exterior problem by coupling the natural boundary element method and finite element method. The convergence of these multigrid algorithms is obtained even with only one smoothing on all levels. The rate of convergence is found uniformly bounded independent of the number of levels and the mesh sizes of all levels, which indicates that these multigrid algorithms are optimal. Some numerical results are also reported.展开更多
文摘Meshless or mesh-free (or shorten as MFree) methods have been proposed and achieved remarkable progress over the past few years. The idea of combining MFree methods with other existing numerical techniques such as the finite element method (FEM) and the boundary element method (BEM), is naturally of great interest in many practical applications. However, the shape functions used in some MFree methods do not have the Kronecker delta function property. In order to satisfy the combined conditions of displacement compatibility, two numerical techniques, using the hybrid displacement shape function and the modified variational form, are developed and discussed in this paper. In the first technique, the original MFree shape functions are modified to the hybrid forms that possess the Kronecker delta function property. In the second technique, the displacement compatibility is satisfied via a modified variational form based on the Lagrange multiplier method. Formulations of several coupled methods are presented. Numerical exam- ples are presented to demonstrate the effectiveness of the present coupling methods.
文摘基于A,φ-A法和库伦规范,推导了导体区域和非导体区域的有限元方程及自由空间的边界元方程,通过引入交界面条件,实现了将边界元矩阵等效为有限元矩阵求解的有限元-边界元耦合法(finite element and boundary element coupling method,FE-BECM)。将FE-BECM应用于TEAM-7问题的计算,验证了该方法处理开域涡流问题的有效性。当FE-BECM应用于运动导体涡流场(moving conductor eddy current,MCEC)问题时,用有限元离散源电流区域和运动部件,用边界元离散自由空间并关联相互独立的有限元区域。该方法克服了常规有限元法使用1套网格处理运动问题所遇到的麻烦。使用有限元-边界元耦合法对单级线圈炮问题进行了计算,验证了算法处理运动导体涡流场问题的有效性。
文摘In this paper, based on the natural boundary reduction advanced by Feng and Yu, we couple the finite elementapproach with the natural boundary element method to study theweak solvability and Galerkin approximation of a class ofnonlinear exterior boundary value problems. The analysis is mainlybased on the variational formulation with constraints.We provethe error estimate of the finite element solution and obtain theasymptotic rate of convergence. Finally, we also give anumerical example.
基金Project supported by China Postdoctoral Science Foundation (No.2004036145)
文摘A domain decomposition algorithm coupling the finite element and the boundary element was presented. It essentially involves subdivision of the analyzed domain into sub-regions being independently modeled by two methods, i.e., the finite element method （FEM） and the boundary element method （BEM）. The original problem was restored with continuity and equilibrium conditions being satisfied on the interface of the two sub-regions using an iterative algorithm. To speed up the convergence rate of the iterative algorithm, a dynamically changing relaxation parameter during iteration was introduced. An advantage of the proposed algorithm is that the locations of the nodes on the interface of the two sub-domains can be inconsistent. The validity of the algorithm is demonstrated by the consistence of the results of a numerical example obtained by the proposed method and those by the FEM, the BEM and a present finite element-boundary element （FE-BE） coupling method.
基金This WOrk is supported by the National Basic Research Program of China under the grant 2005CB321701the National Natural Science Foundation of China under the grant 10531080 and 10601045the Research Starting Fund of Nankai University
文摘In this paper, some V-cycle multigrid algorithms are presented for the coupling system arising from the discretization of the Dirichlet exterior problem by coupling the natural boundary element method and finite element method. The convergence of these multigrid algorithms is obtained even with only one smoothing on all levels. The rate of convergence is found uniformly bounded independent of the number of levels and the mesh sizes of all levels, which indicates that these multigrid algorithms are optimal. Some numerical results are also reported.
