Focuses on a study which determined the use of the global convergences of the domain decomposition methods with Lagrangian multiplier and nonmatching grids in solving the second order elliptic boundary value problems....Focuses on a study which determined the use of the global convergences of the domain decomposition methods with Lagrangian multiplier and nonmatching grids in solving the second order elliptic boundary value problems. Background on domain decomposition and global superconvergence; Correction scheme and estimates; Numerical examples.展开更多
In this paper, we are concerned with a non-overlapping domain decomposition method （DDM） for exterior transmission problems in the plane. Based on the natural boundary integral operator, we combine the DDM with a Di...In this paper, we are concerned with a non-overlapping domain decomposition method （DDM） for exterior transmission problems in the plane. Based on the natural boundary integral operator, we combine the DDM with a Dirichlet-to-Neumann （DtN） mapping and provide the numerical analysis with nonmatching grids. The weak continuity of the approximation solutions on the interface is imposed by a dual basis multiplier. We show that this multiplier space can generate optimal error estimate and obtain the corresponding rate of convergence. Finally, several numerical examples confirm the theoretical results.展开更多
Focuses on the construction of domain decomposition methods (DDM) with non-matching grids based on mixed finite element methods for the unilateral problem. Information on DDM with nonmatching grids; Discussion on doma...Focuses on the construction of domain decomposition methods (DDM) with non-matching grids based on mixed finite element methods for the unilateral problem. Information on DDM with nonmatching grids; Discussion on domain decomposition; Details on error estimates.展开更多
In this paper we are concerned with a domain decomposition method with nonmatching grids for Raviart-Thomas finite elements. In this method, the normal complement of the resulting approximation is not continuous acros...In this paper we are concerned with a domain decomposition method with nonmatching grids for Raviart-Thomas finite elements. In this method, the normal complement of the resulting approximation is not continuous across the interface. To handle such non-conformity, a new matching condition will be introduced. Such matching condition still results in a symmetric and positive definite stiffness matrix. It will be shown that the approximate solution generated by the domain decomposition possesses the optimal energy error estimate.展开更多
Flexible discretization techniques for the approximative solution of coupled wave propagation problems are investigated.In particular,the advantages of using non-matching grids are presented,when one subregion has to ...Flexible discretization techniques for the approximative solution of coupled wave propagation problems are investigated.In particular,the advantages of using non-matching grids are presented,when one subregion has to be resolved by a substantially finer grid than the other subregion.We present the non-matching grid technique for the case of amechanical-acoustic coupled aswell as for acoustic-acoustic coupled systems.For the first case,the problem formulation remains essentially the same as for the matching situation,while for the acoustic-acoustic coupling,the formulation is enhanced with Lagrangemultipliers within the framework ofMortar Finite Element Methods.The applications will clearly demonstrate the superiority of the Mortar Finite Element Method over the standard Finite Element Method both concerning the flexibility for the mesh generation as well as the computational time.展开更多
基金This research was supported by National Science Foundation grant 19971050 and the 973 grant numberG1998030420.
文摘Focuses on a study which determined the use of the global convergences of the domain decomposition methods with Lagrangian multiplier and nonmatching grids in solving the second order elliptic boundary value problems. Background on domain decomposition and global superconvergence; Correction scheme and estimates; Numerical examples.
基金This work was supported by the National Basic Research Program of China under the grant G19990328, 2005CB321701, and the National Natural Science Foundation of China under the grant 10531080.
文摘In this paper, we are concerned with a non-overlapping domain decomposition method （DDM） for exterior transmission problems in the plane. Based on the natural boundary integral operator, we combine the DDM with a Dirichlet-to-Neumann （DtN） mapping and provide the numerical analysis with nonmatching grids. The weak continuity of the approximation solutions on the interface is imposed by a dual basis multiplier. We show that this multiplier space can generate optimal error estimate and obtain the corresponding rate of convergence. Finally, several numerical examples confirm the theoretical results.
基金NSFC grant number 19971050 and by 973 grant number G1998030420.
文摘Focuses on the construction of domain decomposition methods (DDM) with non-matching grids based on mixed finite element methods for the unilateral problem. Information on DDM with nonmatching grids; Discussion on domain decomposition; Details on error estimates.
基金supported by Special Funds for Major State Basic Research Projects of China(Grant No.1999032804)National Natural Science Foundation of China(Grant No.10371129).
文摘In this paper we are concerned with a domain decomposition method with nonmatching grids for Raviart-Thomas finite elements. In this method, the normal complement of the resulting approximation is not continuous across the interface. To handle such non-conformity, a new matching condition will be introduced. Such matching condition still results in a symmetric and positive definite stiffness matrix. It will be shown that the approximate solution generated by the domain decomposition possesses the optimal energy error estimate.
基金supported by the German Research Foundation(DFG)under grant WO 671/6-2the Austrian Science Foundation(FWF)under grant I 533-N20.We would like to thank the DFG and the FWF for their support.
文摘Flexible discretization techniques for the approximative solution of coupled wave propagation problems are investigated.In particular,the advantages of using non-matching grids are presented,when one subregion has to be resolved by a substantially finer grid than the other subregion.We present the non-matching grid technique for the case of amechanical-acoustic coupled aswell as for acoustic-acoustic coupled systems.For the first case,the problem formulation remains essentially the same as for the matching situation,while for the acoustic-acoustic coupling,the formulation is enhanced with Lagrangemultipliers within the framework ofMortar Finite Element Methods.The applications will clearly demonstrate the superiority of the Mortar Finite Element Method over the standard Finite Element Method both concerning the flexibility for the mesh generation as well as the computational time.
