By coupling natural boundary element method (NBEM) with FEM based on domain decomposition, the torsion problem of the square cross-sections bar with cracks have been studied, the stresses of the nodes of the cross-sec...By coupling natural boundary element method (NBEM) with FEM based on domain decomposition, the torsion problem of the square cross-sections bar with cracks have been studied, the stresses of the nodes of the cross-sections and the stress intensity factors have been calculated, and some distribution pictures of the stresses have been drawn. During computing, the effect of the relaxed factors to the convergence speed of the iterative method has been discussed. The results of the computation have confirmed the advantages of the NBEM and its coupling with the FEM.展开更多
The artificial boundary method is applied to solve three-dimensional exterior problems. Two kind of rotating ellipsoids are chosen as the artificial boundaries and the exact artificial boundary conditions are derived ...The artificial boundary method is applied to solve three-dimensional exterior problems. Two kind of rotating ellipsoids are chosen as the artificial boundaries and the exact artificial boundary conditions are derived explicitly in terms of an infinite series. Then the well-posedness of the coupled variational problem is obtained. It is found that error estimates derived depend on the mesh size, truncation term and the location of the artificial boundary. Three numerical examples are presented to demonstrate the effectiveness and accuracy of the proposed method.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
基金the State Key Laboratory of Science and Engineering Computation
文摘By coupling natural boundary element method (NBEM) with FEM based on domain decomposition, the torsion problem of the square cross-sections bar with cracks have been studied, the stresses of the nodes of the cross-sections and the stress intensity factors have been calculated, and some distribution pictures of the stresses have been drawn. During computing, the effect of the relaxed factors to the convergence speed of the iterative method has been discussed. The results of the computation have confirmed the advantages of the NBEM and its coupling with the FEM.
基金subsidized by the National Basic Research Program of China under the grant 2005CB321701the National Natural Science Foundation of China under the grant 10531080the Beijing Natural Science Foundation under the grant 1072009 and the Research Project of Zhejiang Ocean University (X08M013,X08Z04)
文摘The artificial boundary method is applied to solve three-dimensional exterior problems. Two kind of rotating ellipsoids are chosen as the artificial boundaries and the exact artificial boundary conditions are derived explicitly in terms of an infinite series. Then the well-posedness of the coupled variational problem is obtained. It is found that error estimates derived depend on the mesh size, truncation term and the location of the artificial boundary. Three numerical examples are presented to demonstrate the effectiveness and accuracy of the proposed method.
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.
