Recently, M. Hanke and M. Neumann([4]) have derived a necessary and sufficient condition on a splitting of A = U-V, which leads to a fixed point system, such that the iterative sequence converges to the least squares ...Recently, M. Hanke and M. Neumann([4]) have derived a necessary and sufficient condition on a splitting of A = U-V, which leads to a fixed point system, such that the iterative sequence converges to the least squares solution of minimum a-norm of the system Ax = b. In this paper, we give a necessary and sufficient condition on the splitting such that the iterative sequence converges to the weighted Moore-Penrose solution of the system Ax = b for every to is an element of C-n and every b is an element of C-m. We also provide a necessary and sufficient condition such that the iterative sequence is convergent for every to x(0) is an element of C-n.展开更多
To improve the computational efficiency and hold calculation accuracy at the same time,we study the parallel computation for radiation heat transfer. In this paper, the discrete ordinates method（DOM） and the spatial...To improve the computational efficiency and hold calculation accuracy at the same time,we study the parallel computation for radiation heat transfer. In this paper, the discrete ordinates method（DOM） and the spatial domain decomposition parallelization（DDP） are combined by message passing interface（MPI） language. The DDP–DOM computation of the radiation heat transfer within the rectangular furnace is described. When the result of DDP–DOM along one-dimensional direction is compared with that along multi-dimensional directions, it is found that the result of the latter one has higher precision without considering the medium scattering. Meanwhile, an in-depth study of the convergence of DDP–DOM for radiation heat transfer is made. Analyzing the cause of the weak convergence, we relate the total number of iteration steps when the convergence is obtained to the number of sub-domains. When we decompose the spatial domain along one-,two- and three-dimensional directions, different linear relationships between the number of total iteration steps and the number of sub-domains will be possessed separately, then several equations are developed to show the relationships. Using the equations, some phenomena in DDP–DOM can be made clear easily. At the same time, the correctness of the equations is verified.展开更多
文摘Recently, M. Hanke and M. Neumann([4]) have derived a necessary and sufficient condition on a splitting of A = U-V, which leads to a fixed point system, such that the iterative sequence converges to the least squares solution of minimum a-norm of the system Ax = b. In this paper, we give a necessary and sufficient condition on the splitting such that the iterative sequence converges to the weighted Moore-Penrose solution of the system Ax = b for every to is an element of C-n and every b is an element of C-m. We also provide a necessary and sufficient condition such that the iterative sequence is convergent for every to x(0) is an element of C-n.
基金co-supported by the National Nature Science Foundation of China(No.51176039)the Ph.D.Programs Foundation of Ministry of Education of China(No.20102302110015)
文摘To improve the computational efficiency and hold calculation accuracy at the same time,we study the parallel computation for radiation heat transfer. In this paper, the discrete ordinates method（DOM） and the spatial domain decomposition parallelization（DDP） are combined by message passing interface（MPI） language. The DDP–DOM computation of the radiation heat transfer within the rectangular furnace is described. When the result of DDP–DOM along one-dimensional direction is compared with that along multi-dimensional directions, it is found that the result of the latter one has higher precision without considering the medium scattering. Meanwhile, an in-depth study of the convergence of DDP–DOM for radiation heat transfer is made. Analyzing the cause of the weak convergence, we relate the total number of iteration steps when the convergence is obtained to the number of sub-domains. When we decompose the spatial domain along one-,two- and three-dimensional directions, different linear relationships between the number of total iteration steps and the number of sub-domains will be possessed separately, then several equations are developed to show the relationships. Using the equations, some phenomena in DDP–DOM can be made clear easily. At the same time, the correctness of the equations is verified.
