Based on domain decomposition, a parallel two-level finite element method for the stationary Navier-Stokes equations is proposed and analyzed. The basic idea of the method is first to solve the Navier-Stokes equations...Based on domain decomposition, a parallel two-level finite element method for the stationary Navier-Stokes equations is proposed and analyzed. The basic idea of the method is first to solve the Navier-Stokes equations on a coarse grid, then to solve the resulted residual equations in parallel on a fine grid. This method has low communication complexity. It can be implemented easily. By local a priori error estimate for finite element discretizations, error bounds of the approximate solution are derived. Numerical results are also given to illustrate the high efficiency of the method.展开更多
Based on two-grid discretization,a simplified parallel iterative finite element method for the simulation of incompressible Navier-Stokes equations is developed and analyzed.The method is based on a fixed point iterat...Based on two-grid discretization,a simplified parallel iterative finite element method for the simulation of incompressible Navier-Stokes equations is developed and analyzed.The method is based on a fixed point iteration for the equations on a coarse grid,where a Stokes problem is solved at each iteration.Then,on overlapped local fine grids,corrections are calculated in parallel by solving an Oseen problem in which the fixed convection is given by the coarse grid solution.Error bounds of the approximate solution are derived.Numerical results on examples of known analytical solutions,lid-driven cavity flow and backward-facing step flow are also given to demonstrate the effectiveness of the method.展开更多
Based on fully overlapping domain decomposition,a parallel finite element algorithm for the unsteady Oseen equations is proposed and analyzed.In this algorithm,each processor independently computes a finite element ap...Based on fully overlapping domain decomposition,a parallel finite element algorithm for the unsteady Oseen equations is proposed and analyzed.In this algorithm,each processor independently computes a finite element approximate solution in its own subdomain by using a locally refined multiscale mesh at each time step,where conforming finite element pairs are used for the spatial discretizations and backward Euler scheme is used for the temporal discretizations,respectively.Each subproblem is defined in the entire domain with vast majority of the degrees of freedom associated with the particular subdomain that it is responsible for and hence can be solved in parallel with other subproblems using an existing sequential solver without extensive recoding.The algorithm is easy to implement and has low communication cost.Error bounds of the parallel finite element approximate solutions are estimated.Numerical experiments are also given to demonstrate the effectiveness of the algorithm.展开更多
基金Project supported by the National Natural Science Foundation of China(No.11001061)the Science and Technology Foundation of Guizhou Province of China(No.[2008]2123)
文摘Based on domain decomposition, a parallel two-level finite element method for the stationary Navier-Stokes equations is proposed and analyzed. The basic idea of the method is first to solve the Navier-Stokes equations on a coarse grid, then to solve the resulted residual equations in parallel on a fine grid. This method has low communication complexity. It can be implemented easily. By local a priori error estimate for finite element discretizations, error bounds of the approximate solution are derived. Numerical results are also given to illustrate the high efficiency of the method.
基金supported by the Natural Science Foundation of China(No.11361016)the Project Sponsored by the Scientific Research Foundation for the Returned Overseas Chinese Scholars,State Education Ministry+1 种基金the Scientific Research Foundation of Southwest University,Fundamental Research Funds for the Central Universities(No.XDJK2014C160,SWU113095)the Science and Technology Foundation of Guizhou Province,China(No.[2013]2212).
文摘Based on two-grid discretization,a simplified parallel iterative finite element method for the simulation of incompressible Navier-Stokes equations is developed and analyzed.The method is based on a fixed point iteration for the equations on a coarse grid,where a Stokes problem is solved at each iteration.Then,on overlapped local fine grids,corrections are calculated in parallel by solving an Oseen problem in which the fixed convection is given by the coarse grid solution.Error bounds of the approximate solution are derived.Numerical results on examples of known analytical solutions,lid-driven cavity flow and backward-facing step flow are also given to demonstrate the effectiveness of the method.
基金supported by the Natural Science Foundation of China(No.11361016)the Basic and Frontier Explore Program of Chongqing Municipality,China(No.cstc2018jcyjAX0305)Funds for the Central Universities(No.XDJK2018B032).
文摘Based on fully overlapping domain decomposition,a parallel finite element algorithm for the unsteady Oseen equations is proposed and analyzed.In this algorithm,each processor independently computes a finite element approximate solution in its own subdomain by using a locally refined multiscale mesh at each time step,where conforming finite element pairs are used for the spatial discretizations and backward Euler scheme is used for the temporal discretizations,respectively.Each subproblem is defined in the entire domain with vast majority of the degrees of freedom associated with the particular subdomain that it is responsible for and hence can be solved in parallel with other subproblems using an existing sequential solver without extensive recoding.The algorithm is easy to implement and has low communication cost.Error bounds of the parallel finite element approximate solutions are estimated.Numerical experiments are also given to demonstrate the effectiveness of the algorithm.
