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A parallel two-level finite element method for the Navier-Stokes equations
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作者 尚月强 罗振东 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2010年第11期1429-1438,共10页
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
关键词 Navier-Stokes equations finite element two-level method overlapping domain decomposition parallel algorithm
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A Parallel Finite Element Algorithm for the Unsteady Oseen Equations
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作者 Qi Ding Yueqiang Shang 《Advances in Applied Mathematics and Mechanics》 SCIE 2021年第6期1501-1519,共19页
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
关键词 Oseen equations finite element overlapping domain decomposition backward Euler scheme parallel algorithm
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