Pseudospectral method is an efficient and high accuracy numerical method for simulating seismic wave propaga- tion in heterogeneous earth medium. Since its derivative operator is global, this method is commonly consid...Pseudospectral method is an efficient and high accuracy numerical method for simulating seismic wave propaga- tion in heterogeneous earth medium. Since its derivative operator is global, this method is commonly considered not suitable for parallel computation. In this paper, we introduce the parallel overlap domain decomposition scheme and give a parallel pseudospectral method implemented on distributed memory PC cluster system for modeling seismic wave propagation in heterogeneous medium. In this parallel method, the medium is decomposed into several subdomains and the wave equations are solved in each subdomain simultaneously. The solutions in each subdomain are connected through the transferring at the overlapped region. Using 2D models, we compared the parallel and traditional pseudospectral method, analyzed the accuracy of the parallel method. The results show that the parallel method can efficiently reduce computation time for the same accuracy as the traditional method. This method could be applied to large scale modeling of seismic wave propagation in 3D heterogeneous medium.展开更多
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
采用Mortar有限单元法(mortar finite element method,MFEM)能够得到正定、对称的系数矩阵,而且刚度矩阵是分块对称的,这种特点适合于并行迭代求解。阐述了非重叠Mortar有限单元法(non-overlapping MFEM,NO-MFEM)的基本原理,介绍了适合...采用Mortar有限单元法(mortar finite element method,MFEM)能够得到正定、对称的系数矩阵,而且刚度矩阵是分块对称的,这种特点适合于并行迭代求解。阐述了非重叠Mortar有限单元法(non-overlapping MFEM,NO-MFEM)的基本原理,介绍了适合于NO-MFEM并行计算的区域分解策略以及并行求解的基本流程。针对简单2维静电场问题,使用NO-MFEM进行了并行计算,并与理论值和串行计算结果进行对比,验证了所提方法的有效性。同时,对于非协调网格造成的计算误差进行了分析。NO-MFEM法的并行计算为工程应用中优化设计问题的区域分解和并行求解提供了一种新的选择。展开更多
基金National Natural Science Foundation of China (40474012 and 40521002)
文摘Pseudospectral method is an efficient and high accuracy numerical method for simulating seismic wave propaga- tion in heterogeneous earth medium. Since its derivative operator is global, this method is commonly considered not suitable for parallel computation. In this paper, we introduce the parallel overlap domain decomposition scheme and give a parallel pseudospectral method implemented on distributed memory PC cluster system for modeling seismic wave propagation in heterogeneous medium. In this parallel method, the medium is decomposed into several subdomains and the wave equations are solved in each subdomain simultaneously. The solutions in each subdomain are connected through the transferring at the overlapped region. Using 2D models, we compared the parallel and traditional pseudospectral method, analyzed the accuracy of the parallel method. The results show that the parallel method can efficiently reduce computation time for the same accuracy as the traditional method. This method could be applied to large scale modeling of seismic wave propagation in 3D heterogeneous medium.
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.
文摘采用Mortar有限单元法(mortar finite element method,MFEM)能够得到正定、对称的系数矩阵,而且刚度矩阵是分块对称的,这种特点适合于并行迭代求解。阐述了非重叠Mortar有限单元法(non-overlapping MFEM,NO-MFEM)的基本原理,介绍了适合于NO-MFEM并行计算的区域分解策略以及并行求解的基本流程。针对简单2维静电场问题,使用NO-MFEM进行了并行计算,并与理论值和串行计算结果进行对比,验证了所提方法的有效性。同时,对于非协调网格造成的计算误差进行了分析。NO-MFEM法的并行计算为工程应用中优化设计问题的区域分解和并行求解提供了一种新的选择。
