共查询到19条相似文献,搜索用时 140 毫秒
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旋转球层中热对流运动的数值模拟是地球发电机模型的重要组成部分,对研究地球发电机作用机理具有重要意义.本文设计一个基于国产超级计算平台并行性能良好的地球外核热对流运动并行数值模型.时间积分方案采用与Crank-Nicolson格式和二阶Adams-Bashford公式相结合的近似分解分步法,空间离散基于立方球网格的二阶精度有限体积格式.所得到的两个大规模稀疏线性代数方程组采用带预处理的Krylov子空间迭代法进行求解.为加速迭代求解过程及提高并行性能,迭代过程采用区域分解多重网格的多层限制型加法Schwarz预处理子,减少了求解程序的计算时间,提高了数值模型的并行性能,模型被很好地扩展到上万处理器核数.数值模拟结果与基准模型算例0的参考值吻合得很好. 相似文献
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文章考察了相邻双侧边盖驱动方腔流动(即上壁面向右运动和左侧壁面向下运动)的三维线性整体稳定性.首先,采用Taylor-Hood有限元方法并经由Newton迭代过程计算得到双侧边盖驱动方腔流动的二维稳态基本流.其次,Taylor-Hood有限元在Chebyshev Gauss配置点上进行离散,同时Gauss配置点也可以用于线性稳定性方程的高阶有限差分格式离散.然后,离散得到的矩阵形式的广义特征值问题可以结合shift-and-invert算法采用隐式重启Arnoldi方法计算.最后,通过对线性稳定性方程特征值的计算,发现了一个最不稳定的驻定模态和两对对称行波模态.最不稳定的三维驻定模态的临界Reynolds数为Rec=261.5,远远小于二维不稳定的临界Reynolds数Rec2d=1 061.7.通过画出这3类三维不稳定模态的流向扰动速度和扰动涡量的空间等值面图像,可以发现不稳定扰动位于稳态基本流的两个主涡区域,因此可以认为主涡区域是三维扰动失稳的主要能量来源地. 相似文献
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粒子输运离散纵标方程基于界面修正的并行计算方法 总被引:1,自引:1,他引:0
为了改造粒子输运方程求解的隐式格式,研究设计适应大型并行计算机的并行计算方法,介绍一类求解粒子输运方程离散纵标方程组的基于界面修正的源迭代并行计算方法.应用空间区域分解,在子区域内界面处首先采用迎风显式差分格式进行预估,构造子区域的入射边界条件,然后,在各个子区域内部进行源迭代求解隐式离散纵标方程组.在源迭代过程中,在内界面入射边界处采用隐式格式进行界面修正.数值算例表明该并行计算方法在精度、并行度、简单性诸方面均具有良好的性质. 相似文献
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任意马赫数非定常流动数值模拟的统一算法 总被引:2,自引:0,他引:2
发展适用于从低速到高速任意马赫数非定常流动数值模拟的统一算法.通过引入一个伪时间导数项和一个新的预处理矩阵,得到双时间非定常预处理可压缩Navier-Stokes方程.方程的对流项采用三阶Roe通量近似差分格式离散,粘性项采用二阶中心差分格式离散.基于数值通量的线性化技术,实现伪时间步的隐式ADI-LU格式迭代,进而获得物理时间步的二阶推进精度.重点以低马赫数流动为例,求解了圆柱绕流和NACA0015翼型等速上仰动态失速问题.计算结果表明该统一算法能够较好地模拟低马赫数乃至任意马赫数非定常流动. 相似文献
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《物理学报》2016,(20)
本文采用湍流热对流的并行直接数值模拟(PDM-DNS),计算了系列Ra数的二维方腔和三维扁方腔的Rayleigh-Bénard热对流.针对平均场计算结果,选取Ra=10~9,10~(10),5×10~(10),讨论了二维方腔和展向平均三维扁方腔热对流流动特性.发现二维方腔和三维扁方腔流动中都存在大尺度环流和角涡,而且随着Ra数的增加,大尺度环流的形状变圆,角涡尺寸变小.在二维方腔流动中,大尺度环流呈椭圆形,有四个角涡,而展向平均三维扁方腔流动中,大尺度环流呈梭形,只有两个角涡.由于角涡特性的不同,二维方腔流动中羽流向上运动的范围比展向平均三维扁方腔流动更广,造成二维流动局部区域温度分布高温层厚度变大.温度边界层厚度λ_θ与Ra数之间存在标度关系,二维方腔和三维扁方腔热对流温度边界层变化的标度指数基本一致,标度关系的系数稍有不同. 相似文献
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P. Thum T. Clees G. Weyns G. Nelissen J. Deconinck 《Journal of computational physics》2010,229(19):7260-7276
The article discusses components and performance of an algebraic multigrid (AMG) preconditioner for the fully coupled multi-ion transport and reaction model (MITReM) with nonlinear boundary conditions, important for electrochemical modeling. The governing partial differential equations (PDEs) are discretized in space by a combined finite element and residual distribution method. Solution of the discrete system is obtained by means of a Newton-based nonlinear solver, and an AMG-preconditioned BICGSTAB Krylov linear solver. The presented AMG preconditioner is based on so-called point-based classical AMG. The linear solver is compared to a standard direct and several one-level iterative solvers for a range of geometries and chemical systems with scientific and industrial relevance. The results indicate that point-based AMG methods, carefully designed, are an attractive alternative to more commonly employed numerical methods for the simulation of complex electrochemical processes. 相似文献
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在基于漂移-扩散模型的三维半导体器件数值模拟中,通过有限体积法进行数值离散,采用完全耦合的牛顿迭代求解非线性代数方程组,并使用基于代数多重网格预条件子的GMRES方法求解牛顿迭代中的线性方程组,构造一种稳健且高度可扩展的非结构四面体网格上求解半导体方程的并行算法.基于PHG平台实现该算法的并行计算程序,并对PN结和MOS场效应晶体管等问题进行了最大网格规模达到5亿单元、最大并行规模达到1 024进程的大规模数值模拟实验,结果表明,该算法计算效率高,可扩展性好. 相似文献
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Travis M. Austin Marian Brezina Ben Jamroz Chetan Jhurani Thomas A. Manteuffel John Ruge 《Journal of computational physics》2012,231(14):4694-4708
High-order finite elements often have a higher accuracy per degree of freedom than the classical low-order finite elements. However, in the context of implicit time-stepping methods, high-order finite elements present challenges to the construction of efficient simulations due to the high cost of inverting the denser finite element matrix. There are many cases where simulations are limited by the memory required to store the matrix and/or the algorithmic components of the linear solver. We are particularly interested in preconditioned Krylov methods for linear systems generated by discretization of elliptic partial differential equations with high-order finite elements. Using a preconditioner like Algebraic Multigrid can be costly in terms of memory due to the need to store matrix information at the various levels. We present a novel method for defining a preconditioner for systems generated by high-order finite elements that is based on a much sparser system than the original high-order finite element system. We investigate the performance for non-uniform meshes on a cube and a cubed sphere mesh, showing that the sparser preconditioner is more efficient and uses significantly less memory. Finally, we explore new methods to construct the sparse preconditioner and examine their effectiveness for non-uniform meshes. We compare results to a direct use of Algebraic Multigrid as a preconditioner and to a two-level additive Schwarz method. 相似文献
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This paper is concerned with preconditioning the stiffness matrix resulting from finite element discretizations of Maxwell’s equations in the high frequency regime. The moving PML sweeping preconditioner, first introduced for the Helmholtz equation on a Cartesian finite difference grid, is generalized to an unstructured mesh with finite elements. The method dramatically reduces the number of GMRES iterations necessary for convergence, resulting in an almost linear complexity solver. Numerical examples including electromagnetic cloaking simulations are presented to demonstrate the efficiency of the proposed method. 相似文献
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Paul T. Lin John N. Shadid Marzio Sala Raymond S. Tuminaro Gary L. Hennigan Robert J. Hoekstra 《Journal of computational physics》2009,228(17):6250-6267
In this study results are presented for the large-scale parallel performance of an algebraic multilevel preconditioner for solution of the drift-diffusion model for semiconductor devices. The preconditioner is the key numerical procedure determining the robustness, efficiency and scalability of the fully-coupled Newton–Krylov based, nonlinear solution method that is employed for this system of equations. The coupled system is comprised of a source term dominated Poisson equation for the electric potential, and two convection–diffusion-reaction type equations for the electron and hole concentration. The governing PDEs are discretized in space by a stabilized finite element method. Solution of the discrete system is obtained through a fully-implicit time integrator, a fully-coupled Newton-based nonlinear solver, and a restarted GMRES Krylov linear system solver. The algebraic multilevel preconditioner is based on an aggressive coarsening graph partitioning of the nonzero block structure of the Jacobian matrix. Representative performance results are presented for various choices of multigrid V-cycles and W-cycles and parameter variations for smoothers based on incomplete factorizations. Parallel scalability results are presented for solution of up to 108 unknowns on 4096 processors of a Cray XT3/4 and an IBM POWER eServer system. 相似文献
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In this paper, a framework of using h-adaptive finite element method for the Kohn–Sham equation on the tetrahedron mesh is presented. The Kohn–Sham equation is discretized by the finite element method, and the h-adaptive technique is adopted to optimize the accuracy and the efficiency of the algorithm. The locally optimal block preconditioned conjugate gradient method is employed for solving the generalized eigenvalue problem, and an algebraic multigrid preconditioner is used to accelerate the solver. A variety of numerical experiments demonstrate the effectiveness of our algorithm for both the all-electron and the pseudo-potential calculations. 相似文献
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Feng-Nan Hwang Zih-Hao Wei Tsung-Ming Huang Weichung Wang 《Journal of computational physics》2010,229(8):2932-2947
We develop a parallel Jacobi–Davidson approach for finding a partial set of eigenpairs of large sparse polynomial eigenvalue problems with application in quantum dot simulation. A Jacobi–Davidson eigenvalue solver is implemented based on the Portable, Extensible Toolkit for Scientific Computation (PETSc). The eigensolver thus inherits PETSc’s efficient and various parallel operations, linear solvers, preconditioning schemes, and easy usages. The parallel eigenvalue solver is then used to solve higher degree polynomial eigenvalue problems arising in numerical simulations of three dimensional quantum dots governed by Schrödinger’s equations. We find that the parallel restricted additive Schwarz preconditioner in conjunction with a parallel Krylov subspace method (e.g. GMRES) can solve the correction equations, the most costly step in the Jacobi–Davidson algorithm, very efficiently in parallel. Besides, the overall performance is quite satisfactory. We have observed near perfect superlinear speedup by using up to 320 processors. The parallel eigensolver can find all target interior eigenpairs of a quintic polynomial eigenvalue problem with more than 32 million variables within 12 minutes by using 272 Intel 3.0 GHz processors. 相似文献
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This paper describes a new three-dimensional (3D) analysis of tonal noise radiated from non-axisymmetric turbofan inlets. The novelty of the method is in combining a standard finite element discretisation of the acoustic field in the axial and radial coordinates with a Fourier spectral representation in the circumferential direction. The boundary conditions at the farfield, fan face and acoustic liners are treated using the same spectral representation. The resulting set of discrete acoustic equations are solved employing the well-established BICGSTAB or QMR iterative algorithms and a very effective specialised preconditioner based on the axisymmetric mean geometry and flow field. Numerical examples demonstrate the suitability of the new method to engine configurations with realistic 3D features, such as relatively large degrees of asymmetry and spliced acoustic liners. The examples also illustrate the two advantages of the new method over a traditional 3D finite element approach. The new method requires a significantly smaller number of unknowns as relatively few circumferential Fourier modes in the spectral solution ensure an accurate field representation. Also, due to the effective preconditioner, the spectral linear solver benefits from stable iterations at a high rate of convergence. 相似文献