共查询到20条相似文献,搜索用时 0 毫秒
1.
Zhi Wang Quan Hu Xiao-Fang Zhu Bin Li Yu-Lu Hu Tao Huang Zhong-Hai Yang Liang Li 《Entropy (Basel, Switzerland)》2022,24(8)
At present, electron optical simulator (EOS) takes a long time to solve linear FEM systems. The algebraic multigrid preconditioned conjugate gradient (AMGPCG) method can improve the efficiency of solving systems. This paper is focused on the implementation of the AMGPCG method in EOS. The aggregation-based scheme, which uses two passes of a pairwise matching algorithm and the K-cyle scheme, is adopted in the aggregation-based algebraic multigrid method. Numerical experiments show the advantages and disadvantages of the AMG algorithm in peak memory and solving efficiency. The AMGPCG is more efficient than the iterative methods used in the past and only needs one coarsening when EOS computes the particle motion trajectory. 相似文献
2.
提出了代数多重网格法(AMG)的一种新算法。新算法改进了插值公式和粗网格方程,并把它应用到求解一维的分裂格式Euler方程。数值结果表明,对于具有高CFL条件数的Euler方程,代数多重网格法可以求解;对于Gaus-Seidel方法求解不能收敛的代数方程组,代数多重网格法求解可以收敛。新算法改进了代数多重网格法的收敛性和扩展了它的应用范围,数值结果表明了它的有效性和强壮性。 相似文献
3.
对当今求解大型稀疏线性代数方程组最有效的迭代方法之--代数多重网格(AMG)算法的并行计算进行可扩展性能分析.给出一套并行计算可扩展性能分析方法,用于分析和指导并行迭代算法及实现技术的设计与优化并应用于并行AMG算法.分析表明,网格算子的平均模式大小和迭代过程的算法效率分别制约了AMG算法启动阶段和迭代求解阶段并行性能的发挥,成为该类算法急需解决的两个关键问题. 相似文献
4.
In this paper, based on the stabilization technique, the Oseen iterative method and the two-level finite element algorithm are combined to numerically solve the stationary incompressible magnetohydrodynamic (MHD) equations. For the low regularity of the magnetic field, when dealing with the magnetic field sub-problem, the Lagrange multiplier technique is used. The stabilized method is applied to approximate the flow field sub-problem to circumvent the inf-sup condition restrictions. One- and two-level stabilized finite element algorithms are presented, and their stability and convergence analysis is given. The two-level method uses the Oseen iteration to solve the nonlinear MHD equations on a coarse grid of size H, and then employs the linearized correction on a fine grid with grid size h. The error analysis shows that when the grid sizes satisfy , the two-level stabilization method has the same convergence order as the one-level one. However, the former saves more computational cost than the latter one. Finally, through some numerical experiments, it has been verified that our proposed method is effective. The two-level stabilized method takes less than half the time of the one-level one when using the second class Nédélec element to approximate magnetic field, and even takes almost a third of the computing time of the one-level one when adopting the first class Nédélec element. 相似文献
5.
提出一种数值求解定常不可压缩Stokes方程的并行两水平Grad-div稳定有限元算法。首先在粗网格中求解Grad-div稳定化的全局解, 再在相互重叠的细网格子区域上并行纠正。通过对稳定化参数、粗细网格尺寸恰当的选取, 该方法可得到最优收敛率, 数值结果验证了算法的高效性。 相似文献
6.
Algebraic Multigrid Preconditioning for Finite Element Solution of Inhomogeneous Elastic Inclusion Problems in Articular Cartilage 下载免费PDF全文
In studying biomechanical deformation in articular cartilage, the presence of
cells (chondrocytes) necessitates the consideration of inhomogeneous elasticity
problems in which cells are idealized as soft inclusions within a stiff extracellular matrix.
An analytical solution of a soft inclusion problem is derived and used to
evaluate iterative numerical solutions of the associated linear algebraic
system based on discretization via the finite element method, and use of an
iterative conjugate gradient method with algebraic multigrid preconditioning (AMG-PCG).
Accuracy and efficiency of the AMG-PCG algorithm is compared to two other
conjugate gradient algorithms with diagonal preconditioning (DS-PCG) or a
modified incomplete LU decomposition (Euclid-PCG) based on comparison to the analytical solution.
While all three algorithms are shown to be accurate, the AMG-PCG algorithm
is demonstrated to provide significant savings in CPU time as the number of nodal unknowns is increased.
In contrast to the other two algorithms, the AMG-PCG algorithm also
exhibits little sensitivity of CPU time and number of iterations to
variations in material properties that are known to significantly affect model variables.
Results demonstrate the benefits of algebraic multigrid preconditioners
for the iterative solution of assembled linear systems based on finite
element modeling of soft elastic inclusion problems and may be particularly
advantageous for large scale problems with many nodal unknowns. 相似文献
7.
A Two-Level Method for Pressure Projection Stabilized P1 Nonconforming Approximation of the Semi-Linear Elliptic Equations 下载免费PDF全文
Sufang Zhang Hongxia Yan & Hongen Jia 《advances in applied mathematics and mechanics.》2016,8(3):386-398
In this paper, we study a new stabilized method based on the local pressure
projection to solve the semi-linear elliptic equation. The proposed scheme combines
nonconforming finite element pairs NCP1−P1triangle element and two-level method,
which has a number of attractive computational properties: parameter-free, avoiding
higher-order derivatives or edge-based data structures, but have more favorable stability
and less support sets. Stability analysis and error estimates have been done. Finally,
numerical experiments to check estimates are presented. 相似文献
8.
基于粒子有限元方法(particle finite element method,PFEM),利用细分混合单元的界面识别思想,模拟种类任意多的不可压多介质流问题.对分步算法采用基于有限增量微积分理论的稳定措施,以适应流体特性差异;将混合单元细分为代表单一流体的小单元,进而得到流体间的边界;通过加密边界、控制粒子速度、自动检查穿透来防止粒子穿透外部边界.瑞利-泰勒不稳定性和水柱在空气中倒塌的模拟与已有结果的对比验证了PFEM及界面识别方法的可靠性和准确性.七种流体混合的模拟结果表明PFEM可有效处理任意多种类不相溶流体的混合流动问题. 相似文献
9.
Uniform Convergence Analysis of a Higher Order Hybrid Stress Quadrilateral Finite Element Method for Linear Elasticity Problems 下载免费PDF全文
Yanhong Bai Yongke Wu & Xiaoping Xie 《advances in applied mathematics and mechanics.》2016,8(3):399-425
This paper derives a higher order hybrid stress finite element method on
quadrilateral meshes for linear plane elasticity problems. The method employs continuous
piecewise bi-quadratic functions in local coordinates to approximate the displacement
vector and a piecewise-independent 15-parameter mode to approximate the
stress tensor. Error estimation shows that the method is free from Poisson-locking and
has second-order accuracy in the energy norm. Numerical experiments confirm the
theoretical results. 相似文献
10.
Qiaolin He 《advances in applied mathematics and mechanics.》2012,4(2):238-249
In this paper, we propose a new two-level preconditioned C-G method
which uses the quadratic smoothing and the linear correction in distorted but topologically
structured grid. The CPU time of this method is less than that of the
multigrid preconditioned C-G method (MGCG) using the quadratic element, but
their accuracy is almost the same. Numerical experiments and eigenvalue analysis
are given and the results show that the proposed two-level preconditioned method
is efficient. 相似文献
11.
将求解偏微分方程的有限积分法应用于对流-扩散-反应问题,发现对于非对流占优的对流扩散问题,有限积分法的精度比QUICK法高一个数量级,比传统的有限体积法高两个数量级.处理对流占优的对流-扩散-反应问题时,对流项的离散时引进加权参数,通过调节该参数反映输运的方向性.结果表明这种改进的有限积分法的精度比传统的有限体积法至少高四个数量级,同时明显改进了原来的有限积分法的精度和稳定性.对于对流占优的对流-扩散-反应问题,即使采用粗网格,计算结果也未出现非物理振荡现象,表明改进的有限积分法具有很好的稳定性. 相似文献
12.
Jianhong Yang Lei Gang & Jianwei Yang 《advances in applied mathematics and mechanics.》2014,6(5):663-679
In this paper, we consider a two-scale stabilized finite volume method for the two-dimensional
stationary incompressible flow approximated by the lowest equal-order element pair $P_1-P_1$
which does not satisfy the inf-sup condition. The two-scale method consists of solving a small non-linear system
on the coarse mesh and then solving a linear Stokes equations on the fine mesh. Convergence of the optimal
order in the $H^1$-norm for velocity and the $L^2$-norm for pressure is obtained. The error analysis shows
there is the same convergence rate between the two-scale stabilized finite volume solution and the usual
stabilized finite volume solution on a fine mesh with relation $h =\mathcal{O}(H^2)$. Numerical experiments completely
confirm theoretic results. Therefore, this method presented in this paper is of practical importance in
scientific computation. 相似文献
13.
This paper is concerned with a stabilized finite element method
based on two local Gauss integrations for the two-dimensional
non-stationary conduction-convection equations by using the lowest
equal-order pairs of finite elements. This method only offsets the
discrete pressure space by the residual of the simple and symmetry
term at element level in order to circumvent the inf-sup condition.
The stability of the discrete scheme is derived under some
regularity assumptions. Optimal error estimates are obtained by
applying the standard Galerkin techniques. Finally, the numerical
illustrations agree completely with the theoretical expectations. 相似文献
14.
15.
针对二维非定常半线性扩散反应方程,空间导数项采用四阶紧致差分公式离散,时间导数项采用四阶向后Euler公式进行离散,提出一种无条件稳定的高精度五层全隐格式.格式截断误差为O(τ4+τ2h2+h4),即时间和空间均具有四阶精度.对于第一、二、三时间层采用Crank-Nicolson方法进行离散,并采用Richardson外推公式将启动层时间精度外推到四阶.建立适用于该格式的多重网格方法,加快在每个时间层上迭代求解代数方程组的收敛速度,提高计算效率.最后通过数值实验验证格式的精确性和稳定性以及多重网格方法的高效性. 相似文献
16.
Numerical Simulation of a Multi-Frequency Resistivity Logging-While-Drilling Tool Using a Highly Accurate and Adaptive Higher-Order Finite Element Method 下载免费PDF全文
Zhonghua Ma Dejun Liu Hui Li & Xinsheng Gao 《advances in applied mathematics and mechanics.》2012,4(4):439-453
A novel, highly efficient and accurate adaptive higher-order finite element
method ($hp$-FEM) is used to simulate a multi-frequency resistivity logging-while-drilling (LWD)
tool response in a borehole environment. Presented in this study are the vector expression
of Maxwell's equations, three kinds of boundary conditions, stability weak formulation of
Maxwell's equations, and automatic $hp$-adaptivity strategy. The new $hp$-FEM can select
optimal refinement and calculation strategies based on the practical formation model and
error estimation. Numerical experiments show that the new $hp$-FEM has an exponential
convergence rate in terms of relative error in a user-prescribed quantity of interest
against the degrees of freedom, which provides more accurate results than those obtained
using the adaptive $h$-FEM. The numerical results illustrate the high efficiency and
accuracy of the method at a given LWD tool structure and parameters in different physical
models, which further confirm the accuracy of the results using the Hermes
library (http://hpfem.org/hermes) with a multi-frequency resistivity LWD tool
response in a borehole environment. 相似文献
17.
A Method of Lines Based on Immersed Finite Elements for Parabolic Moving Interface Problems 下载免费PDF全文
This article extends the finite element method of lines to a parabolic
initial boundary value problem whose diffusion coefficient is discontinuous
across an interface that changes with respect to time. The method presented
here uses immersed finite element (IFE) functions for the discretization in
spatial variables that can be carried out over a fixed mesh (such as a
Cartesian mesh if desired), and this feature makes it possible to reduce
the parabolic equation to a system of ordinary differential equations (ODE)
through the usual semi-discretization procedure. Therefore, with a suitable
choice of the ODE solver, this method can reliably and efficiently solve a
parabolic moving interface problem over a fixed structured (Cartesian) mesh.
Numerical examples are presented to demonstrate features of this new method. 相似文献
18.
An Inf-Sup Stabilized Finite Element Method by Multiscale Functions for the Stokes Equations 下载免费PDF全文
Zhihao Ge Yinnian He & Lingyu Song 《advances in applied mathematics and mechanics.》2009,1(2):273-287
In the paper, an inf-sup stabilized finite element method by multiscale
functions for the Stokes equations is discussed. The key idea is to use a Petrov-Galerkin approach based on the enrichment of the standard polynomial space for
the velocity component with multiscale functions. The inf-sup condition for $P_1$-$P_0$ triangular element (or $Q_1$-$P_0$ quadrilateral element) is established. And the optimal
error estimates of the stabilized finite element method for the Stokes equations
are obtained. 相似文献
19.
An Iterative Two-Grid Method of a Finite Element PML Approximation for the Two Dimensional Maxwell Problem 下载免费PDF全文
Chunmei Liu Shi Shu Yunqing Huang Liuqiang Zhong & Junxian Wang 《advances in applied mathematics and mechanics.》2012,4(2):175-189
In this paper, we propose an iterative two-grid method for the edge finite
element discretizations (a saddle-point system) of Perfectly Matched Layer (PML)
equations to the Maxwell scattering problem in two dimensions. Firstly, we use
a fine space to solve a discrete saddle-point system of $H(grad)$ variational problems,
denoted by auxiliary system 1. Secondly, we use a coarse space to solve the
original saddle-point system. Then, we use a fine space again to solve a discrete$\boldsymbol{H}(curl)$-elliptic variational problems, denoted by auxiliary system 2. Furthermore,
we develop a regularization diagonal block preconditioner for auxiliary system 1
and use $H$-$X$ preconditioner for auxiliary system 2. Hence we essentially transform
the original problem in a fine space to a corresponding (but much smaller)
problem on a coarse space, due to the fact that the above two preconditioners are
efficient and stable. Compared with some existing iterative methods for solving
saddle-point systems, such as PMinres, numerical experiments show the competitive
performance of our iterative two-grid method. 相似文献
20.
二维多介质可压缩流的RKDG有限元方法 总被引:1,自引:0,他引:1
应用RKDG(Runge-Kutta Discontinuous Galerkin)有限元方法、Level Set方法和Ghost Fluid方法数值模拟二维多介质可压缩流,其中Euler方程组、Level Set方程和重新初始化方程的空间离散采用DG(Discontinuous Galerkin)有限元方法,时间离散采用Runge-Kutta方法.对二维的气-气和气-液两相流进行了数值计算,得到了分辨率较高的计算结果. 相似文献