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A Preconditioned Multigrid Method for Efficient Simulation of Three-dimensional Compressible and Incompressible Flows 认领 引用 被引量：15
1
作者 Han Zhonghua He Fei Song Wenping Qiao Zhide 《Chinese Journal of Aeronautics》 SCIE EI CAS 2007年第4期289-296,共8页
To develop an efficient and robust aerodynamic analysis method for numerical optimization designs of wing and complex configuration, a combination of matrix preconditioning and multigrid method is presented and invest... To develop an efficient and robust aerodynamic analysis method for numerical optimization designs of wing and complex configuration, a combination of matrix preconditioning and multigrid method is presented and investigated. The time derivatives of three-dimensional Navier-Stokes equations are preconditioned by Choi-Merkle preconditioning matrix that is originally designed for two-dimensional low Mach number viscous flows. An extension to three-dimensional viscous flow is implemented, and a method improving the convergence for transonic flow is proposed. The space discretizaition is performed by employing a finite-volume cell-centered scheme and using a central difference. The time marching is based on an explicit Rtmge-Kutta scheme proposed by Jameson. An efficient FAS multigrid method is used to accelerate the convergence to steady-state solutions. Viscous flows over ONERA M6 wing and M100 wing are numerically simulated with Mach numbers ranging from 0.010 to 0.839. The inviscid flow over the DLR-F4 wing-body configuration is also calculated to preliminarily examine the performance of the presented method for complex configuration. The computed results are compared with the experimental data and good agreement is achieved. It is shown that the presented method is efficient and robust for both compressible and incompressible flows and is very attractive for aerodynamic optimization designs of wing and complex configuration. 展开更多
关键词 Navier-Stokes equations preconditioning method multigrid method numerical simulation
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The V-cycle Multigrid Method for a Hermite-type Rectangular Element 认领 引用
2
作者 ZHAO Yan-min SHI Dong-yang 《Chinese Quarterly Journal of Mathematics》 2010年第1期140-145,共6页
In this paper, a V-cycle multigrid method is presented for a Hermite rectangular element. By defining proper mesh-dependent inner product and transfer operator, we obtain its convergence property and the uniform conve... In this paper, a V-cycle multigrid method is presented for a Hermite rectangular element. By defining proper mesh-dependent inner product and transfer operator, we obtain its convergence property and the uniform convergence rate independent of mesh size and level are established. 展开更多
关键词 V-cycle Hermite-type multigrid method transfer operator
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Geometric Multigrid Method for Isogeometric Analysis 认领 引用
3
作者 Houlin Yang Bingquan Zuo +2 位作者 Zhipeng Wei Huixin Luo Jianguo Fei 《Computer Modeling in Engineering & Sciences》 SCIE EI 2021年第3期1033-1052,共20页
The isogeometric analysis method(IGA)is a new type of numerical method solving partial differential equations.Compared with the traditional finite element method,IGA based on geometric spline can keep the model consis... The isogeometric analysis method(IGA)is a new type of numerical method solving partial differential equations.Compared with the traditional finite element method,IGA based on geometric spline can keep the model consistency between geometry and analysis,and provide higher precision with less freedom.However,huge stiffness matrix fromthe subdivision progress still leads to the solution efficiency problems.This paper presents amultigrid method based on geometric multigrid(GMG)to solve the matrix system of IGA.This method extracts the required computational data for multigrid method fromthe IGA process,which also can be used to improve the traditional algebraic multigrid method(AGM).Based on this,a full multigrid method(FMG)based on GMG is proposed.In order to verify the validity and reliability of these methods,this paper did some test on Poisson’s equation and Reynolds’equation and compared the methods on different subdivision methods,different grid degrees of freedom,different cyclic structure degrees,and studied the convergence rate under different subdivision strategies.The results show that the proposed method is superior to the conventional algebraic multigrid method,and for the standard relaxed V-cycle iteration,the method still has a convergence speed independent of the grid size at the same degrees. 展开更多
关键词 Isogeometric method geometric multigrid method reflecting matrix subdivision strategy
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THE MULTIGRID METHOD FOR RESERVOIR SIMULATION 认领 引用
4
作者 陈天翔 吕涛 林爱民 《Applied Mathematics and Mechanics(English Edition)》 SCIE 1989年第7期647-654,共8页
This paper describes a way of solving the reservoir simulation pressure equation using mulligrid technique. The subroutine MG of four-grid method is presented. The result for 2-D two-phase problem is exactly the same ... This paper describes a way of solving the reservoir simulation pressure equation using mulligrid technique. The subroutine MG of four-grid method is presented. The result for 2-D two-phase problem is exactly the same as that of the SOR method and the CPU time is much less than that of the latter one. 展开更多
关键词 THE MULTIGRID METHOD FOR RESERVOIR SIMULATION Simulation ERR cycle
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A New Extrapolation Economy Cascadic Multigrid Method for Image Restoration Problems 认领 引用
5
作者 Zhaoteng Chu Ziqi Yan Chenliang Li 《American Journal of Computational Mathematics》 2023年第2期323-341,共19页
In this paper, a new extrapolation economy cascadic multigrid method is proposed to solve the image restoration model. The new method combines the new extrapolation formula and quadratic interpolation to design a nonl... In this paper, a new extrapolation economy cascadic multigrid method is proposed to solve the image restoration model. The new method combines the new extrapolation formula and quadratic interpolation to design a nonlinear prolongation operator, which provides more accurate initial values for the fine grid level. An edge preserving denoising operator is constructed to remove noise and preserve image edges. The local smoothing operator reduces the influence of staircase effect. The experiment results show that the new method not only improves the computational efficiency but also ensures good recovery quality. 展开更多
关键词 Extrapolation Economy Cascadic Multigrid Method New Extrapolation Formula Edge Preserving Denoising Operator Local Smoothing Operator
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Multigrid Method for the Numerical Solution of the Modified Equal Width Wave Equation 认领 引用
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作者 Yasser M. Abo Essa 《Applied Mathematics》 2016年第10期1140-1147,共8页
Numerical solutions of the modified equal width wave equation are obtained by using the multigrid method and finite difference method. The motion of a single solitary wave, interaction of two solitary waves and develo... Numerical solutions of the modified equal width wave equation are obtained by using the multigrid method and finite difference method. The motion of a single solitary wave, interaction of two solitary waves and development of the Maxwellian initial condition into solitary waves are studied using the proposed method. The numerical solutions are compared with the known analytical solutions. Using error norms and conservative properties of mass, momentum and energy, accuracy and efficiency of the mentioned method will be established through comparison with other methods. 展开更多
关键词 Multigrid Method Finite Difference Method MEW Equation
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Modulus-Based Cascadic Multigrid Method forQuasi-variational Inequality Problems 认领 引用
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作者 Ke-Yu Gao Chen-Liang Li 《Communications on Applied Mathematics and Computation》 EI CSCD 2025年第5期1977-1992,共16页
We propose the modulus-based cascadic multigrid(MCMG)method and the modulus-based economical cascadic multigrid method for solving the quasi-variational inequalities problem.The modulus-based matrix splitting iterativ... We propose the modulus-based cascadic multigrid(MCMG)method and the modulus-based economical cascadic multigrid method for solving the quasi-variational inequalities problem.The modulus-based matrix splitting iterative method is adopted as a smoother,which can accelerate the convergence of the new methods.We also give the convergence analysis of these methods.Finally,some numerical experiments confirm the theoretical analysis and show that the new methods can achieve high efficiency and lower costs simultaneously. 展开更多
关键词 Quasi-variational inequality Modulus-based cascadic multigrid(MCMG)method Modulus-based matrix splitting iteration method Convergence
A full multigrid method for nonlinear eigenvalue problems 认领 引用 被引量：8
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作者 JIA ShangHui XIE HeHu +1 位作者 XIE ManTing XU Fei 《Science China Mathematics》 SCIE CSCD 2016年第10期2037-2048,共12页
We introduce a type of full multigrid method for the nonlinear eigenvalue problem. The main idea is to transform the solution of the nonlinear eigenvalue problem into a series of solutions of the corresponding linear ... We introduce a type of full multigrid method for the nonlinear eigenvalue problem. The main idea is to transform the solution of the nonlinear eigenvalue problem into a series of solutions of the corresponding linear boundary value problems on the sequence of finite element spaces and nonlinear eigenvalue problems on the coarsest finite element space. The linearized boundary value problems are solved by some multigrid iterations.Besides the multigrid iteration, all other efficient iteration methods for solving boundary value problems can serve as the linear problem solver. We prove that the computational work of this new scheme is truly optimal,the same as solving the linear corresponding boundary value problem. In this case, this type of iteration scheme certainly improves the overfull efficiency of solving nonlinear eigenvalue problems. Some numerical experiments are presented to validate the efficiency of the new method. 展开更多
关键词 nonlinear eigenvalue problem full multigrid method multilevel correction finite element method
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Finite element multigrid method for multi-term time fractional advection diffusion equations 认领 引用 被引量：6
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作者 Weiping Bu Xiangtao Liu +1 位作者 Yifa Tang Jiye Yang 《International Journal of Modeling, Simulation, and Scientific Computing》 EI 2015年第1期1-25,共25页
In this paper,a class of multi-term time fractional advection diffusion equations(MTFADEs)is considered.By finite difference method in temporal direction and finite element method in spatial direction,two fully discre... In this paper,a class of multi-term time fractional advection diffusion equations(MTFADEs)is considered.By finite difference method in temporal direction and finite element method in spatial direction,two fully discrete schemes of MTFADEs with different definitions on multi-term time fractional derivative are obtained.The stability and convergence of these numerical schemes are discussed.Next,a V-cycle multigrid method is proposed to solve the resulting linear systems.The convergence of the multigrid method is investigated.Finally,some numerical examples are given for verification of our theoretical analysis. 展开更多
关键词 Multi-term time fractional advection diffusion equation finite element method stability convergence V-cycle multigrid method
Economical cascadic multigrid method(ECMG) 认领 引用 被引量：15
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作者 Zhong-ci SHI Xue-jun XU Yun-qing HUANG 《Science China Mathematics》 2007年第12期1765-1780,共16页
In this paper,an economical cascadic multigrid method is proposed.Compared with the usual cascadic multigrid method developed by Bornemann and Deuflhard,the new one requires less iterations on each level,especially on... In this paper,an economical cascadic multigrid method is proposed.Compared with the usual cascadic multigrid method developed by Bornemann and Deuflhard,the new one requires less iterations on each level,especially on the coarser grids.Many operations can be saved in the new cascadic multigrid algorithms.The main ingredient is the control of the iteration numbers on the each level to preserve the accuracy without over iterations.The theoretical justification is based on the observations that the error reduction rate of an iteration scheme in terms of the smoothing property is no longer accurate while the iteration number is big enough.A new formulae of the error reduction rate is employed in our new algorithm.Numerical experiments are reported to support our theory. 展开更多
关键词 economical cascadic multigrid method(ECMG) cascadic multigrid method(CMG)
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Local grid refinement in multigrid method for point contact problems of polycrystalline anisotropic material under dry and lubricated conditions 认领 引用 被引量：2
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作者 Binbin ZHANG Tristan G.VLOGMAN +2 位作者 Predrag ANDRIC Ton C.BOR Cornelis H.VENNER 《Friction》 SCIE EI CAS CSCD 2022年第12期2086-2110,共25页
Predicting rolling bearing fatigue life requires knowledge of the three-dimensional(3D)stress fields in the roller and raceway near the lubricated contact.Owing to the increasingly severe operating conditions,the effe... Predicting rolling bearing fatigue life requires knowledge of the three-dimensional(3D)stress fields in the roller and raceway near the lubricated contact.Owing to the increasingly severe operating conditions,the effect of localized features such as surface roughness,subsurface inclusions,and even the crystallographic structure of the material becomes important.Achieving such detail requires(locally)extremely dense gridding in simulations,which in 3D is a major challenge.Multigrid techniques have been demonstrated to be capable of solving such problems.In this study,multigrid techniques are shown to further increase the efficiency of the solution by exploiting local grid refinement while maintaining the simplicity of a uniform discretization.This is achieved by employing increasingly finer grids only locally,where the highest resolution is required.Results are presented for dry contact and elastohydrodynamically lubricated contact cases,circular as well as elliptic,with varying crystallographic structure,and with surface roughness.The results show that the developed algorithm is very well suited for detailed analysis,with also excellent prospects for computational diagnostics involving actual material crystallographic structure from electron backscatter diffraction measurements. 展开更多
关键词 local grid refinement multigrid method polycrystalline anisotropic material dry and lubricated contact
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A Shifted-Inverse Adaptive Multigrid Method for the Elastic Eigenvalue Problem 认领 引用 被引量：2
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作者 Bo Gong Jiayu Han +1 位作者 Jiguang Sun Zhimin Zhang 《Communications in Computational Physics》 SCIE 2020年第1期251-273,共23页
A shifted-inverse iteration is proposed for the finite element discretization of the elastic eigenvalue problem.The method integrates the multigrid scheme and adaptive algorithm to achieve high efficiency and accuracy... A shifted-inverse iteration is proposed for the finite element discretization of the elastic eigenvalue problem.The method integrates the multigrid scheme and adaptive algorithm to achieve high efficiency and accuracy.Error estimates and optimal convergence for the proposed method are proved.Numerical examples show that the proposed method inherits the advantages of both ingredients and can compute low regularity eigenfunctions effectively. 展开更多
关键词 Elastic eigenvalue problem shifted-inverse iteration adaptive multigrid method
PRECONDITIONING HIGHER ORDER FINITE ELEMENT SYSTEMS BY ALGEBRAIC MULTIGRID METHOD OF LINEAR ELEMENTS 认领 引用 被引量：2
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作者 Yun-qing Huang Shi Shu Xi-jun Yu 《Journal of Computational Mathematics》 SCIE EI 2006年第5期657-664,共8页
We present and analyze a robust preconditioned conjugate gradient method for the higher order Lagrangian finite element systems of a class of elliptic problems. An auxiliary linear element stiffness matrix is chosen t... We present and analyze a robust preconditioned conjugate gradient method for the higher order Lagrangian finite element systems of a class of elliptic problems. An auxiliary linear element stiffness matrix is chosen to be the preconditioner for higher order finite elements. Then an algebraic multigrid method of linear finite element is applied for solving the preconditioner. The optimal condition number which is independent of the mesh size is obtained. Numerical experiments confirm the efficiency of the algorithm. 展开更多
关键词 Finite element Algebraic multigrid methods Preconditioned Conjugate Gradient Condition number.
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Extrapolation cascadic multigrid method on piecewise uniform grid 认领 引用 被引量：3
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作者 CHEN ChuanMiao HU HongLing 《Science China Mathematics》 SCIE EI 2013年第12期2711-2722,共12页
The triangular linear finite elements on piecewise uniform grid for an elliptic problem in convex polygonal domain are discussed. Global superconvergence in discrete Hi-norm and global extrapolation in discrete L2-nor... The triangular linear finite elements on piecewise uniform grid for an elliptic problem in convex polygonal domain are discussed. Global superconvergence in discrete Hi-norm and global extrapolation in discrete L2-norm are proved. Based on these global estimates the conjugate gradient method （CG） is effective, which is applied to extrapolation cascadic multigrid method （EXCMG）. The numerical experiments show that EXCMG is of the global higher accuracy for both function and gradient. 展开更多
关键词 linear finite element piecewise uniform grid superconvergence extrapolation extrapolation cas-cadic multigrid method
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CASCADIC MULTIGRID METHOD FOR THE MORTAR ELEMENT METHOD FOR P1 NONCONFORMING ELEMENT 认领 引用 被引量：4
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作者 Chun-jia Bi Dan-hui Hong 《Journal of Computational Mathematics》 SCIE EI 2005年第4期425-440,共16页
In this paper, we consider the cascadic multigrid method for the mortar P1 nonconforming element which is used to solve the Poisson equation and prove that the cascadic conjugate gradient method is accurate with optim... In this paper, we consider the cascadic multigrid method for the mortar P1 nonconforming element which is used to solve the Poisson equation and prove that the cascadic conjugate gradient method is accurate with optimal complexity. 展开更多
关键词 Mortar P1 nonconforming element Cascadic multigrid method
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An Efficient Multigrid Method for Molecular Mechanics Modeling in Atomic Solids 认领 引用 被引量：1
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作者 Jingrun Chen Pingbing Ming 《Communications in Computational Physics》 SCIE 2011年第6期70-89,共20页
We propose a multigrid method to solve the molecular mechanics model(molecular dynamics at zero temperature).The Cauchy-Born elasticity model is employed as the coarse grid operator and the elastically deformed state ... We propose a multigrid method to solve the molecular mechanics model(molecular dynamics at zero temperature).The Cauchy-Born elasticity model is employed as the coarse grid operator and the elastically deformed state as the initial guess of the molecular mechanics model.The efficiency of the algorithm is demonstrated by three examples with homogeneous deformation,namely,one dimensional chain under tensile deformation and aluminum under tension and shear deformations.The method exhibits linear-scaling computational complexity,and is insensitive to parameters arising from iterative solvers.In addition,we study two examples with inhomogeneous deformation:vacancy and nanoindentation of aluminum.The results are still satisfactory while the linear-scaling property is lost for the latter example. 展开更多
关键词 Multigrid method linear-scaling algorithm Cauchy-Born rule nanoindentation
GAUSS-SEIDEL-TYPE MULTIGRID METHODS 认领 引用 被引量：3
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作者 Zhao-hui Huang Qian-shun Chang 《Journal of Computational Mathematics》 SCIE EI 2003年第4期421-434,共14页
By making use of the Gauss-Seidel-type solution method, the procedure for computing the interpolation operator of multigrid methods is simplified. This leads to a saving of computational time. Three new kinds of inter... By making use of the Gauss-Seidel-type solution method, the procedure for computing the interpolation operator of multigrid methods is simplified. This leads to a saving of computational time. Three new kinds of interpolation formulae are obtained by adopting different approximate methods, to try to enhance the accuracy of the interpolatory operator. A theoretical study proves the two-level convergence of these Gauss-Seidel-type MG methods. A series of numerical experiments is presented to evaluate the relative performance of the methods with respect to the convergence factor, CPU-time(for one V-cycle and the setup phase) and computational complexity. 展开更多
关键词 Multigrid methods Gauss-Seidel solution Interpolation formula Convergence.
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A MULTIGRID METHOD FOR NONLINEAR PARABOLIC PROBLEMS 认领 引用 被引量：1
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作者 x.J. Yu 《Journal of Computational Mathematics》 SCIE EI 1996年第4期363-382,共20页
The multigrid algorithm in [13] is developed for solving nonlinear parabolic equations arising from the finite element discretization. The computational cost of the algorithm is approximate O(NkN) where N-k is the dim... The multigrid algorithm in [13] is developed for solving nonlinear parabolic equations arising from the finite element discretization. The computational cost of the algorithm is approximate O(NkN) where N-k is the dimension of the finite element space and N is the number of time steps. 展开更多
关键词 Th Math A MULTIGRID METHOD FOR NONLINEAR PARABOLIC PROBLEMS UC
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A Constrained Cauchy-Born Elasticity Accelerated Multigrid Method for Nanoindentation 认领 引用
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作者 Jingrun Chen Pingbing Ming Jerry Zhijian Yang 《Communications in Computational Physics》 SCIE 2014年第2期470-486,共17页
We introduce a new multigrid method to study the lattice statics model arising from nanoindentation.A constrained Cauchy-Born elasticity model is used as the coarse-grid operator.This method accelerates the relaxation... We introduce a new multigrid method to study the lattice statics model arising from nanoindentation.A constrained Cauchy-Born elasticity model is used as the coarse-grid operator.This method accelerates the relaxation process and considerably reduces the computational cost.In particular,it saves quite a bit when dislocations nucleate and move,as demonstrated by the simulation results. 展开更多
关键词 Multigrid method constrained Cauchy-Born elasticity nanoindentation CauchyBorn rule.
MULTIGRID METHODS FOR MORLEY ELEMENT ON NONNESTED MESHES 认领 引用
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作者 Shi, ZC Xie, ZH 《Journal of Computational Mathematics》 SCIE EI 1998年第5期385-394,共10页
In this paper, we consider some multigrid algorithms for the biharmonic problem discretized by Morley element on nonnested meshes. Through taking the averages of the nodal variables we construct an intergrid transfer ... In this paper, we consider some multigrid algorithms for the biharmonic problem discretized by Morley element on nonnested meshes. Through taking the averages of the nodal variables we construct an intergrid transfer operator that satisfies a certain stable approximation property. The so-called regularity-approximation assumption is then established. Optimal convergence properties of the W-cycle and a uniform condition number estimate for the variable V-cycle preconditioner are presented. This technique is applicable to other nonconforming plate elements. 展开更多
关键词 multigrid method Morley element nonnested meshes
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