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Three-dimensional inversion of metallic minerals electromagnetic data using efficient multigrid solver 认领 引用
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作者 Yong-fei WANG Rong-wen GUO +2 位作者 Zhuo LIU Ding-hui YANG Deng-kang WANG 《Transactions of Nonferrous Metals Society of China》 SCIE EI CAS CSCD 2026年第3期943-955,共13页
A three-dimensional(3D)electromagnetic(EM)inversion algorithm based on the nonlinear conjugate gradient(NLCG)method and a two-color plane Gauss-Seidel(GS)multigrid(MG)forward solver is developed to improve inversion e... A three-dimensional(3D)electromagnetic(EM)inversion algorithm based on the nonlinear conjugate gradient(NLCG)method and a two-color plane Gauss-Seidel(GS)multigrid(MG)forward solver is developed to improve inversion efficiency.The results indicate that the computational efficiency of each inversion can be improved by approximately a factor of three by using the proposed MG solver.First,the accuracy of the MG solver is validated through a test on a synthetic model.Next,the numerical performance of the inversion algorithm is evaluated using this model.Finally,the inversion algorithm is applied to a field EM data collected at the Beiya gold polymetallic ore district.A 3D resistivity model is obtained,and the formation process of the metal ore is analyzed. 展开更多
关键词 metallic minerals electromagnetic data gradient inversion method multigrid solver
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HIGH ORDER PROBABILISTIC NUMERICAL METHODS FOR FORWARD BACKWARD STOCHASTIC DIFFERENTIAL EQUATIONS 认领 引用
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作者 Qiang Han Yurong Liu 《Journal of Computational Mathematics》 SCIE CSCD 2026年第6期1631-1661,共31页
In this paper,we design novel high order probabilistic numerical algorithms for forward backward stochastic differential equations.Moreover,we derive the error estimates and prove the high order convergence rates of t... In this paper,we design novel high order probabilistic numerical algorithms for forward backward stochastic differential equations.Moreover,we derive the error estimates and prove the high order convergence rates of the proposed schemes.Because the proposed scheme involves conditional expectations,an estimator based on the multilevel Monte Carlo method is applied to approximate the conditional expectations.Furthermore,we theoretically demonstrate that the computational complexity of our numerical method is proportional to the square of prescribed accuracy.Numerical experiments are given to illustrate the theoretical results. 展开更多
关键词 Forward Backward Stochastic Differential Equation Probabilistic Numerical Method Multilevel Monte Carlo Computational Complexity High Order Discretization
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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
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作者 Han Zhonghua He Fei +1 位作者 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 investi... 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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3-D direct current resistivity forward modeling by adaptive multigrid finite element method 认领 引用 被引量：16
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作者 汤井田 王飞燕 +1 位作者 任政勇 郭荣文 《Journal of Central South University》 SCIE EI CAS 2010年第3期587-592,共6页
Based on the fact that 3-D model discretization by artificial could not always be successfully implemented especially for large-scaled problems when high accuracy and efficiency were required, a new adaptive multigrid... Based on the fact that 3-D model discretization by artificial could not always be successfully implemented especially for large-scaled problems when high accuracy and efficiency were required, a new adaptive multigrid finite element method was proposed. In this algorithm, a-posteriori error estimator was employed to generate adaptively refined mesh on a given initial mesh. On these iterative meshes, V-cycle based multigrid method was adopted to fast solve each linear equation with each initial iterative term interpolated from last mesh. With this error estimator, the unknowns were nearly optimally distributed on the final mesh which guaranteed the accuracy. The numerical results show that the multigrid solver is faster and more stable compared with ICCG solver. Meanwhile, the numerical results obtained from the final model discretization approximate the analytical solutions with maximal relative errors less than 1%, which remarkably validates this algorithm. 展开更多
关键词 adaptive multigrid a-posteriori error estimator unstructured mesh V-cycle finite element method
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AUTOMATIC MULTILEVEL THRESHOLDING METHOD BASED ON MAXIMUM ENTROPY 认领 引用 被引量：5
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作者 曹力 史忠科 郑家伟 《Transactions of Nanjing University of Aeronautics and Astronautics》 EI 2005年第4期335-338,共4页
In the multilevel thresholding segmentation of the image, the classification number is always given by the supervisor. To solve this problem, a fast multilevel thresholding algorithm considering both the threshold val... In the multilevel thresholding segmentation of the image, the classification number is always given by the supervisor. To solve this problem, a fast multilevel thresholding algorithm considering both the threshold value and the classification number is proposed based on the maximum entropy, and the self-adaptive criterion of the classification number is given. The algorithm can obtain thresholds and automatically decide the classification number. Experimental results show that the algorithm is effective. 展开更多
关键词 multilevel thresholding maximum entropy classification number nonparametric method
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Multilevel Iteration Methods for Solving Linear Operator Equations of the First Kind 认领 引用 被引量：2
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作者 罗兴钧 《Northeastern Mathematical Journal》 2008年第1期1-9,共9页
In this paper we develop two multilevel iteration methods for solving linear systems resulting from the Galerkin method and Tikhonov regularization for linear ill-posed problems. The two algorithms and their convergen... In this paper we develop two multilevel iteration methods for solving linear systems resulting from the Galerkin method and Tikhonov regularization for linear ill-posed problems. The two algorithms and their convergence analyses are presented in an abstract framework. 展开更多
关键词 operator equations of the first kind ill-posed problem multilevel iteration method Tikhonov regularization
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Fast Multilevel Methods for Solving Ill-posed Problems 认领 引用
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作者 陈仲英 宋丽红 马富明 《Northeastern Mathematical Journal》 2005年第2期131-134,共4页
1 Introduetion Many industrial and engineering applieations require numerieally solving ill-posed Problems. Regularization methods are employed to find approximate solutions of these problems.The choice of regularization
关键词 Ill-posed problem regularization method multilevel method
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The V-cycle Multigrid Method for a Hermite-type Rectangular Element 认领 引用
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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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Risk Assessment of Diary Cattle Brucellosis Based on Systematic Multilevel Grey Relation Entropy Method 认领 引用
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作者 孙向东 江慎铭 刘拥军 《Agricultural Science & Technology》 CAS 2012年第10期2169-2174,2225,共6页
[Objective] The study was to explore the major factors affecting diary cattle brucellosis risk assessment,as well as their strong-to-weak sequence,so as to provide theoretical basis for assessing diary cattle brucello... [Objective] The study was to explore the major factors affecting diary cattle brucellosis risk assessment,as well as their strong-to-weak sequence,so as to provide theoretical basis for assessing diary cattle brucellosis risk level in different regions.[Method] From 4 dimensions of feeding and importing,breeding,housing and polyculture situation,an evaluation index system was set up,and diary cattle brucellosis risk survey was conducted in 3 typical regions.Finally,systematic multilevel grey relation entropy method was applied to perform data analysis.[Result] The strong-to-weak sequence of Level 1 impact factor of diary cattle brucellosis was as follows：feeding and importinghousingpolyculture situationbreeding;the sequence of Level 2 impact factor was U32〉U12〉U11〉U31〉U21〉U42〉U43〉U23〉U22〉U41;the risk level sequence of 3 typical regions was Province A（County A1,A2,A3）Province B（County B1,B2,B3）Province C（County C1,C2,C3）.[Conclusion] According to the weight of Level 1 index strata,administrative departments at all levels and dairy cattle farmers should lay emphasis on the aspects of feeding,importing and housing;viewed from the perspective of Level 2 index strata,dairy cattle farmers should value the siting of cattle field,the brucellosis surveillance before importing and milking modes most.According to the diary cattle brucellosis risk level of 3 typical regions,if administrative departments at all levels strengthen peoples＇ awareness of their personal health and increase investment in this area,with new healthy cultured atmosphere built,the risk level of diary cattle brucellosis will surly decline. 展开更多
关键词 Systematic multilevel grey relation entropy method Diary cattle brucellosis Risk assessment
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A Cascadic Multigrid Algorithm for the Mortar Element Method for Semiliner Ellptic Problems 认领 引用
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作者 邹战勇 《嘉应学院学报》 2015年第11期5-10,共6页
In this paper a cascadic multigrid algorithm for the mortar finite element approximation of the semilinear elliptic problem is proposed,and corresponding theorems aregiven,which display the error estimate and the comp... In this paper a cascadic multigrid algorithm for the mortar finite element approximation of the semilinear elliptic problem is proposed,and corresponding theorems aregiven,which display the error estimate and the computational complexity of the method. 展开更多
关键词 Mortar finite element Cascadic multigrid method Senilinear elliptic problems
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ON ALGEBRAIC MULTILEVEL PRECONDITIONINGMETHODS 认领 引用
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作者 曹志浩 蒋意程 《Numerical Mathematics A Journal of Chinese Universities(English Series)》 1993年第1期25-37,共13页
In the present paper we extend the method presented by 0. Axelsson and P. Vassilevski called AMLP version (i) of recursively constructing preconditioner for the stiffness matrix in the discretization of selfadjoint se... In the present paper we extend the method presented by 0. Axelsson and P. Vassilevski called AMLP version (i) of recursively constructing preconditioner for the stiffness matrix in the discretization of selfadjoint second order elliptic boundary value problems. In our extended method the systems to be eliminated on each level containing the major block matrices of the given matrix can be solved approximately, while they must be solved exactly in the original method. 展开更多
关键词 Preconditioning multilevel method Schur complement.
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Multigrid fictitious boundary method for incompressible viscous flows around moving airfoils 认领 引用
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作者 WAN De-Cheng 《Journal of Marine Science and Application》 2007年第2期51-58,共8页
In this paper, an efficient multigrid fictitious boundary method （MFBM） coupled with the FEM solver package FEATFLOW was used for the detailed simulation of incompressible viscous flows around one or more moving NAC... In this paper, an efficient multigrid fictitious boundary method （MFBM） coupled with the FEM solver package FEATFLOW was used for the detailed simulation of incompressible viscous flows around one or more moving NACA0012 airfoils. The calculations were carded on a fixed multigrid finite element mesh on which fluid equations were satisfied everywhere, and the airfoils were allowed to move freely through the mesh. The MFBM was employed to treat interactions between the fluid and the airfoils The motion of the airfoils was modeled by Newton-Euler equations. Numerical results of experiments verify that this method provides an efficient way to simulate incompressible viscous flows around moving airfoils. 展开更多
关键词 airfoils induced-motion fictitious boundary method FEM multigrid
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An Interactive Intuitionistic Fuzzy Method for Multilevel Linear Programming Problems 认领 引用 被引量：1
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作者 HUANG Chan FANG Debin WAN Zhongping 《Wuhan University Journal of Natural Sciences》 CAS CSCD 2015年第2期113-118,共6页
In this paper, we propose an interactive method for solving the multilevel linear programming problems based on the intuitionistic fuzzy set theory. Firstly, the membership function and the non-membership function are... In this paper, we propose an interactive method for solving the multilevel linear programming problems based on the intuitionistic fuzzy set theory. Firstly, the membership function and the non-membership function are introduced to describe the uncertainty of the decision makers. Secondly, a satisfactory solution is derived by updating the minimum satisfactory degrees with considerations of the overall satisfactory balance among all levels. In addition, the steps of the proposed method are given in this paper. Finally, numerical examples illustrate the feasibility of this method. 展开更多
关键词 intuitionistic fuzzy multilevel linear programming interactive method satisfying degree
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Geometric Multigrid Method for Isogeometric Analysis 认领 引用
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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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Multilevel Characteristic Basis Function Method with ACA for Accelerated Solution of Electrically Large Scattering Problems 认领 引用
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作者 Li Chenlu Sun Yufa +1 位作者 Wang Zhonggen Wang Guohua 《Transactions of Nanjing University of Aeronautics and Astronautics》 EI CSCD 2018年第3期449-454,共6页
The multilevel characteristic basis function method(MLCBFM)with the adaptive cross approximation(ACA)algorithm for accelerated solution of electrically large scattering problems is studied in this paper.In the convent... The multilevel characteristic basis function method(MLCBFM)with the adaptive cross approximation(ACA)algorithm for accelerated solution of electrically large scattering problems is studied in this paper.In the conventional MLCBFM based on Foldy-Lax multiple scattering equations,the improvement is only made in the generation of characteristic basis functions(CBFs).However,it does not provide a change in impedance matrix filling and reducing matrix calculation procedure,which is time-consuming.In reality,all the impedance and reduced matrix of each level of the MLCBFM have low-rank property and can be calculated efficiently.Therefore,ACA is used for the efficient generation of two-level CBFs and the fast calculation of reduced matrix in this study.Numerical results are given to demonstrate the accuracy and efficiency of the method. 展开更多
关键词 multilevel characteristic basis function method(MLCBFM) adaptive cross approximation(ACA) characteristic basis functions(CBFs) electromagnetic scattering
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Performance of Geometric Multigrid Method for Two-Dimensional Burgers’Equations with Non-Orthogonal,Structured Curvilinear Grids 认领 引用
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作者 Daiane Cristina Zanatta Luciano Kiyoshi Araki +1 位作者 Marcio Augusto Villela Pinto Diego Fernando Moro 《Computer Modeling in Engineering & Sciences》 SCIE EI 2020年第12期1061-1081,共21页
This paper seeks to develop an efficient multigrid algorithm for solving the Burgers problem with the use of non-orthogonal structured curvilinear grids in L-shaped geometry.For this,the differential equations were di... This paper seeks to develop an efficient multigrid algorithm for solving the Burgers problem with the use of non-orthogonal structured curvilinear grids in L-shaped geometry.For this,the differential equations were discretized by Finite Volume Method(FVM)with second-order approximation scheme and deferred correction.Moreover,the algebraic method and the differential method were used to generate the non-orthogonal structured curvilinear grids.Furthermore,the influence of some parameters of geometric multigrid method,as well as lexicographical Gauss–Seidel(Lex-GS),η-line Gauss–Seidel(η-line-GS),Modified Strongly Implicit(MSI)and modified incomplete LU decomposition(MILU)solvers on the Central Processing Unit(CPU)time was investigated.Therefore,several parameters of multigrid method and solvers were tested for the problem,with the use of nonorthogonal structured curvilinear grids and multigrid method,resulting in an algorithm with the combination that achieved the best results and CPU time.The geometric multigrid method with Full Approximation Scheme(FAS),V-cycle and standard coarsening ratio for this problem were utilized.This article shows how to calculate the coordinates transformation metrics in the coarser grids.Results show that the MSI and MILU solvers are the most efficient.Moreover,theMSI solver is faster thanMILU for both grids generators;and the solutions are more accurate for the Burgers problem with grids generated using elliptic equations. 展开更多
关键词 Computational fluid dynamics finite volume method Burgers’equation geometric multigrid non-orthogonal curvilinear grids
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THE MULTIGRID METHOD FOR RESERVOIR SIMULATION 认领 引用
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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 Newton multigrid method for steady-state shallow water equations with topography and dry areas 认领 引用
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作者 Kailiang WU Huazhong TANG 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI CSCD 2016年第11期1441-1466,共26页
A Newton multigrid method is developed for one-dimensional （1D） and two- dimensional （2D） steady-state shallow water equations （SWEs） with topography and dry areas. The nonlinear system arising from the well-bal... A Newton multigrid method is developed for one-dimensional （1D） and two- dimensional （2D） steady-state shallow water equations （SWEs） with topography and dry areas. The nonlinear system arising from the well-balanced finite volume discretization of the steady-state SWEs is solved by the Newton method as the outer iteration and a geometric multigrid method with the block symmetric Gauss-Seidel smoother as the inner iteration. The proposed Newton multigrid method makes use of the local residual to regularize the Jacobian matrix of the Newton iteration, and can handle the steady- state problem with wet/dry transition. Several numerical experiments are conducted to demonstrate the efficiency, robustness, and well-balanced property of the proposed method. The relation between the convergence behavior of the Newton multigrid method and the distribution of the eigenvalues of the iteration matrix is detailedly discussed. 展开更多
关键词 Newton method multigrid block symmetric Gauss-Seidel shallow waterequation （SWE） steady-state solution
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The Numerical Solution of the MRLW Equation Using the Multigrid Method 认领 引用 被引量：1
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作者 Yasser Mohamed Abo Essa Ibrahim Abouefarag El-Desouky Rahmo 《Applied Mathematics》 2014年第21期3328-3334,共7页
In this paper, we obtained the numerical solutions of the modified regularized long-wave (MRLW) equation, by using the multigrid method and finite difference method. The solitary wave motion, interaction of two and th... In this paper, we obtained the numerical solutions of the modified regularized long-wave (MRLW) equation, by using the multigrid method and finite difference method. The solitary wave motion, interaction of two and three 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. Usingerror norms and conservative properties of mass, momentum and energy, accuracy and efficiency of the mentioned method will be established through comparison with other techniques. 展开更多
关键词 Multigrid Method Finite Difference Method MRLW Equation
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A Multiscale Multilevel Monte Carlo Method for Multiscale Elliptic PDEs with Random Coefficients 认领 引用
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作者 Junlong Lyu Zhiwen Zhang 《Communications in Mathematical Research》 CSCD 2020年第2期154-192,共39页
We propose a multiscale multilevel Monte Carlo(MsMLMC)method to solve multiscale elliptic PDEs with random coefficients in the multi-query setting.Our method consists of offline and online stages.In the offline stage,... We propose a multiscale multilevel Monte Carlo(MsMLMC)method to solve multiscale elliptic PDEs with random coefficients in the multi-query setting.Our method consists of offline and online stages.In the offline stage,we construct a small number of reduced basis functions within each coarse grid block,which can then be used to approximate the multiscale finite element basis functions.In the online stage,we can obtain the multiscale finite element basis very efficiently on a coarse grid by using the pre-computed multiscale basis.The MsMLMC method can be applied to multiscale RPDE starting with a relatively coarse grid,without requiring the coarsest grid to resolve the smallestscale of the solution.We have performed complexity analysis and shown that the MsMLMC offers considerable savings in solving multiscale elliptic PDEs with random coefficients.Moreover,we provide convergence analysis of the proposed method.Numerical results are presented to demonstrate the accuracy and efficiency of the proposed method for several multiscale stochastic problems without scale separation. 展开更多
关键词 Random partial differential equations(RPDEs) uncertainty quantification(UQ) multiscale finite element method(MsFEM) multilevel Monte Carlo(MLMC) reduced basis convergence analysis
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