In this work, approximate analytical solutions to the lid-driven square cavity flow problem, which satisfied two-dimensional unsteady incompressible Navier-Stokes equations, are presented using the kinetically reduced...In this work, approximate analytical solutions to the lid-driven square cavity flow problem, which satisfied two-dimensional unsteady incompressible Navier-Stokes equations, are presented using the kinetically reduced local Navier-Stokes equations. Reduced differential transform method and perturbation-iteration algorithm are applied to solve this problem. The convergence analysis was discussed for both methods. The numerical results of both methods are given at some Reynolds numbers and low Mach numbers, and compared with results of earlier studies in the review of the literatures. These two methods are easy and fast to implement, and the results are close to each other and other numerical results, so it can be said that these methods are useful in finding approximate analytical solutions to the unsteady incompressible flow problems at low Mach numbers.展开更多
A new iterating method based on homotopy function is developed in this paper. All solutions can be found easily without the need of choosing proper initial values. Compared to the homotopy continuation method, the sol...A new iterating method based on homotopy function is developed in this paper. All solutions can be found easily without the need of choosing proper initial values. Compared to the homotopy continuation method, the solution process of the present method is simplified, and the computation efficiency as well as the reliability for obtaining all solutions is also improved. By application of the method to the mechanisms problems, the results are satisfactory.展开更多
Motivated by the study of regularization for sparse problems,we propose a new regularization method for sparse vector recovery.We derive sufficient conditions on the well-posedness of the new regularization,and design...Motivated by the study of regularization for sparse problems,we propose a new regularization method for sparse vector recovery.We derive sufficient conditions on the well-posedness of the new regularization,and design an iterative algorithm,namely the iteratively reweighted algorithm(IR-algorithm),for efficiently computing the sparse solutions to the proposed regularization model.The convergence of the IR-algorithm and the setting of the regularization parameters are analyzed at length.Finally,we present numerical examples to illustrate the features of the new regularization and algorithm.展开更多
The parallel algorithms of iterated defect correction methods (PIDeCM’s) are constructed, which are of efficiency and high order B-convergence for general nonlinear stiff systems in ODE’S. As the basis of constructi...The parallel algorithms of iterated defect correction methods (PIDeCM’s) are constructed, which are of efficiency and high order B-convergence for general nonlinear stiff systems in ODE’S. As the basis of constructing and discussing PIDeCM’s. a class of parallel one-leg methods is also investigated, which are of particular efficiency for linear systems.展开更多
In this paper, a parallel algorithm with iterative form for solving finite element equation is presented. Based on the iterative solution of linear algebra equations, the parallel computational steps are introduced in...In this paper, a parallel algorithm with iterative form for solving finite element equation is presented. Based on the iterative solution of linear algebra equations, the parallel computational steps are introduced in this method. Also by using the weighted residual method and choosing the appropriate weighting functions, the finite element basic form of parallel algorithm is deduced. The program of this algorithm has been realized on the ELXSI-6400 parallel computer of Xi'an Jiaotong University. The computational results show the operational speed will be raised and the CPU time will be cut down effectively. So this method is one kind of effective parallel algorithm for solving the finite element equations of large-scale structures.展开更多
The Grey Wolf Optimization(GWO)algorithm is acknowledged as an effective method for rock acoustic emission localization.However,the conventional GWO algorithm encounters challenges related to solution accuracy and con...The Grey Wolf Optimization(GWO)algorithm is acknowledged as an effective method for rock acoustic emission localization.However,the conventional GWO algorithm encounters challenges related to solution accuracy and convergence speed.To address these concerns,this paper develops a Simplex Improved Grey Wolf Optimizer(SMIGWO)algorithm.The randomly generating initial populations are replaced with the iterative chaotic sequences.The search process is optimized using the convergence factor optimization algorithm based on the inverse incompleteГfunction.The simplex method is utilized to address issues related to poorly positioned grey wolves.Experimental results demonstrate that,compared to the conventional GWO algorithm-based AE localization algorithm,the proposed algorithm achieves a higher solution accuracy and showcases a shorter search time.Additionally,the algorithm demonstrates fewer convergence steps,indicating superior convergence efficiency.These findings highlight that the proposed SMIGWO algorithm offers enhanced solution accuracy,stability,and optimization performance.The benefits of the SMIGWO algorithm extend universally across various materials,such as aluminum,granite,and sandstone,showcasing consistent effectiveness irrespective of material type.Consequently,this algorithm emerges as a highly effective tool for identifying acoustic emission signals and improving the precision of rock acoustic emission localization.展开更多
Two methods based on a slight modification of the regular traffic assignmentalgorithms are proposed to directly compute turn flows instead of estimating them from link flows orobtaining them by expanding the networks....Two methods based on a slight modification of the regular traffic assignmentalgorithms are proposed to directly compute turn flows instead of estimating them from link flows orobtaining them by expanding the networks. The first one is designed on the path-turn incidencerelationship, and it is similar to the computational procedure of link flows. It applies to thetraffic assignment algorithms that can provide detailed path structures. The second utilizes thelink-turn incidence relationship and the conservation of flow on links, a law deriving from thisrelationship. It is actually an improved version of Dial's logit assignment algorithm. The proposedapproaches can avoid the shortcomings both of the estimation methods, e. g. Furness's model andFrator's model, and of the network-expanding method in precision, stability and computation scale.Finally, they are validated by numerical examples.展开更多
Although full waveform inversion in the frequency domain can overcome the local minima problem in the time direction, such problem still exists in the space direction because of the media subsurface complexity. Based ...Although full waveform inversion in the frequency domain can overcome the local minima problem in the time direction, such problem still exists in the space direction because of the media subsurface complexity. Based on the optimal steep descent methods, we present an algorithm which combines the preconditioned bi-conjugated gradient stable method and the multi-grid method to compute the wave propagation and the gradient space. The multiple scale prosperity of the waveform inversion and the multi-grid method can overcome the inverse problems local minima defect and accelerate convergence. The local inhomogeneous three-hole model simulated results and the Marmousi model certify the algorithm effectiveness.展开更多
A numerical method is proposed to simulate the transverse vibrations of a viscoelastic moving string constituted by an integral law. In the numerical computation, the Galerkin method based on the Hermite functions is ...A numerical method is proposed to simulate the transverse vibrations of a viscoelastic moving string constituted by an integral law. In the numerical computation, the Galerkin method based on the Hermite functions is applied to discretize the state variables, and the Runge- Kutta method is applied to solve the resulting differential-integral equation system. A linear iterative process is designed to compute the integral terms at each time step, which makes the numerical method more efficient and accurate. As examples, nonlinear parametric vibrations of an axially moving viscoelastic string are analyzed.展开更多
In the optimal control problem of nonlinear dynamical system,the Hamiltonian formulation is useful and powerful to solve an optimal control force.However,the resulting Euler-Lagrange equations are not easy to solve,wh...In the optimal control problem of nonlinear dynamical system,the Hamiltonian formulation is useful and powerful to solve an optimal control force.However,the resulting Euler-Lagrange equations are not easy to solve,when the performance index is complicated,because one may encounter a two-point boundary value problem of nonlinear differential algebraic equations.To be a numerical method,it is hard to exactly preserve all the specified conditions,which might deteriorate the accuracy of numerical solution.With this in mind,we develop a novel algorithm to find the solution of the optimal control problem of nonlinear Duffing oscillator,which can exactly satisfy all the required conditions for the minimality of the performance index.A new idea of shape functions method(SFM)is introduced,from which we can transform the optimal control problems to the initial value problems for the new variables,whose initial values are given arbitrarily,and meanwhile the terminal values are determined iteratively.Numerical examples confirm the high-performance of the iterative algorithms based on the SFM,which are convergence fast,and also provide very accurate solutions.The new algorithm is robust,even large noise is imposed on the input data.展开更多
Based on local algorithms,some parallel finite element(FE)iterative methods for stationary incompressible magnetohydrodynamics(MHD)are presented.These approaches are on account of two-grid skill include two major phas...Based on local algorithms,some parallel finite element(FE)iterative methods for stationary incompressible magnetohydrodynamics(MHD)are presented.These approaches are on account of two-grid skill include two major phases:find the FE solution by solving the nonlinear system on a globally coarse mesh to seize the low frequency component of the solution,and then locally solve linearized residual subproblems by one of three iterations(Stokes-type,Newton,and Oseen-type)on subdomains with fine grid in parallel to approximate the high frequency component.Optimal error estimates with regard to two mesh sizes and iterative steps of the proposed algorithms are given.Some numerical examples are implemented to verify the algorithm.展开更多
This paper proposes a numerical solution method for upper bound shakedown analysis of perfectly elasto-plastic thin plates by employing the C^(1) natural element method.Based on the Koiter’s theorem and von Mises yie...This paper proposes a numerical solution method for upper bound shakedown analysis of perfectly elasto-plastic thin plates by employing the C^(1) natural element method.Based on the Koiter’s theorem and von Mises yield criterion,the nonlinear mathematical programming formulation for upper bound shakedown analysis of thin plates is established.In this formulation,the trail function of residual displacement increment is approximated by using the C^(1) shape functions,the plastic incompressibility condition is satisfied by introducing a constant matrix in the objective function,and the time integration is resolved by using the Konig’s technique.Meanwhile,the objective function is linearized by distinguishing the non-plastic integral points from the plastic integral points and revising the objective function and associated equality constraints at each iteration.Finally,the upper bound shakedown load multipliers of thin plates are obtained by direct iterative and monotone convergence processes.Several benchmark examples verify the good precision and fast convergence of this proposed method.展开更多
The order of the projection in the algebraic reconstruction technique(ART)method has great influence on the rate of the convergence.Although many scholars have studied the order of the projection,few theoretical proof...The order of the projection in the algebraic reconstruction technique(ART)method has great influence on the rate of the convergence.Although many scholars have studied the order of the projection,few theoretical proofs are given.Thomas Strohmer and Roman Vershynin introduced a randomized version of the Kaczmarz method for consistent,and over-determined linear systems and proved whose rate does not depend on the number of equations in the systems in 2009.In this paper,we apply this method to computed tomography(CT)image reconstruction and compared images generated by the sequential Kaczmarz method and the randomized Kaczmarz method.Experiments demonstrates the feasibility of the randomized Kaczmarz algorithm in CT image reconstruction and its exponential curve convergence.展开更多
This paper proposes a novel iterative algorithm for optimal design of non-frequency-selective Finite Impulse Response(FIR) digital filters based on the windowing method.Different from the traditional optimization conc...This paper proposes a novel iterative algorithm for optimal design of non-frequency-selective Finite Impulse Response(FIR) digital filters based on the windowing method.Different from the traditional optimization concept of adjusting the window or the filter order in the windowing design of an FIR digital filter,the key idea of the algorithm is minimizing the approximation error by succes-sively modifying the design result through an iterative procedure under the condition of a fixed window length.In the iterative procedure,the known deviation of the designed frequency response in each iteration from the ideal frequency response is used as a reference for the next iteration.Because the approximation error can be specified variably,the algorithm is applicable for the design of FIR digital filters with different technical requirements in the frequency domain.A design example is employed to illustrate the efficiency of the algorithm.展开更多
The initial alignment error equation of an INS (Inertial Navigation System) with large initial azimuth error has been derived and nonlinear characteristics are included. When azimuth error is fairly small, the nonline...The initial alignment error equation of an INS (Inertial Navigation System) with large initial azimuth error has been derived and nonlinear characteristics are included. When azimuth error is fairly small, the nonlinear equation can be reduced to a linear one. Extended Kalman filter, iterated filter and second order filter formulas are derived for the nonlinear state equation with linear measurement equation. Simulations results show that the accuracy of azimuth error estimation using extended Kalman filter is better than that of using standard Kalman filter while the iterated filter and second order filter can give even better estimation accuracy.展开更多
In this paper, we propose a new single-step iterative method for solving non-linear equations in a variable. This iterative method is derived by using the approximation formula of truncated Thiele's continued frac...In this paper, we propose a new single-step iterative method for solving non-linear equations in a variable. This iterative method is derived by using the approximation formula of truncated Thiele's continued fraction. Analysis of convergence shows that the order of convergence of the introduced iterative method for a simple root is four. To illustrate the efficiency and performance of the proposed method we give some numerical examples.展开更多
Iterative methods that take advantage of efficient block operations and block communications are popular research topics in parallel computation. These methods are especially important on Massively Parallel Processors...Iterative methods that take advantage of efficient block operations and block communications are popular research topics in parallel computation. These methods are especially important on Massively Parallel Processors (MPP). This paper presents a block variant of the GMRES method for solving general unsymmetric linear systems. It is shown that the new algorithm with block size s, denoted by BVGMRES(s,m), is theoretically equivalent to the GMRES(s. m) method. The numerical results show that this algorithm can be more efficient than the standard GMRES method on a cache based single CPU computer with optimized BLAS kernels. Furthermore, the gain in efficiency is more significant on MPPs due to both efficient block operations and efficient block data communications. Our numerical results also show that in comparison to the standard GMRES method, the more PEs that are used on an MPP, the more efficient the BVGMRES(s,m) algorithm is.展开更多
文摘In this work, approximate analytical solutions to the lid-driven square cavity flow problem, which satisfied two-dimensional unsteady incompressible Navier-Stokes equations, are presented using the kinetically reduced local Navier-Stokes equations. Reduced differential transform method and perturbation-iteration algorithm are applied to solve this problem. The convergence analysis was discussed for both methods. The numerical results of both methods are given at some Reynolds numbers and low Mach numbers, and compared with results of earlier studies in the review of the literatures. These two methods are easy and fast to implement, and the results are close to each other and other numerical results, so it can be said that these methods are useful in finding approximate analytical solutions to the unsteady incompressible flow problems at low Mach numbers.
文摘A new iterating method based on homotopy function is developed in this paper. All solutions can be found easily without the need of choosing proper initial values. Compared to the homotopy continuation method, the solution process of the present method is simplified, and the computation efficiency as well as the reliability for obtaining all solutions is also improved. By application of the method to the mechanisms problems, the results are satisfactory.
基金Project supported by the National Natural Science Foundation of China(No.61603322)the Research Foundation of Education Bureau of Hunan Province of China(No.16C1542)
文摘Motivated by the study of regularization for sparse problems,we propose a new regularization method for sparse vector recovery.We derive sufficient conditions on the well-posedness of the new regularization,and design an iterative algorithm,namely the iteratively reweighted algorithm(IR-algorithm),for efficiently computing the sparse solutions to the proposed regularization model.The convergence of the IR-algorithm and the setting of the regularization parameters are analyzed at length.Finally,we present numerical examples to illustrate the features of the new regularization and algorithm.
文摘The parallel algorithms of iterated defect correction methods (PIDeCM’s) are constructed, which are of efficiency and high order B-convergence for general nonlinear stiff systems in ODE’S. As the basis of constructing and discussing PIDeCM’s. a class of parallel one-leg methods is also investigated, which are of particular efficiency for linear systems.
基金This work has been carried out as of a research project which has been supported by the National Structural Strength & Vibration Laboratory of Xi'an Jiaotong University with National Fund
文摘In this paper, a parallel algorithm with iterative form for solving finite element equation is presented. Based on the iterative solution of linear algebra equations, the parallel computational steps are introduced in this method. Also by using the weighted residual method and choosing the appropriate weighting functions, the finite element basic form of parallel algorithm is deduced. The program of this algorithm has been realized on the ELXSI-6400 parallel computer of Xi'an Jiaotong University. The computational results show the operational speed will be raised and the CPU time will be cut down effectively. So this method is one kind of effective parallel algorithm for solving the finite element equations of large-scale structures.
基金support from the National Science Foundation of China(52304137,5192780752274124,52325403)Tiandi Science and Technology Co.,Ltd.(2022-2-TDMS012 and SKLIS202417)Sichuan University(SKHL2215).
文摘The Grey Wolf Optimization(GWO)algorithm is acknowledged as an effective method for rock acoustic emission localization.However,the conventional GWO algorithm encounters challenges related to solution accuracy and convergence speed.To address these concerns,this paper develops a Simplex Improved Grey Wolf Optimizer(SMIGWO)algorithm.The randomly generating initial populations are replaced with the iterative chaotic sequences.The search process is optimized using the convergence factor optimization algorithm based on the inverse incompleteГfunction.The simplex method is utilized to address issues related to poorly positioned grey wolves.Experimental results demonstrate that,compared to the conventional GWO algorithm-based AE localization algorithm,the proposed algorithm achieves a higher solution accuracy and showcases a shorter search time.Additionally,the algorithm demonstrates fewer convergence steps,indicating superior convergence efficiency.These findings highlight that the proposed SMIGWO algorithm offers enhanced solution accuracy,stability,and optimization performance.The benefits of the SMIGWO algorithm extend universally across various materials,such as aluminum,granite,and sandstone,showcasing consistent effectiveness irrespective of material type.Consequently,this algorithm emerges as a highly effective tool for identifying acoustic emission signals and improving the precision of rock acoustic emission localization.
文摘Two methods based on a slight modification of the regular traffic assignmentalgorithms are proposed to directly compute turn flows instead of estimating them from link flows orobtaining them by expanding the networks. The first one is designed on the path-turn incidencerelationship, and it is similar to the computational procedure of link flows. It applies to thetraffic assignment algorithms that can provide detailed path structures. The second utilizes thelink-turn incidence relationship and the conservation of flow on links, a law deriving from thisrelationship. It is actually an improved version of Dial's logit assignment algorithm. The proposedapproaches can avoid the shortcomings both of the estimation methods, e. g. Furness's model andFrator's model, and of the network-expanding method in precision, stability and computation scale.Finally, they are validated by numerical examples.
基金supported by the China State Key Science and Technology Project on Marine Carbonate Reservoir Characterization (No. 2011ZX05004-003)the Basic Research Programs of CNPC during the 12th Five-Year Plan Period (NO.2011A-3603)+1 种基金the Natural Science Foundation of China (No.41104066)the RIPED Young Professional Innovation Fund (NO.2010-13-16-02, 2010-A-26-02)
文摘Although full waveform inversion in the frequency domain can overcome the local minima problem in the time direction, such problem still exists in the space direction because of the media subsurface complexity. Based on the optimal steep descent methods, we present an algorithm which combines the preconditioned bi-conjugated gradient stable method and the multi-grid method to compute the wave propagation and the gradient space. The multiple scale prosperity of the waveform inversion and the multi-grid method can overcome the inverse problems local minima defect and accelerate convergence. The local inhomogeneous three-hole model simulated results and the Marmousi model certify the algorithm effectiveness.
基金supported by the National Outstanding Young Scientists Fund of China (No. 10725209)the National ScienceFoundation of China (No. 10672092)+1 种基金Shanghai Municipal Education Commission Scientific Research Project (No. 07ZZ07)Shanghai Leading Academic Discipline Project (No. Y0103).
文摘A numerical method is proposed to simulate the transverse vibrations of a viscoelastic moving string constituted by an integral law. In the numerical computation, the Galerkin method based on the Hermite functions is applied to discretize the state variables, and the Runge- Kutta method is applied to solve the resulting differential-integral equation system. A linear iterative process is designed to compute the integral terms at each time step, which makes the numerical method more efficient and accurate. As examples, nonlinear parametric vibrations of an axially moving viscoelastic string are analyzed.
文摘In the optimal control problem of nonlinear dynamical system,the Hamiltonian formulation is useful and powerful to solve an optimal control force.However,the resulting Euler-Lagrange equations are not easy to solve,when the performance index is complicated,because one may encounter a two-point boundary value problem of nonlinear differential algebraic equations.To be a numerical method,it is hard to exactly preserve all the specified conditions,which might deteriorate the accuracy of numerical solution.With this in mind,we develop a novel algorithm to find the solution of the optimal control problem of nonlinear Duffing oscillator,which can exactly satisfy all the required conditions for the minimality of the performance index.A new idea of shape functions method(SFM)is introduced,from which we can transform the optimal control problems to the initial value problems for the new variables,whose initial values are given arbitrarily,and meanwhile the terminal values are determined iteratively.Numerical examples confirm the high-performance of the iterative algorithms based on the SFM,which are convergence fast,and also provide very accurate solutions.The new algorithm is robust,even large noise is imposed on the input data.
基金Project supported by the National Natural Science Foundation of China(Nos.11971410 and12071404)the Natural Science Foundation of Hunan Province of China(No.2019JJ40279)+2 种基金the Excellent Youth Program of Scientific Research Project of Hunan Provincial Department of Education(Nos.18B064 and 20B564)the China Postdoctoral Science Foundation(Nos.2018T110073 and 2018M631402)the International Scientific and Technological Innovation Cooperation Base of Hunan Province for Computational Science(No.2018WK4006)。
文摘Based on local algorithms,some parallel finite element(FE)iterative methods for stationary incompressible magnetohydrodynamics(MHD)are presented.These approaches are on account of two-grid skill include two major phases:find the FE solution by solving the nonlinear system on a globally coarse mesh to seize the low frequency component of the solution,and then locally solve linearized residual subproblems by one of three iterations(Stokes-type,Newton,and Oseen-type)on subdomains with fine grid in parallel to approximate the high frequency component.Optimal error estimates with regard to two mesh sizes and iterative steps of the proposed algorithms are given.Some numerical examples are implemented to verify the algorithm.
基金supported by the Chinese Postdoctoral Science Foundation(2013M540934)supported by the National Key Research and Development Program of China(2016YFC0801905,2017YFF0210704).
文摘This paper proposes a numerical solution method for upper bound shakedown analysis of perfectly elasto-plastic thin plates by employing the C^(1) natural element method.Based on the Koiter’s theorem and von Mises yield criterion,the nonlinear mathematical programming formulation for upper bound shakedown analysis of thin plates is established.In this formulation,the trail function of residual displacement increment is approximated by using the C^(1) shape functions,the plastic incompressibility condition is satisfied by introducing a constant matrix in the objective function,and the time integration is resolved by using the Konig’s technique.Meanwhile,the objective function is linearized by distinguishing the non-plastic integral points from the plastic integral points and revising the objective function and associated equality constraints at each iteration.Finally,the upper bound shakedown load multipliers of thin plates are obtained by direct iterative and monotone convergence processes.Several benchmark examples verify the good precision and fast convergence of this proposed method.
基金National Natural Science Foundation of China(No.61171179,No.61171178)Natural Science Foundation of Shanxi Province(No.2010011002-1,No.2010011002-2and No.2012021011-2)
文摘The order of the projection in the algebraic reconstruction technique(ART)method has great influence on the rate of the convergence.Although many scholars have studied the order of the projection,few theoretical proofs are given.Thomas Strohmer and Roman Vershynin introduced a randomized version of the Kaczmarz method for consistent,and over-determined linear systems and proved whose rate does not depend on the number of equations in the systems in 2009.In this paper,we apply this method to computed tomography(CT)image reconstruction and compared images generated by the sequential Kaczmarz method and the randomized Kaczmarz method.Experiments demonstrates the feasibility of the randomized Kaczmarz algorithm in CT image reconstruction and its exponential curve convergence.
基金the National Grand Fundamental Research 973 Program of China (No.2004CB318109)the National High-Technology Research and Development Plan of China (No.2006AA01Z452)
文摘This paper proposes a novel iterative algorithm for optimal design of non-frequency-selective Finite Impulse Response(FIR) digital filters based on the windowing method.Different from the traditional optimization concept of adjusting the window or the filter order in the windowing design of an FIR digital filter,the key idea of the algorithm is minimizing the approximation error by succes-sively modifying the design result through an iterative procedure under the condition of a fixed window length.In the iterative procedure,the known deviation of the designed frequency response in each iteration from the ideal frequency response is used as a reference for the next iteration.Because the approximation error can be specified variably,the algorithm is applicable for the design of FIR digital filters with different technical requirements in the frequency domain.A design example is employed to illustrate the efficiency of the algorithm.
文摘The initial alignment error equation of an INS (Inertial Navigation System) with large initial azimuth error has been derived and nonlinear characteristics are included. When azimuth error is fairly small, the nonlinear equation can be reduced to a linear one. Extended Kalman filter, iterated filter and second order filter formulas are derived for the nonlinear state equation with linear measurement equation. Simulations results show that the accuracy of azimuth error estimation using extended Kalman filter is better than that of using standard Kalman filter while the iterated filter and second order filter can give even better estimation accuracy.
基金Supported by the National Natural Science Foundation of China(Grant No.11571071)the Natural Science Key Foundation of Education Department of Anhui Province(Grant No.KJ2013A183)+1 种基金the Project of Leading Talent Introduction and Cultivation in Colleges and Universities of Education Department of Anhui Province(Grant No.gxfxZD2016270)the Incubation Project of the National Scientific Research Foundation of Bengbu University(Grant No.2018GJPY04)
文摘In this paper, we propose a new single-step iterative method for solving non-linear equations in a variable. This iterative method is derived by using the approximation formula of truncated Thiele's continued fraction. Analysis of convergence shows that the order of convergence of the introduced iterative method for a simple root is four. To illustrate the efficiency and performance of the proposed method we give some numerical examples.
文摘Iterative methods that take advantage of efficient block operations and block communications are popular research topics in parallel computation. These methods are especially important on Massively Parallel Processors (MPP). This paper presents a block variant of the GMRES method for solving general unsymmetric linear systems. It is shown that the new algorithm with block size s, denoted by BVGMRES(s,m), is theoretically equivalent to the GMRES(s. m) method. The numerical results show that this algorithm can be more efficient than the standard GMRES method on a cache based single CPU computer with optimized BLAS kernels. Furthermore, the gain in efficiency is more significant on MPPs due to both efficient block operations and efficient block data communications. Our numerical results also show that in comparison to the standard GMRES method, the more PEs that are used on an MPP, the more efficient the BVGMRES(s,m) algorithm is.
