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
A fast compound direct iterative algorithm for solving transient line contact elastohydrodynamic lubrication （EHL） problems is presented. First, by introducing a special matrix splitting iteration method into the tr...A fast compound direct iterative algorithm for solving transient line contact elastohydrodynamic lubrication （EHL） problems is presented. First, by introducing a special matrix splitting iteration method into the traditional compound direct iterative method, the full matrices for the linear systems of equations are transformed into sparse banded ones with any half-bandwidth; then, an extended Thomas method which can solve banded linear systems with any half-bandwidth is derived to accelerate the computing speed. Through the above two steps, the computational complexity of each iteration is reduced approximately from O（N^3/3） to O（β^2N）, where N is the total number of nodes, and β is the half-bandwidth. Two kinds of numerical results of transient EHL line contact problems under sinusoidal excitation or pure normal approach process are obtained. The results demonstrate that the new algorithm increases computing speed several times more than the traditional compound direct iterative method with the same numerical precision. Also the results show that the new algorithm can get the best computing speed and robustness when the ratio, half-bandwidth to total number of nodes, is about 7.5% 10.0% in moderate load cases.展开更多
In this paper,the backward Euler method and the shifted Grünwald-Letnikov formulas are utilized to discretize the space-fractional diffusion equations.The discretized result is a system of linear equations with a...In this paper,the backward Euler method and the shifted Grünwald-Letnikov formulas are utilized to discretize the space-fractional diffusion equations.The discretized result is a system of linear equations with a coefficient matrix being the sum of a diagonal matrix and a non-Hermitian Toeplitz matrix.By utilizing the Hermitian and skew-Hermitian splitting of the Toeplitz matrix,we develop a two-parameter DThsS iteration method to solve the linear systems.The convergence is also discussed.A DTHsS-t(α,γ)preconditioner is proposed and the preconditioned GMRES method combined with the proposed preconditioner is applied to solve the linear systems.The spectral analysis of the DThsS-τ(α,γ)preconditioned matrix is provided.Experimental results demonstrate the effectiveness of the proposed methods in solving the space-fractional diffusion equations.展开更多
基金National Natural Science Foundation of China(12161027)Guangxi Natural Science Foundation,China(2020GXNSFAA159143)Science and Technology Project of Guangxi,China(AD23023002).
文摘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.
文摘A fast compound direct iterative algorithm for solving transient line contact elastohydrodynamic lubrication （EHL） problems is presented. First, by introducing a special matrix splitting iteration method into the traditional compound direct iterative method, the full matrices for the linear systems of equations are transformed into sparse banded ones with any half-bandwidth; then, an extended Thomas method which can solve banded linear systems with any half-bandwidth is derived to accelerate the computing speed. Through the above two steps, the computational complexity of each iteration is reduced approximately from O（N^3/3） to O（β^2N）, where N is the total number of nodes, and β is the half-bandwidth. Two kinds of numerical results of transient EHL line contact problems under sinusoidal excitation or pure normal approach process are obtained. The results demonstrate that the new algorithm increases computing speed several times more than the traditional compound direct iterative method with the same numerical precision. Also the results show that the new algorithm can get the best computing speed and robustness when the ratio, half-bandwidth to total number of nodes, is about 7.5% 10.0% in moderate load cases.
基金the National Natural Science Foundation of China(No.11971215)Science and Technology Project of Gansu Province of China(No.22JR5RA391)+1 种基金Center for Data Science of Lanzhou University,Chinathe Key Laboratory of Applied Mathematics and Complex Systems of Lanzhou University,China.
文摘In this paper,the backward Euler method and the shifted Grünwald-Letnikov formulas are utilized to discretize the space-fractional diffusion equations.The discretized result is a system of linear equations with a coefficient matrix being the sum of a diagonal matrix and a non-Hermitian Toeplitz matrix.By utilizing the Hermitian and skew-Hermitian splitting of the Toeplitz matrix,we develop a two-parameter DThsS iteration method to solve the linear systems.The convergence is also discussed.A DTHsS-t(α,γ)preconditioner is proposed and the preconditioned GMRES method combined with the proposed preconditioner is applied to solve the linear systems.The spectral analysis of the DThsS-τ(α,γ)preconditioned matrix is provided.Experimental results demonstrate the effectiveness of the proposed methods in solving the space-fractional diffusion equations.
