The Experts below are selected from a list of 19503 Experts worldwide ranked by ideXlab platform
I M Davis - One of the best experts on this subject based on the ideXlab platform.
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A Fourier–Karhunen–Loève Discretization Scheme for stationary random material properties in SFEM
International Journal for Numerical Methods in Engineering, 2008Co-Authors: Chenfeng Li, Y T Feng, D F Li, David Owen, I M DavisAbstract:In order to overcome the computational difficulties in Karhunen–Loeve (K–L) expansions of stationary random material properties in stochastic finite element method (SFEM) analysis, a Fourier–Karhunen–Loeve (F–K–L) Discretization Scheme is developed in this paper, by following the harmonic essence of stationary random material properties and solving a series of specific technical challenges encountered in its development. Three numerical examples are employed to investigate the overall performance of the new Discretization Scheme and to demonstrate its use in practical SFEM simulations. The proposed F–K–L Discretization Scheme exhibits a number of advantages over the widely used K–L expansion Scheme based on FE meshes, including better computational efficiency in terms of memory and CPU time, convenient a priori error-control mechanism, better approximation accuracy of random material properties, explicit methods for predicting the associated eigenvalue decay speed and geometrical compatibility for random medium bodies of different shapes. Copyright © 2007 John Wiley & Sons, Ltd.
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a fourier karhunen loeve Discretization Scheme for stationary random material properties in sfem
International Journal for Numerical Methods in Engineering, 2008Co-Authors: Chenfeng Li, Y T Feng, D R J Owen, D F Li, I M DavisAbstract:In order to overcome the computational difficulties in Karhunen–Loeve (K–L) expansions of stationary random material properties in stochastic finite element method (SFEM) analysis, a Fourier–Karhunen–Loeve (F–K–L) Discretization Scheme is developed in this paper, by following the harmonic essence of stationary random material properties and solving a series of specific technical challenges encountered in its development. Three numerical examples are employed to investigate the overall performance of the new Discretization Scheme and to demonstrate its use in practical SFEM simulations. The proposed F–K–L Discretization Scheme exhibits a number of advantages over the widely used K–L expansion Scheme based on FE meshes, including better computational efficiency in terms of memory and CPU time, convenient a priori error-control mechanism, better approximation accuracy of random material properties, explicit methods for predicting the associated eigenvalue decay speed and geometrical compatibility for random medium bodies of different shapes. Copyright © 2007 John Wiley & Sons, Ltd.
M. P. Rajan - One of the best experts on this subject based on the ideXlab platform.
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A posteriori parameter choice with an efficient Discretization Scheme for solving ill-posed problems
Applied Mathematics and Computation, 2008Co-Authors: M. P. RajanAbstract:Abstract Recently, Rajan [M.P. Rajan, An efficient Discretization Scheme for solving the ill-posed problems, Journal of Mathematical Analysis and Applications 313 (2) (2006) 654–677] considered a Discretization Scheme for solving ill-posed problems and obtained optimal error estimates under an a priori parameter choice strategy with a particular smoothness assumption on the solution. It is shown that the computational information for solving the system is far less than the traditional projection Schemes. Neubauer [A. Neubauer, An a posteriori parameter choice for Tikhonov regularization in the presence of modeling error, Applied Numerical Mathematics 4 (1988) 507–519] and Engl and Gfrerer [H.W. Engl, H. Gfrerer, A posteriori parameter choice for general regularization methods for solving ill-posed problems, Applied Numerical Mathematics 4 (1988) 395–417] suggested an a posteriori method for choosing the regularization parameter which does not require any knowledge about the exact solution, respectively under finite dimensional as well as general setting. In this paper, we consider an a posteriori parameter choice for finite dimensional approximation which does not require any information about the smoothness of the exact solution and apply to the Discretization Scheme considered by Rajan. The computational efficiency of the Scheme is illustrated through numerical examples.
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an efficient Discretization Scheme for solving ill posed problems
Journal of Mathematical Analysis and Applications, 2006Co-Authors: M. P. RajanAbstract:In this paper, we consider a finite-dimensional approximation Scheme combined with Tikhonov regularization for solving ill-posed problems. Error estimates are obtained by an a priori parameter choice strategy and the results show that the amount of discrete information required for solving the problem is far less than the traditional finite-dimensional approach.
Yidu Yang - One of the best experts on this subject based on the ideXlab platform.
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multiscale Discretization Scheme based on the rayleigh quotient iterative method for the steklov eigenvalue problem
Mathematical Problems in Engineering, 2012Co-Authors: Hai Bi, Yidu YangAbstract:This paper discusses efficient numerical methods for the Steklov eigenvalue problem and establishes a new multiscale Discretization Scheme and an adaptive algorithm based on the Rayleigh quotient iterative method. The efficiency of these Schemes is analyzed theoretically, and the constants appeared in the error estimates are also analyzed elaborately. Finally, numerical experiments are provided to support the theory.
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A Two-Scale Discretization Scheme for Mixed Variational Formulation of Eigenvalue Problems
Abstract and Applied Analysis, 2012Co-Authors: Yidu Yang, Yu Zhang, Wei Jiang, Wenjun Wang, Hai BiAbstract:This paper discusses highly efficient Discretization Schemes for mixed variational formulation of eigenvalue problems. A new finite element two-scale Discretization Scheme is proposed by combining the mixed finite element method with the shifted-inverse power method for solving matrix eigenvalue problems. With this Scheme, the solution of an eigenvalue problem on a fine grid is reduced to the solution of an eigenvalue problem on a much coarser grid and the solution of a linear algebraic system on the fine grid . Theoretical analysis shows that the Scheme has high efficiency. For instance, when using the Mini element to solve Stokes eigenvalue problem, the resulting solution can maintain an asymptotically optimal accuracy by taking , and when using the - element to solve eigenvalue problems of electric field, the calculation results can maintain an asymptotically optimal accuracy by taking . Finally, numerical experiments are presented to support the theoretical analysis.
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a two grid Discretization Scheme for the steklov eigenvalue problem
Journal of Applied Mathematics and Computing, 2011Co-Authors: Qin Li, Yidu YangAbstract:In the paper, a two-grid Discretization Scheme is discussed for the Steklov eigenvalue problem. With the Scheme, the solution of the Steklov eigenvalue problem on a fine grid is reduced to the solution of the Steklov eigenvalue problem on a much coarser grid and the solution of a linear algebraic system on the fine grid. Using spectral approximation theory, it is shown theoretically that the two-scale Scheme is efficient and the approximate solution obtained by the Scheme maintains the asymptotically optimal accuracy. Finally, numerical experiments are carried out to confirm the considered theory.
Chenfeng Li - One of the best experts on this subject based on the ideXlab platform.
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A Fourier–Karhunen–Loève Discretization Scheme for stationary random material properties in SFEM
International Journal for Numerical Methods in Engineering, 2008Co-Authors: Chenfeng Li, Y T Feng, D F Li, David Owen, I M DavisAbstract:In order to overcome the computational difficulties in Karhunen–Loeve (K–L) expansions of stationary random material properties in stochastic finite element method (SFEM) analysis, a Fourier–Karhunen–Loeve (F–K–L) Discretization Scheme is developed in this paper, by following the harmonic essence of stationary random material properties and solving a series of specific technical challenges encountered in its development. Three numerical examples are employed to investigate the overall performance of the new Discretization Scheme and to demonstrate its use in practical SFEM simulations. The proposed F–K–L Discretization Scheme exhibits a number of advantages over the widely used K–L expansion Scheme based on FE meshes, including better computational efficiency in terms of memory and CPU time, convenient a priori error-control mechanism, better approximation accuracy of random material properties, explicit methods for predicting the associated eigenvalue decay speed and geometrical compatibility for random medium bodies of different shapes. Copyright © 2007 John Wiley & Sons, Ltd.
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a fourier karhunen loeve Discretization Scheme for stationary random material properties in sfem
International Journal for Numerical Methods in Engineering, 2008Co-Authors: Chenfeng Li, Y T Feng, D R J Owen, D F Li, I M DavisAbstract:In order to overcome the computational difficulties in Karhunen–Loeve (K–L) expansions of stationary random material properties in stochastic finite element method (SFEM) analysis, a Fourier–Karhunen–Loeve (F–K–L) Discretization Scheme is developed in this paper, by following the harmonic essence of stationary random material properties and solving a series of specific technical challenges encountered in its development. Three numerical examples are employed to investigate the overall performance of the new Discretization Scheme and to demonstrate its use in practical SFEM simulations. The proposed F–K–L Discretization Scheme exhibits a number of advantages over the widely used K–L expansion Scheme based on FE meshes, including better computational efficiency in terms of memory and CPU time, convenient a priori error-control mechanism, better approximation accuracy of random material properties, explicit methods for predicting the associated eigenvalue decay speed and geometrical compatibility for random medium bodies of different shapes. Copyright © 2007 John Wiley & Sons, Ltd.
D F Li - One of the best experts on this subject based on the ideXlab platform.
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A Fourier–Karhunen–Loève Discretization Scheme for stationary random material properties in SFEM
International Journal for Numerical Methods in Engineering, 2008Co-Authors: Chenfeng Li, Y T Feng, D F Li, David Owen, I M DavisAbstract:In order to overcome the computational difficulties in Karhunen–Loeve (K–L) expansions of stationary random material properties in stochastic finite element method (SFEM) analysis, a Fourier–Karhunen–Loeve (F–K–L) Discretization Scheme is developed in this paper, by following the harmonic essence of stationary random material properties and solving a series of specific technical challenges encountered in its development. Three numerical examples are employed to investigate the overall performance of the new Discretization Scheme and to demonstrate its use in practical SFEM simulations. The proposed F–K–L Discretization Scheme exhibits a number of advantages over the widely used K–L expansion Scheme based on FE meshes, including better computational efficiency in terms of memory and CPU time, convenient a priori error-control mechanism, better approximation accuracy of random material properties, explicit methods for predicting the associated eigenvalue decay speed and geometrical compatibility for random medium bodies of different shapes. Copyright © 2007 John Wiley & Sons, Ltd.
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a fourier karhunen loeve Discretization Scheme for stationary random material properties in sfem
International Journal for Numerical Methods in Engineering, 2008Co-Authors: Chenfeng Li, Y T Feng, D R J Owen, D F Li, I M DavisAbstract:In order to overcome the computational difficulties in Karhunen–Loeve (K–L) expansions of stationary random material properties in stochastic finite element method (SFEM) analysis, a Fourier–Karhunen–Loeve (F–K–L) Discretization Scheme is developed in this paper, by following the harmonic essence of stationary random material properties and solving a series of specific technical challenges encountered in its development. Three numerical examples are employed to investigate the overall performance of the new Discretization Scheme and to demonstrate its use in practical SFEM simulations. The proposed F–K–L Discretization Scheme exhibits a number of advantages over the widely used K–L expansion Scheme based on FE meshes, including better computational efficiency in terms of memory and CPU time, convenient a priori error-control mechanism, better approximation accuracy of random material properties, explicit methods for predicting the associated eigenvalue decay speed and geometrical compatibility for random medium bodies of different shapes. Copyright © 2007 John Wiley & Sons, Ltd.