The Experts below are selected from a list of 318 Experts worldwide ranked by ideXlab platform
Bodo Ahrens - One of the best experts on this subject based on the ideXlab platform.
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analysis of the indian summer monsoon system in the regional climate model cosmo clm
Journal of Geophysical Research, 2010Co-Authors: Andreas Dobler, Bodo AhrensAbstract:[1] The Indian summer monsoon (ISM) influences daily lives and economies in many countries in the South Asian region. This study analyzes the representation of the ISM system in the regional climate model COSMO-CLM. Simulations driven by ERA-40 reanalysis and present-day (1960–2000) data from the global climate model ECHAM5 are investigated. The ability of COSMO-CLM to reproduce the ISM better than the Coarser-Grid driving models is tested using a set of well-established, complementary monsoon indices: the all-India monsoon rainfall, vertical wind shear indices, and an outgoing longwave radiation (OLR) index. The results show that regarding these large-scale indices the COSMO-CLM simulations are not more accurate than the driving models. Considering the spatial distribution of rainfall, the ERA-40–driven COSMO-CLM simulations show major overestimations (about 100%) for the west coast of India and underestimations (about 50%) for the Himalayan foothills. Large biases occur in the OLR data over the Arabian Sea and the Bay of Bengal where COSMO-CLM shows high convective activity (OLR < 180 W m−2) at about 3 times as many days as observed in the monsoon season. In the ECHAM5-driven simulation, underestimations of rainfall also appear at the Himalayan foothills. Nevertheless, the application of COSMO-CLM to ECHAM5 improves the temporal correlations of the modeled ISM indices, and the spatial patterns are better simulated in COSMO-CLM with 0.44° horizontal Grid spacing than in the large-scale ECHAM5 data.
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Analysis of the Indian summer monsoon system in the regional climate model COSMO‐CLM
Journal of Geophysical Research, 2010Co-Authors: Andreas Dobler, Bodo AhrensAbstract:[1] The Indian summer monsoon (ISM) influences daily lives and economies in many countries in the South Asian region. This study analyzes the representation of the ISM system in the regional climate model COSMO-CLM. Simulations driven by ERA-40 reanalysis and present-day (1960–2000) data from the global climate model ECHAM5 are investigated. The ability of COSMO-CLM to reproduce the ISM better than the Coarser-Grid driving models is tested using a set of well-established, complementary monsoon indices: the all-India monsoon rainfall, vertical wind shear indices, and an outgoing longwave radiation (OLR) index. The results show that regarding these large-scale indices the COSMO-CLM simulations are not more accurate than the driving models. Considering the spatial distribution of rainfall, the ERA-40–driven COSMO-CLM simulations show major overestimations (about 100%) for the west coast of India and underestimations (about 50%) for the Himalayan foothills. Large biases occur in the OLR data over the Arabian Sea and the Bay of Bengal where COSMO-CLM shows high convective activity (OLR < 180 W m−2) at about 3 times as many days as observed in the monsoon season. In the ECHAM5-driven simulation, underestimations of rainfall also appear at the Himalayan foothills. Nevertheless, the application of COSMO-CLM to ECHAM5 improves the temporal correlations of the modeled ISM indices, and the spatial patterns are better simulated in COSMO-CLM with 0.44° horizontal Grid spacing than in the large-scale ECHAM5 data.
Yidu Yang - One of the best experts on this subject based on the ideXlab platform.
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Local and Parallel Finite Element Discretizations for Eigenvalue Problems
SIAM Journal on Scientific Computing, 2013Co-Authors: Hai Bi, Yidu Yang, Hao LiAbstract:Based on the work of Xu and Zhou [Math. Comp., 69 (2000), pp. 881--909], this paper combines the local defect-correction technique and the shifted-inverse power method to establish new local and parallel finite element three-scale schemes for a class of eigenvalue problems. It is proved that with these schemes, the solution of an eigenvalue problem on a fine Grid $\pi_{h}$ is reduced to the solution of an eigenvalue problem on a much Coarser Grid $\pi_{H}$, the solution of a linear algebraic system on a globally mesoscopic Grid $\pi_{w}$, and the solutions of linear systems on several locally fine Grids in parallel. The principle to determine the diameters of three different scale Grids is given. Especially, this paper devises a new local and parallel finite element multiscale discretization scheme. Theoretical analysis and numerical experiments show that the computational approach proposed in this paper is simple and easy to carry out and can be used to solve singular eigenvalue problems efficiently.
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A Two-Scale Discretization Scheme for Mixed Variational Formulation of Eigenvalue Problems
Abstract and Applied Analysis, 2012Co-Authors: Yidu Yang, Wenjun Wang, Wei Jiang, 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.
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two Grid finite element discretization schemes based on shifted inverse power method for elliptic eigenvalue problems
SIAM Journal on Numerical Analysis, 2011Co-Authors: Yidu Yang, Hai BiAbstract:This paper discusses highly efficient discretization schemes for solving self-adjoint elliptic differential operator eigenvalue problems. Several new two-Grid discretization schemes, including the conforming and nonconforming finite element schemes, are proposed by combining the finite element method with the shifted-inverse power method for matrix eigenvalue problems. With these schemes, the solution of an eigenvalue problem on a fine Grid $\pi_{h}$ is reduced to the solution of an eigenvalue problem on a much Coarser Grid $\pi_{H}$ and the solution of a linear algebraic system on the fine Grid $\pi_{h}$. Theoretical analysis shows that the schemes have a high efficiency. For instance, the resulting solution can maintain an asymptotically optimal accuracy by using the conforming linear element or the nonconforming Crouzeix-Raviart element by taking $H=O(\sqrt[4]{h})$. Numerical experiments are presented to support the theoretical analysis. In addition, this paper establishes multiGrid discretization schemes and proves their efficiency.
Huayun Shen - One of the best experts on this subject based on the ideXlab platform.
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superconvergence two Grid scheme based on shifted inverse power method for eigenvalue problems by function value recovery
Computer Methods in Applied Mechanics and Engineering, 2017Co-Authors: Shuanghu Wang, Huayun ShenAbstract:Abstract In the paper, an improved two-Grid scheme based on shifted-inverse power method is proposed to solve the elliptic eigenvalue problems. With this new scheme, the solution of the elliptic eigenvalue problem on a fine Grid T h is reduced to the solution of the elliptic eigenvalue problem and the recovered eigenfunction on a much Coarser Grid T H , and the solution of an elliptic boundary value problem and the recovered solution on the fine Grid T h . Theoretical analysis shows that the scheme allows a much Coarser mesh to achieve the superconvergence rate. Finally, some numerical experiments are carried out to confirm the theoretical analysis.
Hai Bi - One of the best experts on this subject based on the ideXlab platform.
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Local and Parallel Finite Element Discretizations for Eigenvalue Problems
SIAM Journal on Scientific Computing, 2013Co-Authors: Hai Bi, Yidu Yang, Hao LiAbstract:Based on the work of Xu and Zhou [Math. Comp., 69 (2000), pp. 881--909], this paper combines the local defect-correction technique and the shifted-inverse power method to establish new local and parallel finite element three-scale schemes for a class of eigenvalue problems. It is proved that with these schemes, the solution of an eigenvalue problem on a fine Grid $\pi_{h}$ is reduced to the solution of an eigenvalue problem on a much Coarser Grid $\pi_{H}$, the solution of a linear algebraic system on a globally mesoscopic Grid $\pi_{w}$, and the solutions of linear systems on several locally fine Grids in parallel. The principle to determine the diameters of three different scale Grids is given. Especially, this paper devises a new local and parallel finite element multiscale discretization scheme. Theoretical analysis and numerical experiments show that the computational approach proposed in this paper is simple and easy to carry out and can be used to solve singular eigenvalue problems efficiently.
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A Two-Scale Discretization Scheme for Mixed Variational Formulation of Eigenvalue Problems
Abstract and Applied Analysis, 2012Co-Authors: Yidu Yang, Wenjun Wang, Wei Jiang, 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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two Grid finite element discretization schemes based on shifted inverse power method for elliptic eigenvalue problems
SIAM Journal on Numerical Analysis, 2011Co-Authors: Yidu Yang, Hai BiAbstract:This paper discusses highly efficient discretization schemes for solving self-adjoint elliptic differential operator eigenvalue problems. Several new two-Grid discretization schemes, including the conforming and nonconforming finite element schemes, are proposed by combining the finite element method with the shifted-inverse power method for matrix eigenvalue problems. With these schemes, the solution of an eigenvalue problem on a fine Grid $\pi_{h}$ is reduced to the solution of an eigenvalue problem on a much Coarser Grid $\pi_{H}$ and the solution of a linear algebraic system on the fine Grid $\pi_{h}$. Theoretical analysis shows that the schemes have a high efficiency. For instance, the resulting solution can maintain an asymptotically optimal accuracy by using the conforming linear element or the nonconforming Crouzeix-Raviart element by taking $H=O(\sqrt[4]{h})$. Numerical experiments are presented to support the theoretical analysis. In addition, this paper establishes multiGrid discretization schemes and proves their efficiency.
A. Goulas - One of the best experts on this subject based on the ideXlab platform.
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Numerical experiments on the efficiency of local Grid refinement based on truncation error estimates
Journal of Computational Physics, 2012Co-Authors: Alexandros Syrakos, Georgios Efthimiou, John G. Bartzis, A. GoulasAbstract:Local Grid refinement aims to optimise the relationship between accuracy of the results and number of Grid nodes. In the context of the finite volume method no single local refinement criterion has been globally established as optimum for the selection of the control volumes to subdivide, since it is not easy to associate the discretisation error with an easily computable quantity in each control volume. Often the Grid refinement criterion is based on an estimate of the truncation error in each control volume, because the truncation error is a natural measure of the discrepancy between the algebraic finite-volume equations and the original differential equations. However, it is not a straightforward task to associate the truncation error with the optimum Grid density because of the complexity of the relationship between truncation and discretisation errors. In the present work several criteria based on a truncation error estimate are tested and compared on a regularised lid-driven cavity case at various Reynolds numbers. It is shown that criteria where the truncation error is weighted by the volume of the Grid cells perform better than using just the truncation error as the criterion. Also it is observed that the efficiency of local refinement increases with the Reynolds number. The truncation error is estimated by restricting the solution to a Coarser Grid and applying the coarse Grid discrete operator. The complication that high truncation error develops at Grid level interfaces is also investigated and several treatments are tested.
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estimate of the truncation error of finite volume discretization of the navier stokes equations on colocated Grids
International Journal for Numerical Methods in Fluids, 2006Co-Authors: Alexandros Syrakos, A. GoulasAbstract:A methodology is proposed for the calculation of the truncation error of finite volume discretizations of the incompressible Navier–Stokes equations on colocated Grids. The truncation error is estimated by restricting the solution obtained on a given Grid to a Coarser Grid and calculating the image of the discrete Navier–Stokes operator of the coarse Grid on the restricted velocity and pressure field. The proposed methodology is not a new concept but its application to colocated finite volume discretizations of the incompressible Navier–Stokes equations is made possible by the introduction of a variant of the momentum interpolation technique for mass fluxes where the pressure part of the mass fluxes is not dependent on the coefficients of the linearized momentum equations. The theory presented is supported by a number of numerical experiments. The methodology is developed for two-dimensional flows, but extension to three-dimensional cases should not pose problems. Copyright © 2005 John Wiley & Sons, Ltd.