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Multiscale Methods (multiscale + methods)

Distribution by Scientific Domains
Mathematics and Statistics66%
Engineering33%

Selected Abstracts

Multiscale Methods in Computational Mechanics

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 8-9 2010
Ted Belytschko
No abstract is available for this article. [source]

Multiscale methods for elliptic homogenization problems,

NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS, Issue 2 2006
Zhangxin ChenArticle first published online: 10 JUN 200
Abstract In this article we study two families of multiscale methods for numerically solving elliptic homogenization problems. The recently developed multiscale finite element method [Hou and Wu, J Comp Phys 134 (1997), 169,189] captures the effect of microscales on macroscales through modification of finite element basis functions. Here we reformulate this method that captures the same effect through modification of bilinear forms in the finite element formulation. This new formulation is a general approach that can handle a large variety of differential problems and numerical methods. It can be easily extended to nonlinear problems and mixed finite element methods, for example. The latter extension is carried out in this article. The recently introduced heterogeneous multiscale method [Engquist and Engquist, Comm Math Sci 1 (2003), 87,132] is designed for efficient numerical solution of problems with multiscales and multiphysics. In the second part of this article, we study this method in mixed form (we call it the mixed heterogeneous multiscale method). We present a detailed analysis for stability and convergence of this new method. Estimates are obtained for the error between the homogenized and numerical multiscale solutions. Strategies for retrieving the microstructural information from the numerical solution are provided and analyzed. Relationship between the multiscale finite element and heterogeneous multiscale methods is discussed. © 2005 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2006 [source]

Simulations of the turbulent channel flow at Re, = 180 with projection-based finite element variational multiscale methods

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 5 2007
Volker John
Abstract Projection-based variational multiscale (VMS) methods, within the framework of an inf,sup stable second order finite element method for the Navier,Stokes equations, are studied in simulations of the turbulent channel flow problem at Re, = 180. For comparison, the Smagorinsky large eddy simulation (LES) model with van Driest damping is included into the study. The simulations are performed on very coarse grids. The VMS methods give often considerably better results. For second order statistics, however, the differences to the reference values are sometimes rather large. The dependency of the results on parameters in the eddy viscosity model is much weaker for the VMS methods than for the Smagorinsky LES model with van Driest damping. It is shown that one uniform refinement of the coarse grids allows an underresolved direct numerical simulations (DNS). Copyright © 2007 John Wiley & Sons, Ltd. [source]

Multiscale methods for elliptic homogenization problems,

NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS, Issue 2 2006
Zhangxin ChenArticle first published online: 10 JUN 200
Abstract In this article we study two families of multiscale methods for numerically solving elliptic homogenization problems. The recently developed multiscale finite element method [Hou and Wu, J Comp Phys 134 (1997), 169,189] captures the effect of microscales on macroscales through modification of finite element basis functions. Here we reformulate this method that captures the same effect through modification of bilinear forms in the finite element formulation. This new formulation is a general approach that can handle a large variety of differential problems and numerical methods. It can be easily extended to nonlinear problems and mixed finite element methods, for example. The latter extension is carried out in this article. The recently introduced heterogeneous multiscale method [Engquist and Engquist, Comm Math Sci 1 (2003), 87,132] is designed for efficient numerical solution of problems with multiscales and multiphysics. In the second part of this article, we study this method in mixed form (we call it the mixed heterogeneous multiscale method). We present a detailed analysis for stability and convergence of this new method. Estimates are obtained for the error between the homogenized and numerical multiscale solutions. Strategies for retrieving the microstructural information from the numerical solution are provided and analyzed. Relationship between the multiscale finite element and heterogeneous multiscale methods is discussed. © 2005 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2006 [source]

Analysis of multiscale methods for stochastic differential equations

COMMUNICATIONS ON PURE & APPLIED MATHEMATICS, Issue 11 2005
E Weinan
We analyze a class of numerical schemes proposed [26] for stochastic differential equations with multiple time scales. Both advective and diffusive time scales are considered. Weak as well as strong convergence theorems are proven. Most of our results are optimal. They in turn allow us to provide a thorough discussion on the efficiency as well as optimal strategy for the method. © 2005 Wiley Periodicals, Inc. [source]