E, Weinan; Engquist, Björn The heterogeneous multi-scale method for homogenization problems. (English) Zbl 1086.65521 Engquist, Björn (ed.) et al., Multiscale methods in science and engineering. Papers presented at the conference, Uppsala, Sweden, January 26–28, 2004. Berlin: Springer (ISBN 3-540-25335-1/pbk). Lecture Notes in Computational Science and Engineering 44, 89-110 (2005). Summary: The heterogeneous multi-scale method, a general framework for efficient numerical modeling of problems with multi-scales, is applied to a large variety of homogenization problems. These problems can be either linear or nonlinear, periodic or nonperiodic, stationary or dynamic. Stability and accuracy issues are analyzed along the lines of the general principles outlined by the authors [Commun. Math. Sci. 1, No. 1, 87–132 (2003; Zbl 1093.35012)]. Strategies for obtaining the microstructural information are discussed.For the entire collection see [Zbl 1070.65500]. Cited in 25 Documents MSC: 65K10 Numerical optimization and variational techniques 49J20 Existence theories for optimal control problems involving partial differential equations 35B27 Homogenization in context of PDEs; PDEs in media with periodic structure Keywords:multiscale problems; homogenization; heterogeneous multiscale method Citations:Zbl 1093.35012 PDFBibTeX XMLCite \textit{W. E} and \textit{B. Engquist}, Lect. Notes Comput. Sci. Eng. 44, 89--110 (2005; Zbl 1086.65521) Full Text: DOI