Mini-workshop: Numerical upscaling: theory and applications (Q2577099)

Summary: Numerical upscaling is often the only way in which various multiscale problems can be handled. Numerics related to solving auxiliary problems appearing in asymptotic homogenization, as well as numerical treatment of multiscale problems with non-separable scales, are discussed here. Among the main topics discussed, are classification of multiscale problems and multiscale numerical algorithms; deriving coarse scale approximations via approximate truncations or based on variational principles; iterations over scales; accuracy and robustness of numerical upscaling algorithms; similarity and differences between different approaches (multigrid, multiscale FEM, heterogeneous multiscale method, etc.); convergence issues; area of applicability of the numerical upscaling, etc. Contributions: --Marcel Arndt (joint with Michael Griebel), Higher Order Gradient Continuum Description of Atomistic Models for Crystalline Solids p.1133 --Sabine Attinger, Coarse Grained Mixing Parameters for Solute Transport p.1136 --Yaslchin Efendiev, Multiscale finite element methods for nonlinear problems p.1138 --Richard Ewing, Upscaled models for porous media flows p.1141 --Chris Farmer, Upscaling: A review of some numerical methods p.1143 --Rainer Helmig, Upscaling of two-phase flow processes in highly heterogeneous porous media including interfaces on different scales p.1145 --Vsevolod Laptev (joint with S. Belouettar), On averaging of the non-periodic conductivity coefficient using two-scale extension p.1149 --Vsevolod Laptev (joint with S. Belouettar), On averaging of the non-periodic conductivity coefficient using two-scale extension p.1151 --Nicolas Neuss, Multiscale preconditioning p.1152 --Petr Plecháč (joint with Markos A. Katsoulakis, Alexandros Sopasakis), Numerical analysis of coarse-grained stochastic lattice dynamics p.1156 --Peter Popov (joint with Oleg Iliev and Andro Mikelic), Toward upscaling of flow in deformable porous media p.1160 --Irina Rybak (joint with Oleg Iliev), On numerical upscaling of flow in anisotropic porous media p.1162 --Rosangela F. Sviercoski (joint with A. W. Warrick, C. L. Winter), Multiscale analytical solutions and homogenization of \(n\)-dimensional generalized elliptic equations p.1165 --Ulrich Trottenberg, From fine to coarse and/or from coarse to fine- an attempt to clarify multiscale terminology p.1168 --Roman Wienands, Selecting coarse grid operators within a multigrid algorithm by local Fourier analysis p.1171