Numerical Analysis of Multiscale Computations: Proceedings of a Winter Workshop at the Banff International Research Station 2009 (Lecture Notes in Computational Science and Engineering Book 82)

Annotation This book is a snapshot of current research in multiscale modeling, computations and applications. It covers fundamental mathematical theory, numerical algorithms as well as practical computational advice for analysing single and multiphysics models containing a variety of scales in time and space. Complex fluids, porous media flow and oscillatory dynamical systems are treated in some extra depth, as well as tools like analytical and numerical homogenization, and fast multipole method Front Matter....Pages i-x Explicit Methods for Stiff Stochastic Differential Equations....Pages 1-22 Oscillatory Systems with Three Separated Time Scales: Analysis and Computation....Pages 23-45 Variance Reduction in Stochastic Homogenization: The Technique of Antithetic Variables....Pages 47-70 A Stroboscopic Numerical Method for Highly Oscillatory Problems....Pages 71-85 The Microscopic Origin of the Macroscopic Dielectric Permittivity of Crystals: A Mathematical Viewpoint....Pages 87-125 Fast Multipole Method Using the Cauchy Integral Formula....Pages 127-144 Tools for Multiscale Simulation of Liquids Using Open Molecular Dynamics....Pages 145-166 Multiscale Methods for Wave Propagation in Heterogeneous Media Over Long Time....Pages 167-186 Numerical Homogenization via Approximation of the Solution Operator....Pages 187-216 Adaptive Multilevel Monte Carlo Simulation....Pages 217-234 Coupled Coarse Graining and Markov Chain Monte Carlo for Lattice Systems....Pages 235-257 Calibration of a Jump-Diffusion Process Using Optimal Control....Pages 259-277 Some Remarks on Free Energy and Coarse-Graining....Pages 279-329 Linear Stationary Iterative Methods for the Force-Based Quasicontinuum Approximation....Pages 331-368 Analysis of an Averaging Operator for Atomic-to-Continuum Coupling Methods by the Arlequin Approach....Pages 369-400 A Coupled Finite Difference – Gaussian Beam Method for High Frequency Wave Propagation....Pages 401-420 Back Matter....Pages 421-427 This book is a snapshot of current research in multiscale modeling, computations and applications. It covers fundamental mathematical theory, numerical algorithms as well as practical computational advice for analysing single and multiphysics models containing a variety of scales in time and space. Complex fluids, porous media flow and oscillatory dynamical systems are treated in some extra depth, as well as tools like analytical and numerical homogenization, and the fast multipole method