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Numerical Analysis of Multiscale Computations: Proceedings of a Winter Workshop at the Banff International Research Station 2009

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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.

Author(s): Assyr Abdulle (auth.), Björn Engquist, Olof Runborg, Yen-Hsi R. Tsai (eds.)
Series: Lecture Notes in Computational Science and Engineering 82
Edition: 1
Publisher: Springer-Verlag Berlin Heidelberg
Year: 2012

Language: English
Pages: 430
Tags: Computational Science and Engineering;Computational Mathematics and Numerical Analysis;Numerical and Computational Physics

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