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Numerical Analysis of Multiscale Computations

Proceedings of a Winter Workshop at the Banff International Research Station 2009

  • Conference proceedings
  • © 2012

Overview

Editors:
  1. Björn Engquist

    1. , Department of Mathematics, University of Texas, Austin, USA

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  2. Olof Runborg

    1. Dept. Numerical Analysis &, Computer Science (NADA), Royal Institute of Technology (KTH), Stockholm, Sweden

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  3. Yen-Hsi R. Tsai

    1. , Department of Mathematics, University of Texas at Austin, Austin, USA

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Part of the book series: Lecture Notes in Computational Science and Engineering (LNCSE, volume 82)

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Table of contents (16 papers)

  1. Front Matter

    Pages i-x
    Download chapter PDF

  2. Explicit Methods for Stiff Stochastic Differential Equations

    • Assyr Abdulle
    Pages 1-22

  3. Oscillatory Systems with Three Separated Time Scales: Analysis and Computation

    • Gil Ariel, Björn Engquist, Yen-Hsi Richard Tsai
    Pages 23-45

  4. Variance Reduction in Stochastic Homogenization: The Technique of Antithetic Variables

    • Xavier Blanc, Ronan Costaouec, Claude Le Bris, Frédéric Legoll
    Pages 47-70

  5. A Stroboscopic Numerical Method for Highly Oscillatory Problems

    • Mari Paz Calvo, Philippe Chartier, Ander Murua, Jesús María Sanz-Serna
    Pages 71-85

  6. The Microscopic Origin of the Macroscopic Dielectric Permittivity of Crystals: A Mathematical Viewpoint

    • Éric Cancès, Mathieu Lewin, Gabriel Stoltz
    Pages 87-125

  7. Fast Multipole Method Using the Cauchy Integral Formula

    • Cristopher Cecka, Pierre-David Létourneau, Eric Darve
    Pages 127-144

  8. Tools for Multiscale Simulation of Liquids Using Open Molecular Dynamics

    • Rafael Delgado-Buscalioni
    Pages 145-166

  9. Multiscale Methods for Wave Propagation in Heterogeneous Media Over Long Time

    • Björn Engquist, Henrik Holst, Olof Runborg
    Pages 167-186

  10. Numerical Homogenization via Approximation of the Solution Operator

    • Adrianna Gillman, Patrick Young, Per-Gunnar Martinsson
    Pages 187-216

  11. Adaptive Multilevel Monte Carlo Simulation

    • Håkon Hoel, Erik von Schwerin, Anders Szepessy, Raúl Tempone
    Pages 217-234

  12. Coupled Coarse Graining and Markov Chain Monte Carlo for Lattice Systems

    • Evangelia Kalligiannaki, Markos A. Katsoulakis, Petr Plecháč
    Pages 235-257

  13. Calibration of a Jump-Diffusion Process Using Optimal Control

    • Jonas Kiessling
    Pages 259-277

  14. Some Remarks on Free Energy and Coarse-Graining

    • Frédéric Legoll, Tony Lelièvre
    Pages 279-329

  15. Linear Stationary Iterative Methods for the Force-Based Quasicontinuum Approximation

    • Mitchell Luskin, Christoph Ortner
    Pages 331-368

  16. Analysis of an Averaging Operator for Atomic-to-Continuum Coupling Methods by the Arlequin Approach

    • Serge Prudhomme, Robin Bouclier, Ludovic Chamoin, Hachmi Ben Dhia, J. Tinsley Oden
    Pages 369-400

  17. A Coupled Finite Difference – Gaussian Beam Method for High Frequency Wave Propagation

    • Nicolay M. Tanushev, Yen-Hsi Richard Tsai, Björn Engquist
    Pages 401-420

  18. Back Matter

    Pages 421-427
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Keywords

About this book

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.

Editors and Affiliations

  • , Department of Mathematics, University of Texas, Austin, USA

    Björn Engquist

  • Dept. Numerical Analysis &, Computer Science (NADA), Royal Institute of Technology (KTH), Stockholm, Sweden

    Olof Runborg

  • , Department of Mathematics, University of Texas at Austin, Austin, USA

    Yen-Hsi R. Tsai

About the editors

The authors are experts in computational science and engineering with backgrounds in mathematics, computer science and engineering.

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