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Numerical Analysis of Multiscale Problems

  • Textbook
  • © 2012

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Editors:
  1. Ivan G. Graham

    1. , Department of Mathematical Sciences, University of Bath, Bath, United Kingdom

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  2. Thomas Y. Hou

    1. , Applied & Computational Mathematics, California Institute of Technology, Pasadena, USA

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  3. Omar Lakkis

    1. , Department of Mathematics, University of Sussex, Brighton, United Kingdom

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  4. Robert Scheichl

    1. , Department of Mathematical Sciences, University of Bath, Bath, United Kingdom

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  • Multiscale Methods is one of the most active areas in computational science.
  • This book is a multi-disciplinary textbook on these methods. Complements nicely the previous volume on Multiscale Methods, LNCSE 44.

Part of the book series: Lecture Notes in Computational Science and Engineering (LNCSE, volume 83)

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Table of contents (10 chapters)

  1. Front Matter

    Pages i-x
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  2. Multiscale Modelling and Inverse Problems

    • James Nolen, Grigorios A. Pavliotis, Andrew M. Stuart
    Pages 1-34

  3. Transported Probability and Mass Density Function (PDF/MDF) Methods for Uncertainty Assessment and Multi-Scale Problems

    • Patrick Jenny, Daniel W. Meyer
    Pages 35-65

  4. A Computational and Theoretical Investigation of the Accuracy of Quasicontinuum Methods

    • Brian Van Koten, Xingjie Helen Li, Mitchell Luskin, Christoph Ortner
    Pages 67-96

  5. Coarse-Grid Multiscale Model Reduction Techniques for Flows in Heterogeneous Media and Applications

    • Yalchin Efendiev, Juan Galvis
    Pages 97-125

  6. Fast Algorithms for High Frequency Wave Propagation

    • Björn Engquist, Lexing Ying
    Pages 127-161

  7. Uncertainty Quantification for Subsurface Flow Problems Using Coarse-Scale Models

    • Louis J. Durlofsky, Yuguang Chen
    Pages 163-202

  8. Sparse Tensor Approximation of Parametric Eigenvalue Problems

    • Roman Andreev, Christoph Schwab
    Pages 203-241

  9. Mixed Multiscale Methods for Heterogeneous Elliptic Problems

    • Todd Arbogast
    Pages 243-283

  10. On Stability of Discretizations of the Helmholtz Equation

    • S. Esterhazy, J. M. Melenk
    Pages 285-324

  11. Why it is Difficult to Solve Helmholtz Problems with Classical Iterative Methods

    • O. G. Ernst, M. J. Gander
    Pages 325-363

  12. Back Matter

    Pages 365-371
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Keywords

About this book

The 91st London Mathematical Society Durham Symposium took place from July 5th to 15th 2010, with more than 100 international participants attending. The Symposium focused on Numerical Analysis of Multiscale Problems and this book contains 10 invited articles from some of the meeting's key speakers, covering a range of topics of contemporary interest in this area. Articles cover the analysis of forward and inverse PDE problems in heterogeneous media, high-frequency wave propagation, atomistic-continuum modeling and high-dimensional problems arising in modeling uncertainty. Novel upscaling and preconditioning techniques, as well as applications to turbulent multi-phase flow, and to problems of current interest in materials science are all addressed. As such this book presents the current state-of-the-art in the numerical  analysis of multiscale problems and will be of interest to both practitioners and mathematicians working in those fields.

Editors and Affiliations

  • , Department of Mathematical Sciences, University of Bath, Bath, United Kingdom

    Ivan G. Graham, Robert Scheichl

  • , Applied & Computational Mathematics, California Institute of Technology, Pasadena, USA

    Thomas Y. Hou

  • , Department of Mathematics, University of Sussex, Brighton, United Kingdom

    Omar Lakkis

About the editors

Ivan Graham is Professor of Numerical analysis at the University of Bath. Thomas Hou is Charles Lee Powell Professor of Applied and Computational Mathematics at California Institute of Technology. Omar Lakkis is Senior lecturer in Mathematics at the University of Sussex. Robert Scheichl is Senior Lecturer in Mathematics at the University of Bath.

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