Numerical Analysis of Multiscale Computations [electronic resource] : Proceedings of a Winter Workshop at the Banff International Research Station 2009 /
Workshop on Numerical Analysis and Multiscale ComputationsCorporate Author
Workshop on Numerical Analysis and Multiscale Computations(2009 :Banff International Research Station)
Workshop on Numerical Analysis and Multiscale Computations
Banff International Research Station for Mathematics Innovation & Discovery.
Engquist, Björn.editor.
Runborg, Olof.editor.
Tsai, Yen-Hsi R.editor.
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.
Description based upon print version of record.
Numerical Analysis of Multiscale Computations; Preface; Acknowledgements; Contents; Explicit Methods for Stiff Stochastic Differential Equations; 1 Introduction; 2 Stiff Stochastic Systems and Stability; 3 Chebyshev Methods; 4 The S-ROCK Methods; 4.1 Construction of the S-ROCK Methods; 4.2 Accuracy of the S-ROCK Methods; 5 Extended Mean-Square Stability and Damping; 6 Numerical Illustrations; References; Oscillatory Systems with Three Separated Time Scales:Analysis and Computation; 1 Introduction; 2 Effective Behavior Across Different Time Scales; 2.1 Slowly Changing Quantities
2.2 Multiscale Charts3 A Homogenization Approach; 3.1 A Two Scales Example; 3.2 Three Scales: Example 1; 3.3 Three Scales: Example 2; 3.4 Observations; 4 Numerical Algorithms; 4.1 Accuracy and Efficiency; 5 Examples; 5.1 Harmonic Oscillators; 5.2 An Example Motivated by the Fermi-Pasta-Ulam (FPU) Problem; 6 Summary; References; Variance Reduction in Stochastic Homogenization: The Technique of Antithetic Variables; 1 Introduction; 1.1 Homogenization Theoretical Setting; 1.2 Numerical Approach; 1.3 The Technique of Antithetic Variables; 1.4 A Brief Summary of Our Former Results
2 Variance Reduction for Problems Involving Correlations or Anisotropy2.1 Correlated Cases; 2.1.1 Influence of Correlation: Identical Local Behaviour; 2.1.2 Centered vs Equidistributed Correlation Structure; 2.1.3 Longer Correlation Lengths; 2.2 Anisotropic Cases; 2.2.1 Test Cases; 2.2.2 Numerical Results; 3 Variance Reduction for Eigenproblems; References; A Stroboscopic Numerical Method for HighlyOscillatory Problems; 1 Introduction; 2 A Modified Equation Approach to Averaging; 3 A Numerical Method; 4 Examples; 5 Numerical Experiments; 5.1 Constant Step-Sizes; 5.2 Variable Step-Sizes
ReferencesThe Microscopic Origin of the Macroscopic Dielectric Permittivity of Crystals: A Mathematical Viewpoint; 1 Introduction; 2 Electronic Structure Models for Finite Systems; 2.1 The N-Body Schrödinger Model; 2.2 The N-Body Schrödinger Model for Non-interacting Electrons; 2.3 Density Operators; 2.4 The Hartree Model and Other Density Operator Models of Electronic Structures; 3 The Hartree Model for Crystals; 3.1 Basics of Fourier and Bloch-Floquet Theories; 3.2 Perfect Crystals; 3.3 Crystals with Local Defects; 4 Dielectric Response of a Crystal
4.1 Series Expansion of the Time-Independent Response4.2 Properties of Qm,0F and m,0F for Small Amplitude Defects; 4.3 Dielectric Operator and Macroscopic DielectricPermittivity; 4.4 Time-Dependent Response; References; Fast Multipole Method Using the Cauchy Integral Formula; 1 Introduction; 2 Cauchy's Integral Formula and Low-Rank Approximations; 3 Connection with Fourier and Laplace Transforms; 4 Construction of Fast Methods; 5 Interpolation and Anterpolation; 6 Error Analysis; 7 Detailed Error Analysis; 8 Preliminary Numerical Results; 9 Conclusion; References
Tools for Multiscale Simulation of Liquids Using Open Molecular Dynamics
Includes bibliographical references.
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.
Computer mathematics.
Physics.
Computational Science and Engineering.
Computational Mathematics and Numerical Analysis.
Numerical and Computational Physics, Simulation.
Lecture Notes in Computational Science and Engineering