Multiscale Methods in Science and Engineering

Jørg Aarnes, Bjørn-Ove Heimsund (auth.), Björn Engquist, Olof Runborg, Per Lötstedt (eds.)9783540253358, 3-540-25335-1, 3-540-43416-X, 3-540-43508-5, 3-540-44363-0

Multiscale problems naturally pose severe challenges for computational science and engineering. The smaller scales must be well resolved over the range of the larger scales. Challenging multiscale problems are very common and are found in e.g. materials science, fluid mechanics, electrical and mechanical engineering. Homogenization, subgrid modelling, heterogeneous multiscale methods, multigrid, multipole, and adaptive algorithms are examples of methods to tackle these problems. This volume is an overview of current mathematical and computational methods for problems with multiple scales with applications in chemistry, physics and engineering.

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Table of contents :
Multiscale Discontinuous Galerkin Methods for Elliptic Problems with Multiple Scales….Pages 1-20
Discrete Network Approximation for Highly-Packed Composites with Irregular Geometry in Three Dimensions….Pages 21-57
Adaptive Monte Carlo Algorithms for Stopped Diffusion….Pages 59-88
The Heterogeneous Multi-Scale Method for Homogenization Problems….Pages 89-110
A Coarsening Multigrid Method for Flow in Heterogeneous Porous Media….Pages 111-132
On the Modeling of Small Geometric Features in Computational Electromagnetics….Pages 133-148
Coupling PDEs and SDEs: The Illustrative Example of the Multiscale Simulation of Viscoelastic Flows….Pages 149-168
Adaptive Submodeling for Linear Elasticity Problems with Multiscale Geometric Features….Pages 169-180
Adaptive Variational Multiscale Methods Based on A Posteriori Error Estimation: Duality Techniques for Elliptic Problems….Pages 181-193
Multipole Solution of Electromagnetic Scattering Problems with Many, Parameter Dependent Incident Waves….Pages 195-203
Introduction to Normal Multiresolution Approximation….Pages 205-224
Combining the Gap-Tooth Scheme with Projective Integration: Patch Dynamics….Pages 225-239
Multiple Time Scale Numerical Methods for the Inverted Pendulum Problem….Pages 241-261
Multiscale Homogenization of the Navier-Stokes Equation….Pages 263-273
Numerical Simulations of the Dynamics of Fiber Suspensions….Pages 275-289