Multiscale Modeling and Simulation in Science

1. Front Matter

   Pages i-xiii

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2. Tutorials

   1. Multiscale Methods for Subsurface Flow

      • Jørg E. Aarnes, Knut—Andreas Lie, Vegard Kippe, Stein Krogstad

      Pages 3-48

   2. Multiscale Modelling of Complex Fluids: A Mathematical Initiation

      • Claude Le Bris, Tony Lelièvre

      Pages 49-137

   3. Fast Algorithms for Boundary Integral Equations

      • Lexing Ying

      Pages 139-193

   4. Wavelets andWavelet Based Numerical Homogenization

      • Olof Runborg

      Pages 195-235

   5. Multiscale Computations for Highly Oscillatory Problems

      • Gil Ariel, Björn Engquist, Heinz-Otto Kreiss, Richard Tsai

      Pages 237-287

3. Projects

   1. Quantum Mechanics/Classical Mechanics Modeling of Biological Systems

      • Hugosson W. Håkan, Hans Ågren

      Pages 291-294

   2. Multiple Scales in Solid State Physics

      • Erik Koch, Eva Pavarini

      Pages 295-298

   3. Climate Sensitivity and Variability Examined in a Global Climate Model

      • Heiner Körnich, Erland Källén

      Pages 299-302

   4. Coarse-scale Modeling of Flow in Gas-injection Processes for Enhanced Oil Recovery

      • James V. Lambers

      Pages 303-306

   5. Photo-Ionization Dynamics Simulation

      • Garrelt Mellema

      Pages 307-310

   6. Time Scales in Molecular Reaction Dynamics

      • Yngve Öhrn, Erik Deumens

      Pages 311-316

   7. Complex Band Structures of Spintronics Materials

      • Peter Zahn, Patrik Thunström, Tomas Johnson

      Pages 317-320

4. Back Matter

   Pages 321-326

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Most problems in science involve many scales in time and space. An example is turbulent ?ow where the important large scale quantities of lift and drag of a wing depend on the behavior of the small vortices in the boundarylayer. Another example is chemical reactions with concentrations of the species varying over seconds and hours while the time scale of the oscillations of the chemical bonds is of the order of femtoseconds. A third example from structural mechanics is the stress and strain in a solid beam which is well described by macroscopic equations but at the tip of a crack modeling details on a microscale are needed. A common dif?culty with the simulation of these problems and many others in physics, chemistry and biology is that an attempt to represent all scales will lead to an enormous computational problem with unacceptably long computation times and large memory requirements. On the other hand, if the discretization at a coarse level ignoresthe?nescale informationthenthesolutionwillnotbephysicallymeaningful. The in?uence of the ?ne scales must be incorporated into the model. This volume is the result of a Summer School on Multiscale Modeling and S- ulation in Science held at Boso ¤n, Lidingo ¤ outside Stockholm, Sweden, in June 2007. Sixty PhD students from applied mathematics, the sciences and engineering parti- pated in the summer school.

• astrophysics
• computational fluid dynamics
• computational science and engineering
• fast algorithms
• fluid dynamics
• homogenization
• multiscale
• porous media

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

  Björn Engquist

• Department of Information Technology, Uppsala University, Uppsala, Sweden

  Per Lötstedt

• Department of Numerical Analysis and Computer Science, Royal Institute of Technology, Stockholm, Sweden

  Olof Runborg

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