Multiscale modeling and computation

Lecturer(s)

Prof. P. Koumoutsakos, Prof. M. Kröger

Hour(s) of lecture(s), exercise(s) and credit points

2L
1E
5CP

Teaching goals

Fundamentals of multiscale modeling and computation with emphasis on the coupling of physical descriptions across different scales and on multiresolution computational methods. Multiscale concepts are introduced using examples from engineering and scientific problems.

Development of fundamental concepts of multiscaling. Description of multiresolution algorithms and multiphysics techniques including stochastic simulations algorithms and their coupling to deterministic schemes.

Summary and outline

I. Multi-Physics Modeling

• Derivation and coupling of Atomistic - Mesoscale -Continuum descriptions
• Hybrid algorithms : Molecular Dynamics - Partial Differential equations
• The Master equation for discrete and continuum systems

II. Multiresolution modeling

• Multigrid Techniques for grid based methods
• Multipole particle methods
• Wavelets

Literature

• Multiscale Flow Simulations using Particles, Annu. Rev. Fluid Mech., 2005
• Models for polymeric and anisotropic liquids (Springer, Berlin, 2005)

Notice

• Students will work on small 2-3 week projects working, in teams of 2 people.
• The class grade is determined by the students performance (not necessarily completion !)
  in these projects.
• Programming experience is necessary.
• Exposure to computational methods such as : molecular dynamics, finite difference and particle methods is desired but not required.