Multiscale methods in nano- and biotechnology

Michael Griebel
University of Bonn, Germany
Applied Mathematics

The mathematical modelling of matter can take place on at least three different scales: On the quantum mechanical level via the Schr\"odinger equation, on an ab-initio level by means of HF or DFT and on the classical level using molecular dynamics methods. The arising numerical problems can efficiently be treated also by multi-scale methods. We discuss these techniques and show our results from numerical simulations for applications from the field of nano-technology and biophysics with special emphasis on the numerical simulation of carbon nanotubes.