Research Area J:

High-Dimensional problems and multi-scale methods

Mathematical modelling of physical phenomena often leads to high-dimensional partial differential equations. Examples are the many particle Schrödinger equation in quantum physics, the description of queueing networks, reaction mechanisms in molecular biology, visco-elasticity in polymer fluids, or models for the pricing of financial derivatives. Also, homogenisation and stochastic modelling usually result in high-dimensional PDEs. Typically, besides their high dimension, these problems involve multiple scales in space and time. In this Research Area we deal with high-dimensional problems and multiscale methods from the perspective of modelling, analysis, and numerical simulation. In the numerical treatment, the so-called curse of dimension is encountered. The computational cost required for an approximate solution scales exponentially with the dimension of the problem, and thus renders classical numerical approaches useless in practise. Therefore, the Research Area focuses on:

  • Dimension-independent discretisation and solution methods
  • Simplified effective models and their macroscopic behaviour of large high-dimensional systems.

Leader of the Research Area

Further Investigators