Computational multiscale methods: algorithms, analysis and applications

Nowadays, computer simulation is essential to create insight in many scientific domains, due to the availability of advanced numerical methods. However, results from simulation are only as meaningful as the model that was used to describe the system. Many physical, chemical and biological problems have a multiscale nature, and cannot be modeled to sufficient accuracy at the macroscopic scale of interest. At the same time, direct simulation with a more fine−scale (microscopic) model may be computationally prohibitive. This research program deals with the resulting ''next challenge'' in numerical and applied mathematics: the development and analysis of numerical techniques that reliably and efficiently couple models at fine and coarse levels of description.