Modul: MAT870 Zurich Colloquium in Applied and Computational Mathematics

## Efficient numerical methods for polarization effects in molecular systems

Prof. Dr. Benjamin Stamm talk

Speaker invited by: Prof. Dr. Rémi Abgrall

**Date:** 27.02.19 **Time:** 16.15 - 17.45 **Room:** Y27H25

In this talk we provide two examples of models and numerical methods involving N-body polarization effects. One characteristic feature of simulations involving molecular systems is that the scaling in the number N of atoms or particles is important and traditional computational methods, like domain decomposition methods for example, may behave differently than problems with a fixed computational domain. We will first see an example in the context of the Poisson-Boltzmann continuum solvation model and present a numerical method that relies on an integral equation coupled with a domain decomposition strategy. Numerical examples illustrate the behaviour of the proposed method. In a second case, we consider a N-body problem of interacting dielectric charged spheres whose solution satisfies an integral equation of the second kind. We present results from an a priori analysis with error bounds that are independent of the number particles N allowing for, in combination with the Fast Multipole Method (FMM), a linear scaling method. Towards the end, we finish the talk with applications to dynamic processes and enhanced stabilization of binary superlattices through polarization effects.