Computational Mathematics and Scientific Computing Seminar

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 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 of a domain decomposition method 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 in accuracy. Towards the end, we finish the talk with applications to dynamic processes and enhanced stabilization of binary superlattices through polarization effects.