Efficient algorithms for electrostatic interactions including dielectric contrasts

Coarse grained models of soft matter are usually combined with implicit solvent models that take the electrostatic polarizability into account via a dielectric background. In biophysical or nanoscale simulations that include water, this constant can vary greatly within the system. Performing molecular dynamics or other simulations that need compute exact electrostatic interactions between charges in those systems is computationally demanding. We review here several algorithms developped by us that perform exactly this task. For planar dielectric surfaces in partial periodic boundary conditions, the arising image charges can be either treated with the MMM2D algorithm in a very efficient and accurate way, or with the ELC term that enables the user to use his favorite 3D periodic Coulomb solver . Arbitrarily shaped interfaces can be dealt with using induced surface charges with the ICC algorithm. Finally, the local electrostatics algorithm MEMD (Maxwell Equations Molecular Dynamics) allows even to employ a smoothly varying dielectric constant in the systems. We introduce the concepts of these three algorithms, and an extension for the inclusion of boundaries that are to be held fixed at constant potential (metal conditions). For each method, we present a showcase application to highlight the importance of dielectric interfaces

Dielektrische Veränderungen in Simulationen geladener weicher Materie

In this thesis, an algorithm to calculate electrostatic interactions in molecular dynamics simulations is extended to include spatial and temporal variations in the dielectric permittivity of the system. The algorithm is implemented, verified, and parallelized. It is then applied to a number of systems containing charged soft matter. Noticeable quantitative and qualitative differences are found between simulations including and excluding dielectric variations. Particularly for the effective charge of colloids, and for the conductivity of polyelectrolytes in aqueous solution, major behavioral changes are shown.Im Rahmen dieser Dissertation wird ein Algorithmus zur Berechnung elektrostatischer Wechselwirkungen in Molekulardynamik-Simulationen erweitert, so dass er örtliche und zeitliche Veränderungen der dielektrischen Permittivität darstellen kann. Der Algorithmus wird implementiert, verifiziert und parallelisiert. Anschließend wird er auf eine Reihe von Systemen geladener weicher Materie angewandt. Es werden Signifikante quantitative und qualitative Unterschiede demonstriert zwischen Simulationen mit und ohne veränderliche Dielektrizität. Insbesondere bei der effektiven Ladung von Kolloiden und der Leitfähigkeit von wässrigen Polyelektrolyt-Lösungen werden grundlegende Änderungen des Verhaltens aufgezeigt

Comparison of scalable fast methods for long-range interactions

Based on a parallel scalable library for Coulomb interactions in particle systems, a comparison between the fast multipole method (FMM), multigrid-based methods, fast Fourier transform (FFT)-based methods, and a Maxwell solver is provided for the case of three-dimensional periodic boundary conditions. These methods are directly compared with respect to complexity, scalability, performance, and accuracy. To ensure comparable conditions for all methods and to cover typical applications, we tested all methods on the same set of computers using identical benchmark systems. Our findings suggest that, depending on system size and desired accuracy, the FMM- and FFT-based methods are most efficient in performance and stability