Eike Hermann Müller: Efficient fast multipole methods for (kinetic) Monte Carlo simulations of interacting particle systems

By Eike Hermann Müller, Department of Mathematical Sciences, University of Bath, UK

Including electrostatics in (kinetic) Monte Carlo simulations of interacting particles is challenging due to the long-range nature of the Coulomb potential. As a result, the computational complexity grows rapidly with N, the number of particles in the system. While the Fast Multipole Method (FMM) allows the computation of electrostatic interactions for a fixed configuration in O(N) time, a full sweep over all particles in a (kinetic) Monte Carlo update is still too expensive if FMM is applied naively. To overcome this issue, we developed modified versions of FMM which require only O(1) computations per particle hop in kinetic Monte Carlo or O(log(N)) operations for a single-particle move in standard Monte Carlo. The algorithms are implemented in a new performance portable Python framework for molecular simulations. Our framework provides an abstraction for typical operations such as loops over all particle pairs, which are orchestrated by control flow in Python. While this allows the easy implementation of simulation algorithms in a high-level language, under the hood code generation guarantees the efficient execution on different parallel computer architectures.

Short CV:

Eike Mueller is an Associate Professor (Senior Lecturer) for Scientific Computing in the Department of Mathematical Sciences at the University of Bath (UK). Originally trained as a physicist, Eike has worked on the development and implementation of efficient numerical algorithms to tackle challenging problems in science and engineering. His work on new multigrid solvers for partial differential equations in atmospheric fluid dynamics has led to significant impact by improving the performance of the UK’s operational climate- and weather forecast model. More generally, Eike’s research focuses on the development of fast, parallel algorithms in interdisciplinary contexts. While collaborating with meteorologists, chemists and physicists, Eike has worked on the application of multilevel methods to predict the spread of atmospheric pollutants, to simulate path integrals in quantum mechanics and to accelerate (kinetic) Monte Carlo simulations. In addition to the design of new numerical methods, Eike is also interested in their efficient implementation, performance portability and sustainable software engineering.
Before joining the University of Bath as a PostDoc in 2011, Eike completed a PhD in computational particle physics in Edinburgh (2009) and worked as a scientist at the UK Meteorological Office (2009-2011). https://people.bath.ac.uk/em459/

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