Fast electrostatic solvers for kinetic Monte Carlo simulations

•New electrostatic algorithm for fast kinetic Monte Carlo (KMC) simulations.•Modified Fast Multipole Method scales linearly in number of particles per KMC step.•Performance portable high-level Python user interface uses code generation.•Demonstrated parallel scalability for 1 million charges and 819...

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Veröffentlicht in:Journal of computational physics 2020-06, Vol.410, p.109379, Article 109379
Hauptverfasser: Saunders, William Robert, Grant, James, Müller, Eike Hermann, Thompson, Ian
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creator Saunders, William Robert
Grant, James
Müller, Eike Hermann
Thompson, Ian
description •New electrostatic algorithm for fast kinetic Monte Carlo (KMC) simulations.•Modified Fast Multipole Method scales linearly in number of particles per KMC step.•Performance portable high-level Python user interface uses code generation.•Demonstrated parallel scalability for 1 million charges and 8192 cores. Kinetic Monte Carlo (KMC) is an important computational tool in theoretical physics and chemistry. In contrast to standard Monte Carlo, KMC permits the description of time dependent dynamical processes and is not restricted to systems in equilibrium. Compared to Molecular Dynamics, it allows simulations over significantly longer timescales. Recently KMC has been applied successfully in modelling of novel energy materials such as Lithium-ion batteries and organic/perovskite solar cells. Motivated by this, we consider general solid state systems which contain free, interacting particles which can hop between localised sites in the material. The KMC transition rates for those hops depend on the change in total potential energy of the system. For charged particles this requires the frequent calculation of electrostatic interactions, which is usually the bottleneck of the simulation. To avoid this issue and obtain results in reasonable times, many studies replace the long-range potential by a phenomenological short range approximation. This, however, leads to systematic errors and unphysical results. On the other hand standard electrostatic solvers such as Ewald summation or fast Poisson solvers are highly inefficient in the KMC setup or introduce uncontrollable systematic errors at high resolution. In this paper we describe how the Fast Multipole Method by Greengard and Rokhlin can be adapted to overcome this issue by dramatically reducing computational costs. We exploit the fact that each update in the transition rate calculation corresponds to a single particle move and changes the configuration only by a small amount. This allows us to construct an algorithm which scales linearly in the number of charges for each KMC step, something which had not been deemed to be possible before. We demonstrate the performance and parallel scalability of the method by implementing it in a performance portable software library, which was recently developed in our group. We describe the high-level Python interface of the code which makes it easy to adapt to specific use cases.
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Kinetic Monte Carlo (KMC) is an important computational tool in theoretical physics and chemistry. In contrast to standard Monte Carlo, KMC permits the description of time dependent dynamical processes and is not restricted to systems in equilibrium. Compared to Molecular Dynamics, it allows simulations over significantly longer timescales. Recently KMC has been applied successfully in modelling of novel energy materials such as Lithium-ion batteries and organic/perovskite solar cells. Motivated by this, we consider general solid state systems which contain free, interacting particles which can hop between localised sites in the material. The KMC transition rates for those hops depend on the change in total potential energy of the system. For charged particles this requires the frequent calculation of electrostatic interactions, which is usually the bottleneck of the simulation. To avoid this issue and obtain results in reasonable times, many studies replace the long-range potential by a phenomenological short range approximation. This, however, leads to systematic errors and unphysical results. On the other hand standard electrostatic solvers such as Ewald summation or fast Poisson solvers are highly inefficient in the KMC setup or introduce uncontrollable systematic errors at high resolution. In this paper we describe how the Fast Multipole Method by Greengard and Rokhlin can be adapted to overcome this issue by dramatically reducing computational costs. We exploit the fact that each update in the transition rate calculation corresponds to a single particle move and changes the configuration only by a small amount. This allows us to construct an algorithm which scales linearly in the number of charges for each KMC step, something which had not been deemed to be possible before. 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To avoid this issue and obtain results in reasonable times, many studies replace the long-range potential by a phenomenological short range approximation. This, however, leads to systematic errors and unphysical results. On the other hand standard electrostatic solvers such as Ewald summation or fast Poisson solvers are highly inefficient in the KMC setup or introduce uncontrollable systematic errors at high resolution. In this paper we describe how the Fast Multipole Method by Greengard and Rokhlin can be adapted to overcome this issue by dramatically reducing computational costs. We exploit the fact that each update in the transition rate calculation corresponds to a single particle move and changes the configuration only by a small amount. This allows us to construct an algorithm which scales linearly in the number of charges for each KMC step, something which had not been deemed to be possible before. 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subjects Algorithms
Charged particles
Computational physics
Computer Science
Computer Science, Interdisciplinary Applications
Computer simulation
Computing costs
Domain specific language
Electrostatics
Fast Multipole Method
Kinetic Monte Carlo
Lithium-ion batteries
Molecular dynamics
Multipoles
Parallel computing
Perovskites
Photovoltaic cells
Physical Sciences
Physics
Physics, Mathematical
Potential energy
Rechargeable batteries
Science & Technology
Software
Solar cells
Solvers
Systematic errors
Technology
Theoretical physics
Time dependence
title Fast electrostatic solvers for kinetic Monte Carlo simulations
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