Related papers: Multilevel Asymptotic-Preserving Monte Carlo for P…
In plasma edge simulations, the behavior of neutral particles is often described by a Boltzmann--BGK equation. Solving this kinetic equation and estimating the moments of its solution are essential tasks, typically carried out using Monte…
We develop a novel Monte Carlo strategy for the simulation of the Boltzmann-BGK model with both low-collisional and high-collisional regimes present. The presented solution to maintain accuracy in low-collisional regimes and remove…
We propose a multilevel Monte Carlo method for a particle-based asymptotic-preserving scheme for kinetic equations. Kinetic equations model transport and collision of particles in a position-velocity phase-space. With a diffusive scaling,…
Kinetic equations model the position-velocity distribution of particles subject to transport and collision effects. Under a diffusive scaling, these combined effects converge to a diffusion equation for the position density in the limit of…
In plasma edge simulations, kinetic Monte Carlo (MC) is often used to simulate neutral particles and estimate source terms. For large-sized reactors, like ITER and DEMO, high particle collision rates lead to a substantial computational cost…
The Kinetic-Diffusion Monte Carlo (KDMC) method is a powerful tool for simulating neutral particles in fusion reactors. It is a hybrid fluid-kinetic method that is significantly faster than pure kinetic methods at the cost of a small bias…
Kinetic equations model distributions of particles in position-velocity phase space. Often, one is interested in studying the long-time behavior of particles in high-collisional regimes in which an approximate (advection)-diffusion model…
We propose and investigate a new multi-level Monte Carlo scheme for numerical solutions of the kinetic Boltzmann equation for neutral species in edge plasmas. In particular, this method explicitly exploits a key structural property of…
A kinetic Monte Carlo (KMC) method is presented to simulate the electrodeposition of a metal on a single crystal surface of the same metal under galvanostatic conditions. This method utilizes the multi-body embedded-atom method (EAM)…
The Dynamic Monte Carlo (DMC) method is an established molecular simulation technique for the analysis of the dynamics in colloidal suspensions. An excellent alternative to Brownian Dynamics or Molecular Dynamics simulation, DMC is…
A common way to simulate the transport and spread of pollutants in the atmosphere is via stochastic Lagrangian dispersion models. Mathematically, these models describe turbulent transport processes with stochastic differential equations…
Ab initio quantum Monte Carlo (QMC) is a stochastic approach for solving the many-body Schr\"odinger equation without resorting to one-body approximations. QMC algorithms are readily parallelizable via ensembles of $N_w$ walkers, making…
Particle-based kinetic Monte Carlo simulations of neutral particles is one of the major computational bottlenecks in tokamak scrape-off layer simulations. This computational cost comes from the need to resolve individual collision events in…
The Kinetic Monte Carlo (KMC) method has become an important tool for examination of phenomena like surface diffusion and thin film growth because of its ability to carry out simulations for time scales that are relevant to experiments. But…
We present in this paper a hybrid, Multi-Level Monte Carlo (MLMC) method for solving the neutral particle transport equation. MLMC methods, originally developed to solve parametric integration problems, work by using a cheap, low fidelity…
This article reviews the basic computational techniques for carrying out multi-scale simulations using statistical methods, with the focus on simulations of epitaxial growth. First, the statistical-physics background behind Monte Carlo…
This paper presents multilevel hybrid transport (MLHT) methods for solving the neutral-particle Boltzmann transport equation. The proposed MLHT methods are formulated on a sequence of spatial grids using a multilevel Monte Carlo (MLMC)…
We present a new, for plasma physics, highly efficient multilevel Monte Carlo numerical method for simulating Coulomb collisions. The method separates and optimally minimizes the finite-timestep and finite-sampling errors inherent in the…
In this paper we study from a numerical analysis perspective the Fractional Step Kinetic Monte Carlo (FS-KMC) algorithms proposed in [1] for the parallel simulation of spatially distributed particle systems on a lattice. FS-KMC are…
We develop new multilevel Monte Carlo (MLMC) methods to estimate the expectation of the smallest eigenvalue of a stochastic convection-diffusion operator with random coefficients. The MLMC method is based on a sequence of finite element…