Title Participants Abstract
"Convergence of the Micro-Macro Parareal Method for a Linear Scale-Separated Ornstein-Uhlenbeck SDE" "Ignace Bossuyt, Stefan Vandewalle, Giovanni Samaey" "Time-parallel methods can reduce the wall clock time required for the accurate numerical solution of differential equations by parallelizing across the time-dimension. In this paper, we present and test the convergence behavior of a multiscale, micro-macro version of a Parareal method for stochastic differential equations (SDEs). In our method, the fine propagator of the SDE is based on a high-dimensional slow-fast microscopic model; the coarse propagator is based on a model-reduced version of the latter, that captures the low-dimensional, effective dynamics at the slow time scales. We investigate how the model error of the approximate model influences the convergence of the micro-macro Parareal algorithm and we support our analysis with numerical experiments."
"Hilbert expansion based fluid models for kinetic equations describing neutral particles in the plasma edge of a fusion device" "Vince Maes, Wouter Dekeyser, Tine Baelmans, Giovanni Samaey"
"A Micro-Macro Markov Chain Monte Carlo Method for Molecular Dynamics using Reaction Coordinate Proposals" "Hannes Vandecasteele, Giovanni Samaey" "We introduce a new micro-macro Markov chain Monte Carlo method to sample invariant distributions of molecular dynamics systems that exhibit a time-scale separation between the microscopic (fast) dynamics, and the macroscopic (slow) dynamics of some low-dimensional set of reaction coordinates. The algorithm enhances exploration of the state space in the presence of metastability by allowing larger proposed moves at the macroscopic level, on which a conditional accept-reject procedure is applied. Only when the macroscopic proposal is accepted, is the full microscopic state reconstructed from the newly sampled reaction coordinate value and is subjected to a second accept/reject procedure. The computational gain stems from the fact that most proposals are rejected at the macroscopic level, at low computational cost, while microscopic states, once reconstructed, are almost always accepted. We analytically show convergence and discuss the rate of convergence of the proposed algorithm, and numerically illustrate its efficiency on two standard molecular test cases."
"A Micro-Macro Markov Chain Monte Carlo Method for Molecular Dynamics using Reaction Coordinate Proposals" "Hannes Vandecasteele, Giovanni Samaey" "We introduce a new micro-macro Markov chain Monte Carlo method to sample invariant distributions of molecular dynamics systems that exhibit a time-scale separation between the microscopic (fast) dynamics, and the macroscopic (slow) dynamics of some low-dimensional set of reaction coordinates. The algorithm enhances exploration of the state space in the presence of metastability by allowing larger proposed moves at the macroscopic level, on which a conditional accept-reject procedure is applied. Only when the macroscopic proposal is accepted, is the full microscopic state reconstructed from the newly sampled reaction coordinate value and is subjected to a second accept/reject procedure. The computational gain stems from the fact that most proposals are rejected at the macroscopic level, at low computational cost, while microscopic states, once reconstructed, are almost always accepted. We analytically show convergence and discuss the rate of convergence of the proposed algorithm, and numerically illustrate its efficiency on two standard molecular test cases."
"Accelerated Simulation of Boltzmann-BGK Equations Near the Diffusive Limit with Asymptotic-Preserving Multilevel Monte Carlo" "Emil Loevbak, Giovanni Samaey"
"Spatially Adaptive Projective Integration Schemes For Stiff Hyperbolic Balance Laws With Spectral Gaps" "Giovanni Samaey"
"Fluid, kinetic and hybrid approaches for neutral and trace ion edge transport modelling in fusion devices" "Wouter Dekeyser, Stefano Carli, Maarten Blommaert, Wim Van Uytven, Tine Baelmans, Giovanni Samaey, Niels Horsten" "Neutral gas physics and neutral interactions with the plasma are key aspects of edge plasma and divertor physics in a fusion reactor including the detachment phenomenon often seen as key to dealing with the power exhaust challenges. A full physics description of the neutral gas dynamics requires a 6D kinetic approach, potentially time dependent, where the details of the wall geometry play a substantial role, to the extent that, e.g., the subdivertor region has to be included. The Monte Carlo (MC) approach used for about 30 years in EIRENE [1], is well suited to solve these types of complex problems. Indeed, the MC approach allows simulating the 6D kinetic equation without having to store the velocity distribution on a 6D grid, at the cost of introducing statistical noise. MC also provides very good flexibility in terms of geometry and atomic and molecular (A&M) processes. However, it becomes computationally extremely demanding in high-collisional regions (HCR) as anticipated in ITER and DEMO. Parallelization on particles helps reducing the simulation wall clock time, but to provide speed-up in situations where single trajectories potentially involve a very large number of A&M events, it is important to derive a hierarchy of models in terms of accuracy and to clearly identify for what type of physics issues they provide reliable answers. It was demonstrated that advanced fluid neutral (AFN) models are very accurate in HCRs, and at least an order of magnitude faster than fully kinetic simulations. Based on these fluid models, three hybrid fluid-kinetic approaches are introduced: a spatially hybrid technique (SpH), a micro-Macro hybrid method (mMH), and an asymptotic-preserving MC (APMC) scheme, to combine the efficiency of a fluid model with the accuracy of a kinetic description. In addition, atomic and molecular ions involved in the edge plasma chemistry can also be treated kinetically within the MC solver, opening the way for further hybridisation by enabling kinetic impurity ion transport calculations. This paper aims to give an overview of methods mentioned and suggests the most prospective combinations to be developed."
"Estimation as a post-processing step for random walk approximations of the Boltzmann-BGK model" "Vince Maes, Giovanni Samaey"
"On the mitigation of cancellation errors in hybrid fluid-kinetic methods for solving kinetic equations describing neutrals in the plasma edge" "Vince Maes, Giovanni Samaey"
"Multilevel asymptotic-preserving Monte Carlo for kinetic-diffusive particle simulations of the Boltzmann-BGK equation" "Pieterjan Robbe, Tine Baelmans, Giovanni Samaey"