This repository contains Python scripts used for the development of a multilevel Monte Carlo method for asymptotic-preserving particle schemes for kinetic equations.

This is not intended to be a software library, but is simply a publication of code used for producing the papers. As such, documentation is minimal, but you can reach me at [email protected] if you want more information. In the future, I hope to release a more mature implementation of these schemes.

Publications making use of this code are:

• E. Løvbak, G. Samaey, S. Vandewalle, A Multilevel Monte Carlo Asymptotic-Preserving Particle Method for Kinetic Equations in the Diffusion Limit. In P. L’Ecuyer, B. Tuffin (eds.) Monte Carlo and Quasi-Monte Carlo Methods 2018, pp. 383-–402. Springer (2020)
• E. Løvbak, G. Samaey, S. Vandewalle, A multilevel Monte Carlo method for asymptotic-preserving particle schemes. Numerische Mathematik 148, 141--186. (2021)
• E. Løvbak, B. Mortier, G. Samaey, S. Vandewalle, Multilevel Monte Carlo with improved correlation for kinetic equations in the diffusive scaling. In V. Krzhizhanovskaya et al. (eds.) Computational Science - ICCS 2020., Lecture Notes in Computer Science, vol 12142. pp. 374-–388. Springer (2020)
• E. Løvbak, G. Samaey, Accelerated simulation of Boltzmann-BGK equations near the diffusive limit with asymptotic-preserving multilevel Monte Carlo. SIAM Journal on Scientific Computing 45(4), pp. A1862 -- A1889. (2023)

In the sub-folder "Results in publications", you can scripts and data corresponding with

• E. Løvbak, G. Samaey, S. Vandewalle, A multilevel Monte Carlo method for asymptotic-preserving particle schemes. Numerische Mathematik 148, 141--186. (2021)
• E. Løvbak, G. Samaey, Accelerated simulation of Boltzmann-BGK equations near the diffusive limit with asymptotic-preserving multilevel Monte Carlo. SIAM Journal on Scientific Computing 45(4), pp. A1862 -- A1889. (2023)

If you find this code useful for your work, please consider citing the relevant articles.