Particle Methods as a General Framework for Computation and Simulation

Implementing complex simulations and algorithms tend to be very hard and time-consuming, especially when it comes to distributed computing. Particle Method based frameworks like the PPM (Parallel Particle Mesh) Library [1] or OpenFPM [2] (scalable open framework for HPC simulations using particles and meshes) can help in this process. The reason to use Particles is that they are known to be a universal numerical concept used form solving PDEs to simulating molecular dynamics. But until now, there has been no formal definition of particle methods. Hence, there was no formal proof of the universality.
In this talk, I will present the preliminary definition of Particle Methods, show how the Turing Powerfulness (the theoretical universality) can be proofed, and give practical examples to showcase the potential and limitations.

[1] I. F. Sbalzarini, J. H. Walther, M. Bergdorf, S. E. Hieber, E. M. Kotsalis, and P. Koumoutsakos. PPM - A Highly Efficient Parallel Particle-Mesh Library for the Simulation of Continuum Systems, Journal of Computational Physics 215(2):566-588, 2006.

[2] P. Incardona, A. Leo, Y. Zaluzhnyi, R. Ramaswamy, and I. F. Sbalzarini. OpenFPM: A scalable open framework for particle and particle-mesh codes on parallel computers. Comput. Phys. Commun., 241:155- 177, 2019.