Particle Methods
This course teaches the foundations of Particle Methods. Particle methods are a numerical simulation framework that allows simulating both discrete and continuous systems. Particles can represent agents, such as cars in a traffic simulation, or mathematical discretization points, such as when numerically solving differential equations. Particle methods are the most versatile simulation framework and indeed the only one that allows seamless treatment of all types of models using the same algorithms and data structures. After this course, you will be able to implement and use particlebased simulations of both continuous and discrete systems.
Contents
particle methods for continuous systems, particle methods for discrete systems, time stepping schemes for particle methods, efficient data structures, efficient neighborfinding algorithms, discretizing differential operators on particles, hybrid particlemesh methods.
Time/Place
Lecture: Mondays, 3. DS (11:1012:40) in APB2026 (computer science building) / FIRST LECTURE: OCT 17
Exercises: upon agreement
Teachers
Lecture: Prof. Ivo F. Sbalzarini
Exercises: Pietro Incardona
Learning goals

Know efficient data structures and algorithms for particle methods

Software engineering and abstractions for particle simulations

Practical implementation of particle methods for discrete and continuous models
Lecture language: ENGLISH
Please find below the lecture syllabus and the handouts:
 Lecture 1  Administration and Introduction: what is modeling and simulation? What are particle methods?
 Lecture 2  Efficient data structures for shortrange interactions: cell lists and Verlet lists
 Lecture 3  Time stepping algorithms: explicit and implicit
 Lecture 4  Error and stability of time stepping
 Lecture 5  Particle methods for itembased models with stochastic dynamics; examples: population dynamics and chemical reactions
 Lecture 6  Particle methods for itembased models with deterministic dynamics; example: granular flows and molecular dynamics
 Lecture 7  Discretizing differential operators on particles: Smooth Particle Hydrodynamics
 Lecture 8  Discretizing differential operators on particles: Particle Strength Exchange
 Lecture 9  DCPSE as a unifying framework for fieldbased particle simulations
 Lecture 10  Eulerian simulations of fieldbased models
 Lecture 11  Lagrangian simulations of fieldbased models
 Lecture 12  Hybrid particlemesh methods and particlemesh interpolation
 Lecture 13  Q & A / Student project presentations
Full lecture notes will be provided to the students of the course.
Project
The student project during the tutorials focuses on software engineering and on implementing a portable software library for particlebased simulations. Then, this library is used to perform different example simulation.