Particle Methods

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 particle-based simulations of both continuous and discrete systems.


particle methods for continuous systems, particle methods for discrete systems, time stepping schemes for particle methods, efficient data structures, efficient neighbor-finding algorithms, discretizing differential operators on particles, hybrid particle-mesh methods.

Summer Term 2021

Lecture: Wednesdays, 3. DS (11:10-12:40), location to be announced. NO LECTURES ON: MAY 5 (dies academicus), MAY 26, JUNE 2, JUNE 30
Exercises: Wednesdays, 1. DS (07:30-09:00), location to be announced. NO TUTORIAL IN THE FIRST WEEK. First tutorial on April 21, 2021

Programs / Modules

M.Sc. Computational Modeling and Simulation, Modules: CMS-CLS-ELG, CMS-CMA-ELV1, CMS-CMA-ELV2, CMS-VC-ELV1, CMS-VC-ELV2

M.Sc./Diplom Computer Science, Module: INF-VERT7

M.Sc. Distributed Systems Engineering, Modules: DSE-14-E13, DSE-14-E14


2 SWS lecture, 2 SWS exercise, self-study

Registration to the course

For students of the Master program Computational Modeling and Simulation: via CampusNet SELMA

For students of other degree programs: via your respective study or examination office


Lecture: Prof. Ivo F. Sbalzarini
Exercises: Dr. Sachin Krishnan

Exam 2020

Date/Time: 31. July 2020, 7:30h - 9:00h

Place: HSZ/AUDI/H, Hörsaalzentrum, room Audimax

Format: written
Duration: 90 minutes

Persons who tested positive for Sars-Cov-2 or are experiencing Covid-19-like symptoms are not admitted to the exam. Distancing of 1,5m min is mandatory. All signs are must be strictly followed. The Covid-19 hygiene regulations for written exams at TU Dresden must be strictly followed.
At the exam, the following may be used:
  • 4 A4 sheets (8 pages if you print duplex) of hand-written summary. We recommend writing the summary by hand, but it can also be machine-written. In the latter case, the font size must be 8 points or larger throughout.
  • A standard pocket calculator (devices with network or bluetooth access, as well as devices capable of storing and displaying documents are not allowed)
Items not adhering to these guidelines will be confiscated in their entirety at the beginning of the exam.

Grade scale:

All exams are graded in absolute terms w.r.t. the following pre-defined grade scale that remains constant over the years:

  • The top grade of 1.0 is reached with 80% of the maximum possible points
  • Half of that, i.e., 40% of the maximum possible points, are required to pass
  • Below 40%, or no-show, is a fail.
Between the top grade and the passing threshold, the grading scale is linear. In the end, grades are rounded to the nearest allowed grade according to the exam regulations: 1.0, 1.3, 1.7, 2.0, 2.3, 2.7, 3.0, 3.3, 3.7, 4.0, 5.0. The grades 0.7, 4.3, and 4.7 are not allowed. Any grade above 4.1 is a fail (see exam regulations). The maximum number of points that can be reached in the exam is given by the number of minutes the exam lasts (i.e., a 90 minute exam yields maximum 90 points). Points are distributed amongst the exam questions to reflect the number of minutes a good student would need to solve the problem. This provides some guidance for your time management in the exam. In order to reduce the risk of correction mistakes, all exams are checked by at least two independent, qualified assessors (typically professors or teaches with officially conferred examination rights). The exam review session (see below) is for you to come look at your exam paper and report correction mistakes you found.

Registration to the exam

For students of the Master program Computational Modeling and Simulation: via CampusNet SELMA

For students of other degree programs: via your respective examination office

Exam Review 2020

You can come and look at your exam, and ask questions about its correction and the answers given during the exam review times. In order to accommodate for everyone's schedule, we offer three exam review dates at different times:

  • October 12, 2020, 2pm CANCELED DUE TO RAIN. NEW DATE: October 19, 2020, 10am
  • October 27, 10am
  • November 4, 4pm

Location for all exam reviews: Outdoors in the seating area in front of the Center for Systems Biology Dresden, Pfotenhauerstr. 108 (yellow building) (Maps Link). The review only takes place if there is no rain. In case of rain, a new date will be found. In order to participate, You MUST wear a face mask and you are only allowed to come forward one by one.

IMPORTANT: All students attending an exam review must fill in and sign the exam review form they are going to receive during the review. Undocumented exam reviews are not permitted.

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 short-range 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 item-based models with stochastic dynamics; examples: population dynamics and chemical reactions
  • Lecture 6 - Particle methods for item-based 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 - DC-PSE as a unifying framework for field-based particle simulations
  • Lecture 10 - Eulerian and Lagrangian simulations of field-based models
  • Lecture 11 - Hybrid particle-mesh methods and particle-mesh interpolation

Full lecture notes can be found here.


The student project during the tutorials focuses on software engineering and on implementing a portable software library for particle-based simulations. Then, this library is used to perform different example simulation.