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.

Topic Prerequisites

Working knowledge of computer programming in any language (e.g. Matlab, Python, Java), basic knowledge of classical physics, and solid undergraduate knowledge in calculus and vector analysis.

Programs / Modules

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

Format

2 SWS lecture, 2 SWS exercise, self-study

Registration

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

Teachers

Lecture: Mr. Serhii Yaskovets, Dr. Nandu Gopan, Prof. Ivo F. Sbalzarini
Exercises: Philipp Helmut Suhrcke

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

Script

Full lecture notes can be found here.

Project

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.

Time/Place

Summer Term 2024

INTRO LECTURE ON APRIL 10, 2024

Lecture: Wednesdays, 3. DS (11:10-12:40), APB E/023.
Exercises: Fridays, 3. DS (11:10-12:40), APB E/009. NO TUTORIAL IN THE FIRST WEEK.
LECTURES AND EXERCISES WILL BE IN PRESENCE FOR THE WHOLE SEMESTER, BUT SUPPORTED WITH ONLINE VIDEO RECORDINGS

Link to the videos in OPAL: https://bildungsportal.sachsen.de/opal/auth/RepositoryEntry/33993129987

Exams

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 2023

You can come and look at your exam solutions and raise any concern that you might have with respect to the grading, IN PERSON on Friday 06/10/2023 (October 6th 2023) between 10:00 AM to 11:30 AM or on Monday 16/10/2023 (October 16th 2023) between 10:00 AM to 11:30 AM in the Seminar Room Ground Floor (CSBD SR Ground Floor) at the Center for Systems Biology Dresden (CSBD), Pfotenhauerstr. 108, Dresden (the yellow building) - (Maps Link).

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

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. Any transcripts, copies or photographs of examinations, examination protocols or other written examination papers made by the student in the course of this inspection or otherwise made available to the student are only for the purpose of personal use and to protect personal interests. Distribution of the same via the Internet or other media is not permitted.

Lecture

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