Instructor: Dr. Bartosz Protas
Office: HH 326, Ext. 24116
Office hours: 13:30-14:30 on Tuesdays and 14:30-15:30 on Thursdays
Teaching Assistant: N/A
Announcements:
None to dateOutline of the Course:
Following a review of the Green's function formalism for differential equations, we will show that a variety of continuous problems in physics and engineering (fluid & solid mechanics, plasma physics, etc.) may be reduced to a system of N interacting "particles", the so-called "N-body problem". We will then discuss various computational aspects of this problem, including kernel regularization techniques, modeling diffusive effects, conservation proprieties and acceleration strategies (different particle-mesh and multipole expansion methods). These ideas will be illustrated with MATLAB codes that will be developed and analyzed during the lectures.Topics:
Dates |
Topics |
Oct 24 - Oct 25 |
particle systems, Lagrangian vs.~Eulerian representation of continuous systems |
Oct 31 |
N-body problems |
Nov 1 |
regularization (smoothing) |
Nov 7 - Nov 8 |
particle-particle, particle-mesh and particle-particle-particle-mesh methods |
Nov 14 |
fast mutipole methods |
Nov 15 |
conservation properties & symplectic integrators |
Nov 21 - Nov 22 |
deterministic & stochastic representation of diffusive effects |
Nov 28 |
vortex methods in hydrodynamics |
Nov 29 |
wrap-up |
Course Objectives:
By the end of the course students should be able to develop and implement a particle method for relevant problems encountered in science and engineering.Supplemental Reference:
Software:
All of the computational examples will be presented using MATLAB. Students are encouraged to purchasePrerequisites:
Partial Differential Equations, Introductory Numerical Analysis and Numerical Algebra, basic programming skills in MATLABAssignment:
There will be one homework assignment which will be posted on November 21 and will be due on November 28 by midnight. Solution to the assignments should be submitted to the instructor via E-mail using the template provided. The solutions will be posted on the course webpage.Class Quiz:
There will be one in-class quiz on November 15. It will last 50 minutes. The quiz will cover analytical issues only (no programming). Only the McMaster standard calculator Casio fx-991 will be allowed during the quiz.Final Exam:
The course will be completed by a take-home final examination. It will be handed out during the last class on November 29 and will be due on December 3 (hour TBA).Marking Scheme:
Excused Absences:
Exemptions from the assignment or quiz for valid reasons are possible, but must be requested from the instructor. In the event of an exemption, no make up test or assignment will be administered, but your course grade will be re-weighted by increasing the weight of the final examination to compensate for the missed test or assignment.Academic Integrity:
You are expected to exhibit honesty and use ethical behaviour in all aspects of the learning process. Academic credentials you earn are rooted in principles of honesty and academic integrity.Important Notice:
The instructor reserves the right to modify elements of the course and will notify students accordingly (in class and post any changes to the course website).