Computer Modelling and Simulation, January-May 2018

When Q Slot; Mondays 8PM to 10:30PM
Where HSB 266

Instructor

Sivaram Ambikasaran,
Office: HSB 241C
Office hours: 9:30 AM to 11:30 AM, Mondays.

Syllabus

The course will broadly cover three topics:
• Spectral method
• Finite Element method
• Finite Volume method
Programming will form a significant part of the course.

Textbooks

Lecture notes will be posted as and when needed. The material covered will be predominantly from the following books.
• Spectral Methods in MATLAB, by Lloyd N. Trefethen
• Introduction to Finite and Spectral Element Methods using MATLAB, C. Pozrikidis
• Finite Volume Methods for Hyperbolic Problems, by Randall J. Leveque

 Evaluation Homework Quiz Project Points 65 10 25

Homework

There will be a total of $$13$$ homework (each worth 5 points) due roughly weekly. Homework will be posted on this website and will be Monday before 5 PM. Late homework will not be accepted. The homework will involve fair amount of programming exercises. Students are strongly encouraged to typeset their solutions using LaTeX/TeX ($$10$$% bonus points for submitting in LaTeX/TeX).

To save trees and keep track of submission on time, students need to send their homework through email to with the subject reading 2018_CMS_HW_#_firstname, where # needs to be replaced with the homework number (between $$1$$ and $$13$$) and firstname is to be replaced with your first name in lower case. Details on how to submit the computing part of the homework will be elaborated in the homework itself. No collaboration is allowed for homework.

The grader will expect you to express your ideas clearly, legibly, and completely, often requiring complete English sentences rather than merely just a long string of equations or unconnected mathematical expressions. This means you could lose points for poorly written proofs or answers. Clear exposition is a crucial ingredient of communication. Clarity of thought and presentation is more important in mathematics & sciences than any other field. The only way to master exposition is by repeated practicing.

$$\LaTeX$$

If you don't have $$\LaTeX$$ on your system, try any of the following online ones.
• https://www.sharelatex.com/
• https://www.overleaf.com/

Computational requirement

Each homework will have a good share of computational exercises. Students must be comfortable with programming and are expected to be comfortable with MATLAB and must have working knowledge in C++/Fortran. If not, they should be able to learn and immediately pick it up.

Quiz

There will be a short surprize (3-5 minutes) quiz once in a while and will account for $$10\%$$ of your total grade.

Project

This could be a work arising out a published article or from material/discussions in class. The project is due April 30th. More details will be provided by the middle of February.

Calendar

Below is a very rough calendar, which will be updated as we progress through the course.
 Week Monday/Tuesday Homework Jan 16: Lecture 1 Floating point arithmetic, Numerical Linear Algebra, Finite Difference, Interpolation Homework 1: Jan 29 Feb 4: Lecture 2 Spectral Methods: Chapter 1, 2, 3 of Trefethen Homework 2: Feb 12 Feb 12: Lecture 3 Spectral Methods: Chapter 4, 5, 6 of Trefethen Homework 3: Feb 19 Feb 19: Lecture 4 Spectral Methods: Chapter 7, 8, 9, 10 of Trefethen Homework 4: Feb 26 Feb 26: Lecture 5 Quadrature; Euler Maclaurin Homework 5: Mar 5 Mar 13: Lecture 6 Finite Element Methods: Chapter 1 of Pozrikidis Homework 6: Mar 19 Mar 26: Lecture 7 Finite Element Methods: Chapter 2 of Pozrikidis Homework 7: Apr 2; RK4 Apr 2 & 3: Lecture 8 & 9 Iterative methods for solving linear systems Homework 8: Apr 9 Apr 9 & 10: Lecture 10 & 11 Boundary Integral Method Representation of solution using Green's function Homework 9: Apr 16 Apr 16 & 17: Lecture 12 & 13 Fast solvers for Boundary Integral Method Gerenalized Rybicki Press Low Rank Direct solver Homework 10: Apr 25 Apr 23: Lecture 14 Finite Volume Method Homework 11: Apr 30 Project: Apr 30