Numerical Methods for Partial Differential Equations
CS555 :: Spring 2019
- Class Time/Place: Wednesday/Friday 11:00am-12:15pm Catalog, 1304 Siebel Center
- Class URL: https://relate.cs.illinois.edu/course/cs555-s19/
- Instructor: Paul Fischer, Office Hours: Monday 12:30-3:30 p.m., Siebel 4320
- TA: Shelby Lockhart, Office Hours: Tuesday/ Thursday 9-10 a.m., Siebel 0207
About the course
This course covers the basics of finite difference schemes, finite volume schemes, and finite element methods (majority). In addition, we'll cover some advanced topics such as discontinuous Galerkin and spectral methods.
One of the goals of this course is to build intuition for these methods. We'll be using Python and will be providing background for many of the computational and mathematical concepts in the course. As such, you do not need to be an expert in PDEs or in coding. But you should have a course in numerical analysis as your background (CS450 or equivalent), be comfortable with differential equations, and have some coding experience.
The course is divided in roughly two parts: advection and elliptic. This is of course a generalization, but it does allow us to focus on finite difference/finite volume methods for one part of the course and finite elements for another part. In addition to model problems we'll look at Stokes and other equations in order to develop a full understanding of the methods.
The course involves several homeworks (usually bi-weekly) and two projects: a midsemester project and a final project. There is also a participation grade based on quizzes.
The course homeworks and examples in class will be in Python. In particular, we'll use numpy and scipy. (Some early examples will be in Matlab.)
- Quiz 1 Due Friday, January 18 at 5 p.m.
- Quiz 2 Due Monday, January 28 at 5 p.m. Solution
- Quiz 3 Due Friday, February 15 at 5 p.m. Solution
- Quiz 4 Due Wednesday, March 13 at 5 p.m. Solution
- Quiz 5 Due Wednesday, March 27 at 5 p.m. Solution
- Quiz 6 Due Wednesday, April 3 at 5 p.m. Solution
- Quiz 7 Due Wednesday, April 17 at 5 p.m.
- Quiz 8 Due Wednesday, April 26 at 5 p.m. Solution
The course involves several homeworks (roughly bi-weekly) and two projects, a midsemester project and a final project. There is also a strong participation grade based on quizzes. The grade breakdown is:
- Homeworks (65) - Projects (20) - Participation/ Quizzes (15)
We will be using Python with the libraries numpy, scipy and matplotlib for assignments. No other languages are permitted. Python has a very gentle learning curve, so you should feel at home even if you've never done any work in Python.
Python and Numpy Help
- Python tutorial
- Facts and myths about Python names and values
- Dive into Python 3
- Project Euler (Lots of practice problems)
- Introduction to Python for Science
- The SciPy lectures
- The Numpy MedKit by StÃ©fan van der Walt
- The Numpy User Guide by Travis Oliphant
- Numpy/Scipy documentation
- More in this reddit thread
- Spyder (a Python IDE, like Matlab) is installed in the virtual machine. (Applications Menu > Development > Spyder)
- An introduction to Numpy and SciPy
- 100 Numpy exercises
- Homework 1 Due Tuesday, February 5 at 6 p.m. Example starting code: .ipynb, .py Solution Solution Notebook
- Homework 2 Due Tuesday, March 5 at 5 p.m. Q1 ipynb Q2-Q3 ipynb Q4 ipynb Q6 ipynb Solution
- Homework 3 Due Friday, March 15 at 6 p.m. Starting code: .ipynb html Q1 ipynb Solution
- Homework 4 Due Friday, April 12 at 11:59 p.m. Q1 ipynb
- Homework 5 Due Wednesday, April 24 at 6 p.m. Case 1 Case 2 Case 3 Case 4 Solution