Numerical Methods for Partial Differential Equations

CS555 :: Spring 2023

• Class Time: Monday/Wednesday 11:00am-12:15pm Catalog
• Class Location: 1035 Campus Instructional Facility (CIF)
• Class URL: go.illinois.edu/cs555
• Slack: cs555-s23
• Instructor: Luke Olson
• Teaching Assistant: Alexey Voronin
• Office Hours: Fill out time poll to help determine OH times.

About the Course

Are you interested in the numerical approximation of solutions to partial differential equations? Then this course is for you!

The course covers roughly three topics: the fundamentals of finite difference approximations, an introduction to finite volume schemes, and comprehensive look at finite element methods.

The course involves several assignments (usually bi-weekly) and a final project that we develop over the semester, culminating in a presentation. There is also a strong participation grade based on handouts and other in-class tasks. The tentative grade breakdown is:

• Homework 50
• Final Project 30
• Quizzes and handouts 20

This will be finalized in the first week of class.

The course assignments and examples in class will be in Python.

Lectures

Lecture	Date	Topic
	01-18	About the course, classifying PDEs, survey of methods Book Chapter 1 notes-0118.pdf
	01-23	Finite differencing for time dependent problems Book Sections 2.2, 3.1, 3.3, 5.1-5.3 05-advection-1d.ipynb  notes-0123.pdf
	01-25	Convergence theory, Stability Book Sections 5.1-5.3 notes-0125.pdf
	01-30	Stabilty, dispersion, and dissipation Book Sections 5.1-5.4 05-advection-ETBS-LW.ipynb

Homework

• Homework 1, Due Wednesday February 8, 6pm.

Guidelines and files

• final-template.tex
• siamart171218.cls
• siamplain.bst
• final-guidelines.pdf
• all homeworks should be typeset in LaTeX. For a template you may start with homework-netid-N.tex.

Books

Computing

We will be using Python with the libraries numpy, scipy and matplotlib for assignments. No other languages are permitted.

Python and Numpy Help

• Python tutorial
• Facts and myths about Python names and values
• Dive into Python 3
• Introduction to Python for Science
• The SciPy lectures
• The Numpy MedKit by Stéfan van der Walt
• The Numpy User Guide by Travis Oliphant
• Numpy/Scipy documentation
• More in this reddit thread
• An introduction to Numpy and SciPy
• 100 Numpy exercises

COVID and Attendance

While face coverings are not required in classrooms (current as of 01/17) we fully support your decision to wear one if you wish.

If you test positive for COVID, then you should not attend class.

If you have any cold-like symptoms or do not feel well, then you should not attend class, regardless of testing negative or positive for COVID.

In either case, your missed attendance due to illness will not impact your grade in the course and we will work with you to cover the material missed in class (via Zoom).