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 reduced order methods 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 quizzes, homeworks (usually bi-weekly) and a final project.
Grading is based on quizzes, team homeworks (roughly bi-weekly) and a final project. The grade breakdown is:
- Homeworks (50) - Projects (25) - Participation/ Quizzes (25)
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.