This course covers the basics of finite difference schemes, finite volume schems, and finite element methods (majority). In addition, we'll cover some advanced topics such as discontinuous Galerkin and least-squares.
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), be comfortable with differential equations, and have some coding experience.
The course is divided in roughly 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 on finite volume methods and a final project on finite element methods. There is also a strong participation grade based on your attendence, in-class, and pre-class work.
The course homeworks and examples in class will be in Python. In particular, we'll use numpy, scipy, and Dolfin from the FEniCS Project.
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.
While you are free to install Python and Numpy on your own computer to do homework, the only supported way to do so is using the supplied virtual machine image.
The course involves several homeworks (roughly bi-weekly) and two projects, a midsemester project on finite volume methods and a final project on finite element methods. There is also a strong participation grade based on your participation (attendence through in-class activities) and several out-of-class, but smaller-than-homework assignments. The grade breakdown is:
- Homeworks (40) - Projects (40) - Participation (20)