Author Topic: Graduate course in Numerical Methods for PDEs  (Read 2358 times)

Victor Ivrii

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Graduate course in Numerical Methods for PDEs
« on: November 28, 2012, 06:22:44 PM »
Dear APM346 students,

Now that you've learnt about PDE, would you like to learn about how to simulate solutions of PDE?  That is, how to find (approximations of) the solutions using a computer and then learn something from that?

I'm teaching a first-year graduate course, Mat1062, next semester. "Introductory Numerical Methods for PDE".  To take it, you need to have
recently taken a PDE course and not be computer-phobic.  I'll use either matlab or python and will provide sample codes.  The course description is below.

http://www.math.toronto.edu/cms/tentative-2012-2013-graduate-courses-descriptions/#MAT1062HS

If your cgpa is 3.2 or higher then I think you can petition to sign up for the course.  Otherwise, you can take the course as a reading course.

It will meet Tuesdays 10:30-12:30 and Thursdays 11:30-12:30 in BA 6183.


sincerely,
Mary Pugh

We will study numerical methods for solving partial differential equations that commonly arise in physics and engineering. We will pay special attention to how numerical methods should be designed in a way that respects the mathematical structure of the equation.

Parabolic PDE w/ finite difference methods
- explicit and implicit discretizations in 1-d consistency, stability, and convergence in 1-d boundary conditions in 1-d multi-dimensional problems

Elliptic PDE
- variational formulations and finite element methods

Hyperbolic PDE
- CFL stabilty condition
- nonlinear conservation laws, shock capturing

Special topics
- pseudospectral methods

Prerequisites: 
You should be familiar with the material that would be taught in a serious undergraduate PDE course. Sample programs will be provided in matlab. If you know matlab, great! If you don't, you're expected to be sufficiently comfortable with computers that you can learn matlab on the fly. Which isn't actually hard at all, unless you hate computers.

References:
My lecture notes from Winter 2008 and Winter 2009 and likely "Numerical Methods for Evolutionary Differential Equations" by Uri Ascher or "Numerical Methods for Scientists and Engineers" by Hamming.