Jay Gopalakrishnan

SEC 156

Tue, Thu: 17:15 - 18:30

Tue 13:15 - 14:15 (in NH 309) or by appointment.

The course aims to introduce mathematically oriented graduate students to multigrid solvers in a geometric multilevel setting. (Multigrid solvers are one of the most efficient solvers available today for the numerical solution of certain partial differential equations.)

Consent of the instructor.

We will begin with a brief discussion of the conjugate gradient method as an iterative solver and how preconditioners help us solve problems that are otherwise intractable.

We then proceed to auxiliary space preconditioners, the fictitious space lemma of Nepomnyaschikh, and the XZ identity.

Next, we introduce the additive multilevel BPX preconditioner, the multiplicative multilevel V-cycle algorithm, and a range of convergence theorems like the Braess-Hackbusch theorem.

Click here for class notes/diary.

There is no textbook. However, these references will be useful:

• Bramble, `Multigrid Methods,' 1993.
• Hackbusch, `Multi-Grid Methods and Applications,' 1985.
• Briggs, Henson, and McCormick, `A Multigrid Tutorial, 2nd Edition,' SIAM publications, 2000.

Course materials will be available at the course D2L page.

Grades will be assigned based on class projects.