MTH 610: Geometric Multilevel Methods

Fall 2014

Jay Gopalakrishnan
SEC 156
Tue, Thu: 17:15 - 18:30
Office Hours
Tue 13:15 - 14:15 (in NH 309) or by appointment.

Course Objective

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.

Technical Outline

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.

Diary of results discussed daily

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.

Jay Gopalakrishnan