APPM 6640, Section 001, Spring 2013, 3 Credits

MULTIGRID METHODS

Lectures:   Mondays & Wednesdays 10:00-10:50 pm, ECCR 1b51
Computer Lab:   Mondays 12:00-12:50 pm, ECCR 143

Prerequisite: Permission of the instructors.


Instructors: Steve McCormick, Toby Jones, Chris Leibs

Email: Steve McCormick, Toby Jones, Chris Leibs

Phone: 2-0662 (but it's better to use email!)


Office Hours in Newton Lab (ECCR 257)
11:00-11:50 Mondays & 9:00-9:50 Wednesdays, Others TBA


Course Slides in Apple Keynote Format (~40 MB) or PDF Format (~27 MB)

Course Slides in 4-Slides-Per-Page PDF Format (~18 MB; useful for in-class note taking)

Additional slides on smoothed aggregation in Apple Keynote Format (~7 MB)

Additional slides on smoothed aggregation in PDF Format (~2.4 MB)

Text: A Multigrid Tutorial, Second Edition, by W. L. Briggs, V. E. Henson, and S. McCormick, SIAM Books, Philadelphia, June, 2000.

Text Corrections: For corrections to the textbook, see the list of errata in pdf format or the textbook with red edits in pdf format.

Introductory Article: For a good introduction to multigrid methods, see the excellent article by Irad Yavneh of Technion, Israel.

Computer Lab

Homework & Project


Special note: Students whose schedules permit will be encouraged to attend all or part of the 16th Copper Mountain Conference on Multigrid Methods, March 17-22, 2013, especially the tutorials on Sunday, March 17, if they occur. Free registration and lodging in the form of shared condominiums will be available for the days of attendance provided this is arranged well in advance.

Overview

The development of modern multigrid methods for solving partial differential equations began in the 70's, but has become a widely used tool only fairly recently. It began as a general fast elliptic solver (some claim it's the fastest for many problems), but has now expanded into many areas of application, some of which include such diverse areas as aerodynamics, astrophysics, chemistry, electromagnetics, hydrology, medical imaging, meteorology/oceanography, quantum mechanics, and statistical physics. The purpose of this course is to develop a fundamental understanding of the principles and techniques of the multigrid methodology, beginning with a basic foundation on iterative methods in general, smoothers in particular, and elliptic multigrid solvers. This first part will be based on the first five chapters of the second edition of the monograph A Multigrid Tutorial by W. Briggs, V. Henson, and S. McCormick.

The rest of the course will be based in part on the remaining five chapters of the monograph. It will develop more sophisticated multigrid methodologies and algorithms, and these will be applied to a more diverse collection of problems. Some of the course work will be tailored to student interests.

These lectures will be based the monograph supplemented by a collection of notes and other research materials. In lieu of tests, there will be several projects, starting with common assignments involving basic and more advanced multigrid schemes, then culminating in individual efforts submitted and presented by the students at the end of the term.

Outline

I. Basic Tutorial: model problems, basic iterative methods, elements of multigrid, implementation, and some theory.

II. Advanced Tutorial: nonlinear problems, selected applications (Neumann boundary value, anisotropic, variable-mesh, and variable-coefficient problems), algebraic multigrid (AMG), multilevel adaptive methods, and finite elements.

III. Computation: error measures, performance measures, programming strategies, simple programming aids, and some development tips.

IV. Applications tailored to student interests.