Instructor:
Andrei Draganescu
Office: MP420
Phone: 410-455-3237
Email: draga@math.umbc.edu
Website: http://www.math.umbc.edu/~draga/courses/2008/Fall/math710
Office hours:
MW 4 - 5 pm, or by appointment.
Prerequisites:
MATH 620, Math 630 or instructor's consent; Math 621, Math 635 are
recommended.
Texts (recommended):
[1] Iterative Methods for Solving Linear Systems, by Anne Greenbaum, SIAM, 1997.
[2] Finite Elements and Fast Iterative Solvers, by Howard Elman, David Sylvester, and Andy Wathen,
Oxford University Press, 2005.
[3] A Multigrid Tutorial, by William
Briggs, Van Emden Henson, and Steve McCormick, second edition,
SIAM, 2000.
[4] Domain Decomposition, by Barry
Smith, Petter Bjorstad, and William Gropp, Cambridge University
Press, 1996.
Course objectives:
The main goal of this course is to introduce students to modern
techniques for solving large-scale linear systems associated with
partial differential equations. At the end students are expected to
(a) know the basics about the most common iterative schemes and
preconditioning techniques for solving various types of linear
systems, (b) learn specific language to the level needed for reading
a technical paper and for following a talk in the field, and (c)
develop a taste for the subject in order to be able, if desired, to
select a related research topic.
Content:
The course will begin with the presentation of three model problems
that motivate the use of iterative methods: Poisson's equation,
convection-diffusion equations, and integral equations (inverse
problems). The first part of the course will follow closely [1] and
will be devoted to commonly used iterative schemes (simple
iteration, conjugate gradient, MINRES, GMRES, BICG). In the second
part preconditioning techniques will be presented with focus on
multigrid [3] and, possibly, domain decomposition [4], both of which
play critical roles in the numerical treatment of (some of) the
model problems as shown in [2]. Emphasis will be placed both on
mathematical analysis and numerical experimentation using Matlab or
C/C++.
Homework and projects: The course assignments will be comprised of homework and two projects. Project themes and deadlines will be announced later.
Grading policy:
Homework - 30%,
Project 1 - 30 %,
Project 2 - 40%
| Score above | 90% | 80% | 65% | 50 % | otherwise |
| Letter grade | A | B | C | D | F |