Math 801: Fall 2000
Selected Problems in Scientific Computing
Fabian Waleffe
Day |
Time |
Place |
TR |
2:30-3:45pm |
B231 Van Vleck Hall |
Math 801 meets with CS/Math 713 exceptionally in Fall 2000.
Which course should you register for?
Office hours: by appointment.
Homework and Problem sets
Demos
REFERENCES: (no textbook required, "A Multigrid tutorial" is very readable)
- Numerical methods for bifurcations of dynamical equilibria,
Willy Govaerts, SIAM 2000 (order code: OT66, list price $61.00)
- Iterative methods for solving linear systems, Anne Greenbaum,
SIAM 1997 (order code: FR17, list price $44.00)
- A Multigrid tutorial, 2nd Edition,
William Briggs, Van Emden Henson,
Steve McCormick, SIAM 2000 (order code: OT72, list price $39.00)
- Templates for iterative methods.
You can purchase these books
online from SIAM .
You may want to
become a student member of SIAM first as this entitles you to
a 20% discount on list prices. Student membership dues is $23 for 1.5 years,
not bad and you receive SIAM news every month.
Other good general references on numerical linear algebra (including iterative
methods) are :
- Matrix Computations, Gene H. Golub, Charles F. Van Loan,
Johns Hopkins Press 1996 (3rd edition) (ON RESERVE QA 188 G65 1996)
- Applied Numerical Linear Algebra, James W. Demmel,
SIAM 1997 (QA 184 D455 1997)
- Numerical Linear Algebra, Lloyd N. Trefethen, David Bau III,
SIAM 1997 (QA 184 T74 1997)
Prerequisites
Advanced Calculus (through Math 321 at least), Linear Algebra (e.g. Math 340),
general physics and chemistry, elementary numerical methods (e.g. CS 412),
familiarity with Matlab or a programming language (e.g. Fortran, C, C++,...).
Description
A complete look at the mathematical, scientific
and computational aspects of a few problems in scientific computing.
Selected problems may be tuned to students' research needs and interests.
The proposed outline for Fall 2000 is
- Numerical methods for nonlinear equations motivated by
calculations of equilibria and bifurcations of equilibria;
Newton and related methods; Homotopy and Continuation;
- Iterative methods for large linear systems (conjugate gradients,
BICG, QMR, GMRES, BCGS,...) featuring lectures by Noel Nachtigal, LLNL, one
of the developers of QMR.
- Multigrid methods
- Fast multipole methods
Future offerings of this course may cover:
- Level set and volume-of-fluid methods for interface tracking;
- Nonlinear optimization, including methods for functions with many
local extrema.
Grading
There will be at least 5 homeworks requiring programming and 2 in-class exams. NO FINAL.