Topics in Computational Science and Engineering
No class on: M Jan/10, W Jan/12, M Feb/17
Term: Spring 2005
Course: ENM 540
Day/Time: Mondays & Wednesdays 1:303:00 PM
Location: Towne 309
Office hours: Drop by or send email to schedule an appointment
Instructor
George Biros
email:
biros@seas.upenn.edu
Class description
Various topics in fast algorithms for computational science will be
covered each year. Emphasis will be given on techniques that can be
used for discretization and computational solution of partial
differential equations.
Examples: Multigrid and multiresolution methods for partial
differential equations; fast numerical linear and nonlinear algebra;
Krylov methods; inexact nonlinear solvers; domain decomposition
methods; computational approximation theory; fast algorithms in
signal processing; computational harmonic analysis; numerical
methods for integral equations; fast summation methods; level sets
for problems with dynamic interfaces; spectral methods; meshfree
methods; adaptivity.
Grading
Homeworks (80%) and final project (20%).
Recommended texts (Spring 2005)

Iterative methods for sparse linear systems
Y. Saad
online

A Multigrid Tutorial, Second Edition
W. L. Briggs, V. E. Henson, S. F. McCormick

Finite elements: an introduction (out of print)
E. B. Becker, G. F. Carey, and J. T. Oden. v.1

A wavelet tour of signal processing
S. Mallat

Level Set Methods and Fast Marching Methods
J. Sethian
Topics (Spring 2005)
 Introductory notes
Complexity analysis in Scientific Computing
Review of Finite Element/Finite Difference methods for elliptic PDEs
Krylov iterative methods and preconditioning
Nonlinear solvers
 Multiresolution algorithms
Error estimation for FEM and FDM for elliptic PDEs
Adaptive algorithms
Multigrid methods
Wavelets for PDEs
Nonequispaced Fast Fourier Transform
 Level set methods (time permitting)
Numerical methods for hyperbolic PDEs
Narrow band and fast marching methods
Prerequisites
Numerical analysis, basic theory of ordinary
and partial differential equations