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 1:30--3:00 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
      Non-equispaced 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