Spectral Methods and Applications, MA5251

News:

  • The project presentations will take place on Monday 14 November, at 14.00 in the seminar room
    at S17 #04-05 SR2. Each group have 20 minutes (15 minutes for the presentation and 5 minutes for questions).
    There are five groups in total.
  • Lecture notes from Lecture 4 updated. There was a typo in the Legendre formulas.
    Please, if you find something strange in a formula in the lecture notes, dubble check with
    any of the course books. You can find almost all formulas in the books. It is very easy to make a typo...
  • Information about the project is added under the heading "Homeworks and Project", below.
  • Second part added to Homework 2. Full Homework 2 is now available for download, see below.
  • Class on Monday 12/9/2011 CANCELED
  • First part of Homework 2 available for download, see below.
  • Updated course outline as of 26/9/11.

Helmholz equations Helmholz equations

    A solution to the inhomogeneous Helmholtz equation u_xx+u_yy+k^2u=-f(x,y) with u=0 on the boundary.
    The solution is computed using a spectral Chebyshev method.
The aim of this course is to present the essentials of spectral methods and related computer algorithms and to show how spectral methods can be used in different applications. It will specially emphasize on how to design efficient and accurate spectral algorithms for solving PDEs. The course consists of both mathematical theory as well as numerical algorithms and their implementation.

Lecturer:

Katarina Gustavsson
Office: S17, 0517
Office hours: Wednesday 3:00 pm-4:30 pm
Email: matgkv at nus.edu.sg

Schedule:

The lectures are scheduled for
  • Mondays 14:00-16:00 in S16-0430
  • Thursdays 14:00-16:00 in S16-0430
The first lecture will be on Thursday August 11, 2011.

Literature:

  • Spectral and High-Order Methods with Applications, Jie Shen and Tao Tang, Science Press, China, 2006
  • Spectral Methods in Matlab, Lloyd N. Trefethen, SIAM, USA, 2000
  • Spectral Methods, Fundamentals in single domains, C Canuto et al., Springer-Verlag, Berlin, 2006 (Can be found as electronic resource at NUS library.)
  • Spectral Methods, Evolution to complex geometries and applications to fluid dynamics, C Canuto et al., Springer-Verlag, Berlin, 2007 ( Can be found as electronic resource at NUS library.)

Course requirements:

The course consists of the following mandatory assignments
  • Homeworks (2 in total)
  • Project (to be done in groups of two)
  • Written examination
To pass the course, you have to pass the written examination, the homeworks and the project. The final grade of the course will be based on the sum of the credits on the homework (max 30) and the exam (max 30), i.e. a total max of 60 The grade of the project will be pass or fail.

Course outline:

A preliminary outline can be found here.

Lecture notes:

Lecture 1, 11/8/11
Lecture 2, 15/8/11
Lecture 3, 18/8/11
Lecture 4 (extended with two pages), 22/8/11. Page 7 updated 13/10/11.
Lecture 5, 25/8/11
Lecture 6 & 7, 29/8/11 and 1/9/11
Lecture 8, 5/9/11
Lecture 9, 8/9/11 Updated the last page, error fixed.
Lecture 10, 26/9/11
Lecture 11, 29/9/11
Lecture 11 (with correction on Galerkin-Legendre method), 29/9/11
Lecture 12 & 13 E-learning week 3/10/11-7/10/11.
Lecture 14, 10/10/11
Lecture 15, 13/10/11
Lecture 16, 17/10/11
Lecture 17, 20/10/11
Lecture 18, 24/10/11
How do you test your program

Homeworks and project:

  • Homework 1: Due 15/9-2011, 2pm. Written report and discussion in class.
  • Homework 2 (including part I): Due 27/10-2011, 2pm. Written report and discussion in class, as last time.
  • Information about the project is now available. Written report and oral presentation in class.
An introduction to MATLAB can be found here.