MA5251 ----- Spectral Methods and Applications

(Semester 2 2015/16)


Lecturer: Weizhu Bao

Office: S17 #08-18

Office Hours: Tuesday, 2:00am -- 3:30pm or by appointment at S17 #08-18.

Phone: 6516-2765(o); E-mail: matbaowz@nus.edu.sg

Course Web: http://www.math.nus.edu.sg/~bao/teach/ma5251/ma5251.html


Lecture time/venue: Tuesday, 4:00pm -- 6:00pm; and Friday, 4:00pm--6:00pm at S17 #04-04.


Textbooks:

  • Spectral Methods: Algorithms, Analysis and Applications (2011), by J. Shen, T. Tang and L. L. Wang. Publisher: Springer.
  • Spectral Methods: Fundamentals in Single Domains (2006), by C. Canuto, M.Y. Hussaini, A. Quarteroni and T.A. Zang. Publisher: Springer-Verlag.
  • Spectral Methods: Evolution to Complex Geometries and Applications to Fluid Dynamics (2007), by C. Canuto, M.Y. Hussaini, A. Quarteroni and T.A. Zang. Publisher: Springer-Verlag.
  • Spectral Methods in Matlab (2000), by L.N. Trefethen. Publisher: SIAM (Socity of Industrial and Applied Mathematics).

    Reference Book :


    Course Outline: This module is designed for graduate students in mathematics and/or applied sciences as well as engineering. It focuses on some basic theoretical results on spectral approximations as well as practical algorithms for implementing spectral methods. It will specially emphasize on how to design efficient and accurate spectral algorithms for solving PDEs of current interest.
    Major topics covered include: Fourier-spectral methods, basic results for polynomial approximations, Galerkin and collocation methods using Legendre and Chebyshev polynomials, fast elliptic solvers using the spectral method and applications to various PDEs of current interest. Detail Outline


    Grading: The course grade will be calculated as follows:

    Schedule of tests:

    Homework Assignments: click here for assignments


    This course outline is available on web site: http://www.math.nus.edu.sg/~bao/teach/ma5251/ma5251.html