Department of Mathematical Sciences, UWM

Lecture Time and Place

      4:00 PM - 4:50 PM, Tuesday and Thursday, EMS Room E425

Instructor

  Dr. Dexuan Xie
  Office: EMS-489
  Telephone:   (414) 229-3528
  E-mail: dxie@csd.uwm.edu
  Homepage:   http://www.uwm.edu/~dxie/
  Office Hours:    3:00 PM - 4:30 PM, Tuesday and Thursday.

Textbook

       A Multigrid Tutorial, William L. Briggs, Van Emden Henson and Steve F. McCormick,SIAM, 2nd Edition, 2000.

Course Overview

     The main purpose of the course is to improve students' understanding to the numerical methodology, computer implementation, and application of scientific computing. The course will focus on the multigrid method, one of  the fastest algorithms for solving partial differential equations. It then will introduce a new standard in Computational Mathematical Modeling, FEniCS ( http://www.fenics.org/). In particular, the class will study a light-weight version of FEniCS written for MATLAB, called  Puffin (http://www.fenics.org/puffin/), and the C++ interface of FEniCS, called Dolfin (http://www.fenics.org/dolfin/). Along with the studying of these two packages, basic programming techniques by MATLAB and C++ programming languages will be discussed. In the end of the course, each student is required to complete a scientific computing project and present it in class.

Prerequisite

      Math 413, Math 715 (Numerical Analysis), or consult to the instructor.

Course Online Tutorial

•  Multigrid Methods
  • Tutorial slides of multigrid methods:  http://www.llnl.gov/casc/people/henson/mgtut/welcome.html.
  • Uli Rüde's Multigrid Workbench: http://www.mgnet.org/mgnet/tutorials/xwb.html.
  • A Matlab program of multigrid method: MGLab. This is a public domain set of Matlab functions written by James Bordner and Faisal Saied. MGLab is an interactive environment for experimenting with multigrid algorithms. MGLab can solve two dimensional elliptic partial differential equations using finite differences and includes several built-in problems (Poisson, Helmholtz, discontinuous coefficient problems, and nonselfadjoint problems). A number of parameters controlling the V cycle can be set using a point and click mechanism. The menu based user interface also allows a choice of several Krylov subspace accelerators (PCG, GMRES(k), and BiCGSTAB). The package exploits Matlab's visualization and sparse matrix features. It has also been structured to be extensible.
•  FEniCS
  •      Puffin User Manual: http://www.fenics.org/pub/documents/puffin/puffin-user-manual/puffin-user-manual.pdf
  •      Dolfin User Manual: http://www.fenics.org/pub/documents/dolfin/dolfin-user-manual/dolfin-user-manual.pdf
  •      Preprint: DOLFIN - Dynamic Object oriented Library for FINite element computation
  •      FEniCS Project Introduction presentations:
    • By Anders Logg: Automating the finite element method at http://www.fenics.org/pub/documents/fenics/presentations/logg-simula-2005-08-23-1.pdf;
    • By Ridgway Scott: The FEniCS project at http://www.fenics.org/pub/documents/fenics/presentations/scott-iowa-2005-05-21.pdf;
    • By Claes Johnson: The FEniCS project at http://www.fenics.org/pub/documents/fenics/presentations/scott-iowa-2005-05-21.pdf;
•  Matlab programming
  • Matlab demos
  • A Very Elementary MATLAB Tutorial from the MathWorks web site.
  • Hypertext reference from Portland State University (55 pages)
  • 3-day MATLAB Tutorial from MIT (25 pages)
  • MATLAB educational resources on the web including tutorials and teaching examples.
  • Matlab Central for Matlab program files exchange. It contains hundreds of Matlab program files contributed by users and developers of MATLAB and related products.
  • The MathTools.Net web site contains many pointers to free tool boxes as well as commercial tool boxes for MATLAB. It also contains pointers to other scientific and engineering resources available on the web.
•   C++ Programming
  • About.com's free C++ programming tutorial: http://cplus.about.com/od/beginnerctutorial/l/blcplustut.htm
  • Introduction to C++ Programming I by Ian Aitchison and Peter King: http://www.cee.hw.ac.uk/~pjbk/pathways/cpp1/cpp1.html

Grading

       The grade will be based on your class attendance (20 %) and your project and presentation (80 %).

Attendance:

      Attendance at the lectures is required. Each class missing results in two-points reduction. The maximum of class missing reduction points is 20. In other words, perfect attendance will gain 20 points of your course grade.

      There is no provision for absences due to vacations, family outings and other social activities, other special plans and appointments, etc. Absences due to illness  require a medical excuse on Physician's letterhead, signed by the physician.

Important Dates

• January 23: First day of classes.
• February 17: Last day to drop without a "W" on record.
• March 17: Last day to drop.
• March 19 to 26: Spring Break.
• May 11: Last day of classes.
• May 19: Project presentation and hand in course project (3:00 - 5:00 PM).

Statement of Academic Misconduct

      The university has a responsibility to promote academic honesty and integrity and to develop procedures to deal effectively with instances of academic dishonestly. Students are responsible for the honest completion and representation of their work, for the appropriate citation of sources, and for respect of others' academic endeavors. Further information can be found at http://www.uwm.edu/Dept/Acad_Aff/policy/academicmisconduct.html.

Statement of Sexual Harassment

      Sexual harassment is reprehensible and will not be tolerated by the University. It subverts the mission of the University and threatens the careers, educational experience, and well being of students, faculty and staff. The University will not tolerate behavior between or among members of the University community which creates an unacceptable working environment.