Biophysics & Soft Matter Physics, London (ON)

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Finite Element Method AM466b/562b:

We will cover the basics of the Finite Element Method (FEM). FEM is a very powerful and general method, and we will focus on the general aspects and the background of the method. After gaining the necessary theoretical background during the first half of the course, in the second half we put the ideas and concepts into practise and study the methods from the computational point of view. This second half will contain a good amount of programming, and it is essential that the students have a good background in C, C++, Java, Fortran or comparable. The course also contains a project work which is of computational nature.
  • Lecturer: Dr. Mikko Karttunen. Email: mkarttu [at] uwo.ca.
    IMPORTANT: When emailing, please include 'AM466b' on the subject line.

  • TA: Chris Smith. Email: csmith8 [at] uwo.ca

  • Practical matters:

    • Textbook: Erik G. Thompson: Introduction to the Finite Element Method. Wiley.
    • Lectures: Mon, Wed, Thu: 08:30-09:30. Middlesex College, room 17
    • First lecture: Monday Jan. 8, 2007.
    • Office hours: by appointment
    • Assessment: Two in-class exams (20% each), problem sets (30%), and a project work (30%).
      • In-class exams: on weeks starting Feb. 19 and Mar. 26. These are one-hour exams.
      • 1st in-class exam: Monday Feb. 19.
      • 2nd in-class exam: Wednesday Mar. 28.

Weekly lecture schedule (on-line material below)

  • Week 1: Level test.
  • Week 2 (Jan. 15-19): Basic concepts, calculus of variations. Chapters 1 and part of Ch. 2 in the book.
  • Week 3 (Jan. 22-26): Calculus of variations. Chapter 2 + supplementary material (lecture notes).
  • The lecture on Jan. 29 will be rescheduled, i.e., no lecture on Monday Jan. 29.
  • Week 4 (Jan. 29 - Feb. 2): Calculus of variations + constraints. The Rayleigh-Ritz variational technique.
  • Week 5 (Feb. 5-9): Matrix factorization, Galerkin method
  • Week 6 (Feb. 12-16): Galerkin method, finite element formulation of the variational method.
  • 1st in-class exam: Monday Feb. 19. Material: Problem sets 1 and 2, lecture notes (up to Feb. 15), Chapters 1-4 in the textbook.
  • Week 7: Midway tutorial & problem solving sessions: Feb. 21, 22
  • Week 8: Reading week: Feb. 26-Mar. 2.
  • Week 9: Mar 5-9: Helpful tools: Gaussian quadrature
  • Week 9: Mar 12-16: Putting it all together. Solving the full problem in 1-D. Stiffness matrix. Helpful tools: Gauss, Green and Stokes.
  • Week 9: Mar 19-23: Generalized coordinates, 2 dimensional problems, deriving interpolation functions
  • 2nd in-class exam: Monday Wed. Mar. 28. Material: Problem sets 3-4, lecture notes (from Feb. 15 up to Mar. 23), Chapters 5-6 in the textbook.
  • The term ends Apr. 12.

Problem sets

More on the finite element method and related matters

  1. FEM Books:

    • S.C. Brenner and L.R. Scott, The Mathematical Theory of Finite Element Methods, Springer-Verlag, 1994
    • A. Tveito and R. Winther: Introduction to Partial Differential Equations; A computational Approach, Springer, 1998
    • C. Johnson: Numerical Solution of PDEs by the Finite Element method, Cambridge University Press, 1995.
    • D. Braess: Finite Elements; Theory, Fast Solvers, and Applications in Solid Mechanics, Cambridge University Press, 1997.
    • O.C. Zienkiewicz and R.L. Taylor: The Finite Element Method, Vol. 1: The Basis, Butterworth-Heinemann, 2000.
    • O.C. Zienkiewicz and R.L. Taylor,:The Finite Element Method, Vol. 2: Solid Mechanics, Butterworth-Heinemann, 2000.
    • O.C. Zienkiewicz and R.L. Taylor: The Finite Element Method, Vol. 3: Fluid Dynamics, Butterworth-Heinemann, 2000.
    • Huebener, Dewhirst, Smith and Byrom: The Finite Element Method for Engineers (Wiley)
    • Solin: Partial Differential Equations and the Finite Element Method (Wiley)
    • H. Grandin Jr.: Fundamentals of the Finite Element Method (MacMillan)
    • Strang/ and Fix: An Analysis of the Finite Element Method (Wellesley-Cambridge)

  2. Matrices, linear algebra:

    • Golub and van Loan: Matrix Computations (Johns Hopkins).

  3. Web resources related to FEM + FEM software:

  4. Programming + friends:
Last modified Friday February 06, 2009