Course Information

Day One Handout

The course meets in slot 18, from 10:30-11:45 AM on Tuesdays and Thursdays, in HH 3017. My office hours are Tuesdays, from 9:00-10:20AM, and Wednesdays, from 10:30 AM - Noon, in HH-2019, or by appointment.

No textbooks are required for this course. Relevant e-books from the library's collection (or elsewhere) include the following; library login may be required for access.

  • Finite Difference Methods for Ordinary and Partial Differential Equations: Steady-State and Time-Dependent Problems by Leveque
  • A First Course in the Numerical Analysis of Differential Equations by Iserles
  • Finite elements and fast iterative solvers with applications in incompressible fluid dynamics by Elman, Silvester, and Wathen
  • Finite Elements: Theory, Fast Solvers, and Applications in Elasticity Theory by Braess
  • Finite Volume Methods by Eymard, Gallouët, and Herbin
  • Iterative methods for sparse linear systems by Saad (full text pdf available here)

    Reference books
    Background material from relevant undergraduate courses includes:
  • A First Course in Numerical Methods by Ascher and Greif
  • Scientific Computing - An Introduction using Maple and MATLAB by Gander, Gander, and Kwok

    This course will not be using D2L; all material online will be posted here.
  • Approximate Schedule

  • 9/7: Introduction; Taylor's theorem and differencing
  • 9/12: Differencing in 1D, Taylor's Theorem in nD, HW1 Distributed, Solutions
  • 9/14: 2D meshes and differencing, approximating DEs
  • 9/19: Convergence Theory, HW2 Distributed, Solutions
  • 9/21: Convergence Theory, continued, HW1 Due
  • 9/26: Boundary conditions, HW3 Distributed, Solutions, Discretization code, Part (a) wrapper, Part (b) wrapper
  • 9/28: Boundary conditions continued, complications, HW2 Due
  • 10/3: Meshless Finite Differences, HW4 Distributed, Solutions, Discretization code for first-order approx, Discretization code for ghost point approach, Wrapper
  • 10/5: Finite volumes in 1D, HW3 Due
  • 10/10: Fall Break, no lecture
  • 10/12: Finite volumes in 2D and 3D, HW4 Due, HW5 Distributed, Solutions
  • 10/17: Spectral Methods
  • 10/19: Fast Fourier Transform and Fast Poisson Solver, HW6 Distributed, Solutions, Fast Poisson Solver, Driver, Spectral Solver, Driver
  • 10/24: Midterm Exam, Solutions
  • 10/26: Weak forms and Ritz-Galerkin
  • 10/31: Approximation Theory
  • 11/2: Piecewise linears, HW5 Due
  • 11/7: Piecewise polynomial approximation, HW7 Distributed, Solutions, 1D linear FEM, Driver
  • 11/9: Hilbert Spaces, Lax-Milgram Lemma, Céa's Lemma, HW6 Due
  • 11/14: Poincaré-Friedrichs, Reaction-convection-diffusion equations, HW8 Distributed, Solutions
  • 11/16: Finite elements in 2D and 3D, approximation properties, HW9 Distributed, Solutions, matrix code, Jacobi, GS, driver, HW7 Due
  • 11/21: Direct Methods
  • 11/23: Iterative Methods and Matrix Splitting, HW8 Due
  • 11/28: Krylov Methods and GMRES
  • 11/30: MINRES and CG, HW9 Due
  • 12/6: Final Exam, 9:00 - 11:00 AM, HH3013