Course Information

Day One Handout

The course meets in slot 19, from 2:00-3:15 PM on Tuesdays and Thursdays, in HH 3015. My office hours are on Mondays and Thursdays from 10:00 - noon, or by appointment.

Textbook
No textbooks are required for this course. Relevant e-books from the library's collection (or elsewhere) include:

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)

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

Approximate Schedule

9/8: Introduction; Taylor's theorem and differencing

9/13: Differencing in 1D, Taylor's Theorem in nD, HW1 Distributed, Solutions

9/15: 2D meshes and differencing, approximating DEs

9/20: Convergence Theory, HW1 Due, HW2 Distributed, Solutions

9/22: Convergence Theory, continued

9/27: Boundary conditions, HW2 Due, HW3 Distributed, Solutions, Matlab routines for HW3: FD Code, Uniform-mesh driver, Random-mesh driver

9/29: Boundary conditions continued, complications

10/4: Meshless Finite Differences, HW3 Due, HW4 Distributed, Solutions, Matlab routines for HW4: Driver, O(h) routine, O(h^2) routine

10/6: Weak forms and Ritz-Galerkin

10/11: Fall Break, no lecture

10/13: Approximation Theory, HW4 Due

10/18: Piecewise linears

10/20: Midterm Exam, Solutions

10/25: Piecewise polynomial approximation, HW5 Distributed, Solutions, Matlab routines for HW5: Driver, solution routine

10/27: Hilbert Spaces, Lax-Milgram Lemma, Céa's Lemma

11/1: Poincaré-Friedrichs, Reaction-convection-diffusion equations, HW6 Distributed, Solutions

11/3: Finite elements in 2D and 3D, approximation properties, HW5 Due

11/8: Finite volumes in 1D, HW7 Distributed, Solutions

11/10: Finite volumes in 2D and 3D, HW6 Due

11/15: Spectral Methods, HW8 Distributed, Solutions, Fast Poisson Solver code and driver, Spectral Method code and driver

11/17: Fast Fourier Transform and Fast Poisson Solver, HW9 Distributed, Solutions, Jacobi, Gauss-Seidel, matrix, and driver routines, HW7 Due

11/22: Direct Methods

11/24: Iterative Methods and Matrix Splitting, HW8 Due

11/29: Krylov Methods and GMRES

12/1: MINRES and CG, HW9 Due

12/8: Final Exam, 9-11am, HH3017