Instructor: Prof. Hans De Sterck, office: MC5016, email: hdesterck@uwaterloo.ca
Lectures: 2:30-3:20MWF (DWE 3522A)
Office hours: 3:30-4:30W (MC5016)
TA: Scott Rostrup, office: MC5133, email: scott.rostrup@sympatico.ca
Office hours: 1:30-2:30Th (MC5133)
Course Objectives:
Mathematical models based on partial differential equations (PDEs) are ubiquitous these days, arising in all areas of science and engineering, and also in finance and economics. In complex models, the PDEs cannot be solved exactly, and one has to rely on approximate solutions obtained using numerical methods on computers.
The goal of this course is threefold. You will receive a solid introduction to the theory of numerical methods for partial differential equations (with derivations of the methods and some proofs). You will learn to implement the computational methods efficiently in Matlab, and you will apply the methods to problems in several fields, for example, fluid mechanics, diffusion processes, wave phenomena, and the biomedical field.
Prerequisites: (AMATH 341/CM 271/CS 371 or CS 370) and (AMATH 351 or AMATH 342/CM 352). You will also be able to enroll in the course through consent of the instructor if you have credit in AMATH 353 (PDE 1).
Tentative Outline:
I. Overview of PDEs (2 weeks)
II. Finite Difference (FD) Methods (4 weeks)
III. Finite Volume (FV) Methods (2 weeks)
IV. Finite Element Methods (FEM) (3 weeks)
V. Iterative Solvers for Linear Systems (1 week)
Course Material: A full set of course notes is available for download at http://www.math.uwaterloo.ca/~hdesterc/websiteW/teaching/AM442CM452.pdf, or for purchase in Pixel Planet.
Course Website: the ACE system will be used extensively for all course communications.
Reference Material:
Books on reserve in library:
1. A first course in the numerical analysis of differential equations, Iserles, Cambridge University Press, 1997. (FD and FEM, Chapters 7-14) (on 1-day reserve in Davis library)
2. Finite volume methods for hyperbolic problems, Leveque, Cambridge, 2002. (FV) (on 1-day reserve in Davis library)
3. An introduction to the finite element method, Reddy, McGraw-Hill, 1993. (FEM, comprehensive introduction with engineering applications) (on 1-day reserve in Davis library)
4. The mathematical theory of finite element methods, Brenner and Scott, Springer, 1994. (FEM, theoretical) (on 1-day reserve in Davis library)
5. Finite difference methods for ordinary and partial differential equations: steady-state and time-dependent problems, Leveque, SIAM, 2007. (FD)(on 1-day reserve in Davis library)
Online resources:
6. Numerical Methods for Partial Differential Equations, MIT Open Course Ware project. (FD, FV and FEM) (download course notes pdf from http://ocw.mit.edu/OcwWeb/Aeronautics-and-Astronautics/16-920JNumerical-Methods-for-Partial-Differential-EquationsSpring2003/LectureNotes/index.htm)
7. Finite difference methods for differential equations, Leveque. (FD) (download course notes pdf from http://www.amath.washington.edu/~rjl/pubs/am58X/amath58X05.pdf)
8. Finite Difference and Spectral Methods for Ordinary and Partial Differential Equations, Trefethen. (FD) (download course notes pdf from http://web.comlab.ox.ac.uk/oucl/work/nick.trefethen/pdetext.html)
Reference material on PDEs:
9. Partial differential equations I, Wainwright and Siegel, Course Notes for AM353 (good general background resource for PDEs; available in MC2018, and on 1-day reserve in Davis library)
Assignments: There will be three Computational Assignments (21% weight in final grade, programming in Matlab), and three smaller Theoretical Assignments (9% weight in final grade). Assignments will generally be due on Mondays.
Academic Honesty: You are allowed to discuss theoretical and computational assignment problems and your solution strategies with your classmates, but you are not allowed to copy any material. All assignment material that you submit (including written documents, program code and graphical output) should be strictly your own work. Compliance will be actively monitored.
Final Grade: 20% Midterm Exam, 50% Final Exam, 9% Theoretical Assignments (3), 21% Computational Assignments (3).