CS 455/CSE 411/MATH 455: Numerical Methods for Partial Differential Equations, Spring 2008

CS 455/CSE 411/MATH 455

Numerical Methods for Partial Differential Equations

Spring 2008

Instructor:

Stephen Bond
Office: 4318 Siebel Center
Phone: 244-5975
Email: sdbond«at»uiuc«dot»edu
Office Hours: 3-4 T, 2-3 W, and by appointment

Location and Time:

1103 Siebel Center
12:30 PM - 01:45 PM

Credit:

3 or 4 Hours

Grading:

35% Homework
10% Quizzes
20% Midterm Exam
35% Final Exam

Required Textbooks:

Numerical Solution of Partial Differential Equations by K. W. Morton and D. F. Mayers, ISBN 0-521-42922-6
Finite Elements: Theory, Fast Solvers, and Applications in Solid Mechanics by D. Braess, ISBN 0-521-70518-5

Recommended Textbooks:

Finite Difference Methods for Ordinary and Partial Differential Equations: Steady-State and Time-Dependent Problems by R. LeVeque, ISBN 0-898-71629-2
Partial Differential Equations - Analytical and Numerical Methods by M. S. Gockenbach, ISBN 0-898-71518-0

Course Materials:

Course Schedule:

.	Date	Lecture Topic	Assignment / Reading
Tue	15-Jan	1. Introduction to PDEs Classification and Characteristics	Notes: PDE0; Book: Braess I.1 HW 1 assigned
Thu	17-Jan	2. Finite Difference Method for Parabolic Problems	Notes: MM1; Book: M&M 2.1-2.7
Tue	22-Jan	3. Implicit Finite Difference Method	Notes: MM2; Book: M&M 2.8-2.12
Thu	24-Jan	4. Method of Lines	.
Tue	29-Jan	5. Maximum Principle	Quiz 1 ( [1] General Intro to PDEs )
Thu	31-Jan	6. Non-Dirichlet Boundary Conditions	HW 1 due by 5 PM; HW 2 assigned Notes: MM3; Book: M&M 2.13-2.15
Tue	5-Feb	7. General Linear Problems	Book: M&M 2.17
Thu	7-Feb	8. Higher Dimensions and Curved Boundaries	Notes: MM4; Book: M&M 3.1-3.5
Tue	12-Feb	9. Hyperbolic Problems	Notes: MM5; Book: M&M 4.1-4.9
Thu	14-Feb	10. Finite Difference for Hyperbolic Problems	.
Tue	19-Feb	11. Finite Volume for Hyperbolic Problems	Book: M&M 4.11-4.12
Thu	21-Feb	12. Finite Difference for Elliptic Problems	HW 2 due by 5 PM; HW 3 assigned Notes: MM6; Book: M&M 6.1-6.5
Tue	26-Feb	13. Weak formulation of Elliptic Problems	Notes: B1
Thu	28-Feb	14. Hilbert and Sobolev Spaces	.
Tue	4-Mar	15. Midterm Study Guide	.
Thu	6-Mar	* Midterm Exam, In Class *
Fri	7-Mar	Undergrad Drop Deadline
Tue	11-Mar	17. Lax-Milgram	Notes: B2
Thu	13-Mar	18. Examples of Weak Formulation	HW 3 due by 5 PM; HW 4 assigned Grad Project Proposal Due
Tue	18-Mar	Spring Vacation
Thu	20-Mar	Spring Vacation
Tue	25-Mar	19. Gauss Divergence Theorem	.
Thu	27-Mar	20. Euler-Lagrange	Quiz 2 ([B1] Weak Formulation) Notes: B3
Tue	1-Apr	21. Galerkin Finite Elements	.
Thu	3-Apr	22. Galerkin Finite Elements	.
Tue	8-Apr	23. Guest Lecture by Prof. Anil Hirani	.
Thu	10-Apr	24. Programming the Finite Element Method	HW 4 due by 5 PM; HW 5 assigned
Fri	11-Apr	Grad Drop Deadline
Tue	15-Apr	25. Programming the Finite Element Method	.
Thu	17-Apr	26. Nonlinear Problems	.
Tue	22-Apr	27. Iterative Methods	.
Thu	24-Apr	28. Multigrid	.
Tue	29-Apr	29. Review for Final	HW5 due by 5 PM
Wed	7-May	Final Exam (7 - 10 PM) in 1302 SC