Numerical Solution of PDEs (Math 6630) – Spring 2016
Lectures: MWF 11:50-12:40, LCB222
Instructor: Aaron Fogelson, LCB312, phone 581–8150, email: fogelson@math.utah.edu
Office hours: TBA
Course Web Site: http://www.math.utah.edu/~fogelson/6630_s16
Texts:
1. R. LeVeque, Finite Difference Methods for Ordinary and Partial Differential
Equations: Steady-State and Time-Dependent Problems, SIAM, 2007.
2. W. Briggs, V. Henson, S. McCormick, A Multigrid Tutorial, 2nd Ed, SIAM,
2000.
3. Lloyd N. Trefethen, Spectral Methods in MATLAB, SIAM, 2000.
These books are available from SIAM to SIAM members (I am one) at a discount
and I plan to place a group order after the first class meeting. If you are a SIAM
member and want to order them before class, please do so. They are also available
from Amazon etc without the SIAM member discount.
Other useful references:
1. K.W. Morton and D.F. Mayers, Numerical Solution of Partial Differential
Equations, 2nd Ed, Cambridge University Press, 2005.
2. J. Strikwerda, Finite Difference Schemes and Partial Differential Equations,
SIAM, 2004.
3. L.N. Trefethen, Useful but not complete book draft on finite difference and
spectral methods for PDEs. https://people.maths.ox.ac.uk/trefethen/pdetext.html
4. U. Trottenberg, C. Oosterlee, A. Schuller, Multigrid, Academic Press, 2000.
5. R. LeVeque, Finite Volume Methods for Hyperbolic Problems, Cambridge
University Press, 2002.
Course Material: This is intended as a second course in numerical methods for partial
differential equations. We will cover major parts of the following material:
1. Review of stability, accuracy, convergence analyses of finite difference methods for simple linear PDEs.
2. Finite difference methods for multidimensional elliptic PDEs in simple regions
and solution by multigrid methods.
3. Finite difference methods for advection-reaction-diffusion equations.
4. Finite-volume methods for nonlinear conservation laws.
5. Finite difference methods for the incompressible Navier Stokes equations.
6. Introduction to spectral methods with emphasis on Navier-Stokes equations.
Course Work: Course work will consist of analysis and implementation of selected
methods that we discuss.
Prerequisite: Math 6610-6620 or its equivalent and prior experience with applied aspects of partial differential equations. This course is not intended as a first exposure to numerical methods for PDEs. In particular, the first topic under course
material is truly intended as a review. If in doubt, consult with instructor.
ADA statement The American with Disabilities Act requires that reasonable accommodations be provided for students with physical, sensory, cognitive, systemic,
learning and psychiatric disabilities. Please contact me at the beginning of the
semester to discuss any such accomodations for the course.