MATH610-600: Numerical Methods for PDE's, Spring 2012
General information
- Instructor: Dr. Raytcho Lazarov, Blocker 505C
- Teaching Assistants: Youli Mao , Blocker 505
- Time: TR 11:10 -- 12:25 (regular class), W 9:10 -- 10:00 am
computer lab
- Classroom: Block 148 (regular class), BLOC 123 computer lab
- Office Hours: TR 10:00 -- 11:00 am or by appointment
- Texts: (basic) Numerical Treatment of Partial Differential Equations,
by C. Grossmann, H.-O. Ross, and M. Stynes, Springer, 2007, and
(additional) Theory and practice of finite elements, by A. Ern
and J-L Guermond, Springer, 2004.
Course description
- This is a one-semester course on numerical methods for partial
differential equations. The course will focus on the basic concepts of the
finite element method for elliptic boundary value problems. These will
include a weak (variational) formulation of the problem and relies on
the coercivity and continuity of certain bilinear forms in the
simplest setting (and inf-sup condition
in more general cases), approximation theory by piece-wise polynomial
functions over partition of the domain into finite elements, error analysis,
stability, and variational "crimes".
- Further,
some basic techniques of finite differences and finite volumes
will be introduced and discussed. Maximum
principle, energy type estimates, and Fourier mode analysis will be used for
studying the stability and accuracy of these methods applied to for elliptic,
parabolic and hyperbolic problems.
- The intention is to develop fairly stong
mathematical knowledge and expertise so after completing the class the
students can read and understand quite advances papers on finite element
methods for PDEs (and partially for finite differences, finite volumes).
The programming assignments will emphasize on
the applications of the numerical techniques to engineering problems.
-
This course covers entirely the numerical analysis part of the
qualifying exam in ApplMath/NA.
Practical Issues
-
Graphics, grid generation, program implementation and
simple iterative techniques will be discussed (mostly in the
labs)
in order to help you
with the programming assignments.
Programming skills (e.g. C, C++ or Matlab) are essential.
- Prerequisite for this class are MATH 417 or 609 or equivalent. However, a basic knowledge of
PDEs or engineering models that lead to boundary and initial value problems are essential. A good basis for this is Math602.
-
The students from engineering departments are encouraged to make their own project
that is related to either to their research funded by the corresponding graduate
program or to their personal interests and/or preferences. Such project should be
assigned by the end of March and completed by the end of April. It could be used
to replace one of the programming assignments.
Exam Schedule
-
Test #1 , Tuesday, February 14, 2012,
-
Test #2, Tuesday, April 3, 2012,
-
Test # 3, Wednesday, May 2, 2012, Blocker 164, 5:30 -- 7:45 pm
Grading Policy
- Your grade for the course will be computed as follows:
- (a) 20% will be determined by the programming
assignments ;
- (b) 50% will be determined by the three tests
(T#1 - 15%, T#2 - 15%, and Final#T - 30 %; the final is comprehensive);
- (c) 20% will be determined by the homework
assignments ;
- your MINIMUM grade will be A, B, C, or D, for averages of 90%, 75%, 60%,
or 50%, respectively.
Americans with Disabilities Act (ADA) Policy Statement
-
The Americans with Disabilities Act (ADA) is a federal anti-discrimination statute that provides
comprehensive civil rights protection for persons with disabilities.
Among other things, this legislation
requires that all students with disabilities be guaranteed a learning environment that provides for
reasonable accommodation of their disabilities.
- If you believe you have a disability requiring an
accommodation, please contact Disability Services, in Cain Hall, Room B118, or call 845-1637. For
additional information visit the site of disability services.
Academic Integrity Statement and Policy
- The Aggie Honor Council Rules and Procedures are on the web:
Aggie Honor System Office.
The essence is:
"An Aggie does not lie, cheat or steal, or tolerate those who do" .
Helpful links:
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