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EGN 5456 INTRO TO COMPUTATIONAL MECHANICS Fall 1998
Van Dommelen
- GOALS
- To familiarize students with basic properties of
partial differential equations and their numerical discretizations.
- PREREQUISITES
- Some familiarity with complex Fourier series
and integrals, fluid mechanics, partial differential equations.
- INSTRUCTOR
- Dr. Leon Van Dommelen
http://www.eng.famu.fsu.edu/dommelen.
dommelen@eng.famu.fsu.edu
Contact me.
T 2:45-3:45 pm, W 5:15-6:00 pm, F 2:00-3:00 pm, in 242 CEB.
Phone: (850) 487-6324. I tend to forget to check my voice mail.
- TIMES
- Class: MWF 12:55-1:45 in 337 CEB.
Final: Thursday 12/11/97 7:30-9:30 am (if the FSU schedule is correct)
- TEXTBOOK
- Selected notes will be provided.
- 1.
- Paul DuChateau and David W Zachmann Partial Differential
Equations Schaum's Outline Series, McGraw-Hill (1986) ISBN
0-07-017897-6.
- REFERENCES
- Some recommended books:
- 1.
- Claudio Canuto, M. Yousuff Hussaini, A. Quarteroni, & T. A. Zang
Spectral Methods in Fluid Mechanics Springer-Verlag (1987) ISBN
3-540-17371-4 (Berlin) 0-387-17371-4 (New York). (Standard reference
on spectral methods.)
- 2.
- Germund Dahlquist and Åke Björck Numerical Methods Prentice
Hall (1974) ISBN 0-13-627315-7. (Excellent introduction to basic
numerical methods.)
- 3.
- Joel H. Ferziger Numerical Methods for Engineering Application
Wiley (1981) ISBN 0-471-06336-3. (Stanford text.)
- 4.
- C.A.J. Fletcher Computational Techniques for Fluid Dynamics
Vols. 1 and 2, Springer-Verlag (1988) ISBN 3-540-19466-5 (Berlin)
0-387-19466-5 (New York). (Good introduction to basic CFD.)
- 5.
- Bertil Gustafsson, Heinz-Otto Kreiss, and Joseph Oliger Time
Dependent Problems and Difference Methods Wiley (1995) ISBN
0-471-50734-2. (Solid introduction to the fundamentals of finite
difference methods.)
- 6.
- Wolfgang Hackbusch, Multi-Grid Methods and Application
Springer-Verlag (1985) ISBN 0-387-12761-5.
- 7.
- Heinz Otto Kreiss Numerical Methods for Solving Time-Dependent
problems for Partial Differential Equations Montreal: Les Presses de
l'Universite de Montreal. Series: Seminaire de mathematiques
superieures 65 (1978) ISBN 0840504306. (Read after Richtmyer &
Morton.)
- 8.
- Leon Lapidus and George F. Pinder Numerical Solution of Partial
Differential Equations in Science and Engineering Wiley-Interscience
(1982) ISBN 0-471-09866-3. (Extensive reference on basic fundamentals.)
- 9.
- J.N. Reddy Functional Analysis and Variational Methods in
Engineering McGraw-Hill (1986) ISBN 0-07-051348-1. (Read after Strang
& Fix.)
- 10.
- Robert D. Richtmyer & K. W. Morton Difference Methods for
Initial Value Problems Interscience, (1967) 2nd Ed. ISBN
0-470-72040-9. (Excellent but abstract introduction to the
fundamentals of finite difference procedures.)
- 11.
- Gilbert Strang and George J. Fix An Analysis of the Finite
Element Method Prentice-Hall, Englewood Cliffs, NJ (1973) ISBN
0-13-032946-0. (Excellent introduction to the fundamentals of the FE
method.)
- 12.
- John C. Strikwerda
Difference Schemes and Partial Differential Equations
Wadsworth & Brooks/Cole, Belmont, CA (1989) ISBN 0-534-09984-X.
(Solid introduction to the fundamentals of finite
difference methods, but hard to read, many mistakes.)
- 13.
- Thomas A. Zang, C. L. Streett, & M. Y. Hussaini
Spectral Methods for CFD
ICASE Report No. 89-13, NASA CR 181803.
(Similar to Canuto, but more concise, recent).
- COURSE OUTLINE
- The following topics are available:
- Partial Differential Equations
- As time and interest permits.
Systems of first order equations arising in heat transfer, fluid and solid
mechanics. Transformation of second order equations to first order systems.
Quasi-linear and linear systems. Conservation laws. Shocks.
Classification of partial differential equations and systems.
Hyperbolic equations:
characteristics, domains of influence and dependence, properly posed
initial-boundary value problems.
Fourier analysis.
Parabolic equations, Fourier solutions, initial and boundary conditions.
Elliptic equations, boundary conditions, Fourier solution, properly posed
problems.
[1,5,12,8]
- Finite Difference Methods in One Dimension
- As time and interest permits.
Finite difference discretizations. Physical justifications. CFL condition,
domain of dependence, maximum principles. Fourier solutions of difference
equations. Taylor series expansions. Consistency, stability, dissipation
and dispersion.
Example problems from solid and fluid mechanics and heat
transfer.
Explicit and implicit schemes, upwinding, monotonicity preservation.
[5,12,8,4]
- Discretization Methods in Multiple Dimensions
- As time and interest permits.
General principles of curvi-linear grid generation.
Finite difference discretizations on these grids.
Finite volume discretizations. Galerkin and
sub-domain finite element disretizations.
[4]
- Finite Element Methods in One Dimension
- As time and interest permits.
Weak formulation, Galerkin, collocation. Rayleigh-Ritz formulation.
Finite elements, Lebesque integration, completeness,
reduction of order.
Energy/extremum principles. Convergence in natural and standard norms.
[11,9].
- Solution Methods in Multiple Dimensions
- As time and interest permits.
Discussion of direct and iterative solution procedures.
Approximate factorization techniques,
ADI and fractional step methods.
Jacobi, Gauss-Seidel, SOR, multigrid, conjugate gradients, ILU methods.
[12,8,3]
- Spectral Methods
- As time and interest permits.
Introduction to the fast Fourier transform.
Spectral accuracy. Spectral Galerkin, Tau, collocation.
[1,13]
- METHODS OF INSTRUCTION
- Lectures, problem solving sessions, solution of selected
problems on computers, examinations.
- STUDENT EVALUATION
- The course grade will be computed as:
- Homework and computer programs 50%
- Examinations 50%
Grading is at the discretion of the instructor.
- IMPORTANT GENERAL REQUIREMENTS
- Please note:
- 1.
- Homework must be handed in at the start of the lecture at which
it is due. It may not be handed in at the departmental office
or at the end of class.
Homework that is not received at the start of class on the due date
listed above cannot be made up unless permission to hand in late has
been given before the homework is due, or it was not humanly
possible to ask for such permission before the class. If there is a
chance you may be late in class, hand the homework in to the
instructor the day before it is due. (Shove it under his door if
necessary.)
- 2.
- Students may not copy homework or tests or allow others to copy their
homework or tests. Violations will result in reduced credit and a
failing final grade. However, you may work together on the
same question. For program asignments, you may consult with each other
about the approach, but you must code your own solution.
Unusual similarities in the way things are coded will be taken
as evidence of cheating.
- 3.
- Homework should be neat. Programs should be very neat and well
written and commented or credit will be lost.
- 4.
- Tests will be loosely based on the homework.
- 5.
- Students are bound by the rules and regulations in their
University bulletin, as well as by those specified in this syllabus,
and by the usual standards applied by the College of Engineering.
Read your academic bulletin. Violations of the rules and regulations
in your bulletin may result in reduced grades and/or other actions.
- 6.
- Students are bound by the honor code of their university. It
requires you to uphold academic integrity and combat academic
dishonesty. Please see your student handbook. Violations of your
honor code may result in reduced grades and/or other actions.
- 7.
- Copying of homework, assignments, or tests is never
allowed and will result in a failing or zero grade for the copied
work. It will also result in a failing or zero grade of the person
whose work is being copied if that person could reasonably have
prevented the copying. However, working together is typically
allowed and encouraged for most homeworks, (and sometimes for other
take-home assignments,) as long as you present the final results in
your own words and using your own line of reasoning. Since close
similarities between solutions will reduce credit, it is better not
to formally put down anything until you have figured out the
problem, and then let each person write their own solution. If it
is unclear whether working together is allowed on any assignment,
check with the instructor beforehand.
- 8.
- Attendance is required. Exams missed, even when rescheduled
from the original date and surprise tests, or homework not handed in
on time due to unexcused absence or lateness will result in a zero
grade for that exam and/or homework. Failure to properly complete
homework, tests, assignments, etcetera due to changes in date,
assignment, etcetera, that you did not know about due to unexcused
absence, lateness, or inattentiveness will not be excused and
cannot be made up.
- 9.
- In undergraduate classes, the total grade is further reduced due
to unexcused absences or lateness. See the instructor for details.
Even a few absences will make it impossible to pass the class.
Typically, four unexcused absences result in an F grade regardless of
numerical performance. Conscientious attendance is required for a
confident determination of your mastery of the subject matter to be
made. In other words, this class cannot be taken like a DIS unless a
faculty member will allow you to do so under formal DIS rules with
appropriately modified grading and testing standards.
- 10.
- The College of Engineering has a restrictive interpretation of
what is considered a valid excuse for an absence. If an absence is
to be excused, make sure you at least get official confirmation by
phone that it will be granted beforehand.
- 11.
- The instructor will make sure that make-up tests are no simpler
than the original, but he will try to make them similarly difficult.
However, he cannot make allowances for increased difficulty due to
the small sample size.
- 12.
- The College of Engineering has a more restrictive drop-add
period than you might think based on your bulletin. Check both your
bulletin and the Dean's office to determine whether drop-add will be
allowed.
- 13.
- Some of these rules may not apply if you fall under the
Americans with Disabilities Act. FAMU students with disabilities
needing academic accommodations should contact Student Health
Services for confirmation of permanent physical disability, FSU
students should register with and provide documentation to the
Student Disability Resource Center. Next bring a letter to the
instructor from the Services or Center indicating you need academic
accommodations. This should be done during the first week of
classes.
- 14.
- The instructor might wave some regulation on a case-by-case
basis depending on his subjective determination of fairness and
appropriateness. This will occur only under exceptional
circumstances and should not be assumed. Especially, never assume
that a seemingly minor regulation will be waved because the
instructor has waved it in the past. A second appeal to wave a
minor regulation will probably indicate to the instructor that the
regulation is not being taken seriously and most likely refused.
Any appeal to the instructor will further be refused apriori unless
it is done at the earliest possible moment by phone and/or by
E-mail. Do not wait until you are back in town, say.
- COMPUTER USE
- Requires knowledge of a major programming language such as Fortran,
C, or Pascal. Fortran is recommended. You also must have an E-mail
address that you check daily and a web browser.
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'Author: Leon van Dommelen'