Math 172 Numerical Methods for Partial Differential Equations Spring 2004
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Announcements
06.09.04: Here is a copy of the exam,
as postscript or pdf file.
And a copy of the exam 1 retake, as
postscript or pdf file.
05.26.04: The final exam is June 7, at 3pm. I have made an exam preparation sheet, which you can get as a
postscript or pdf file.
Note that you will have the option to retake the first exam during the final
exam period. The exam prep sheet has more details regarding this, but does not
cover the material that would be on the retake; for that, see the first exam
prep sheet
(postscript or pdf)
05.18.04: The final homework is posted in the homework section.
05.17.04: Here are some notes on the web on multigrid:
notes
in html by Jim Demmel.
Four part
notes in pdf
by Eric de Sturler.
A
slideshow overview in pdf by my old teacher Paul Heckbert.
05.12.04: For homework 5, you should notice that your approximate
solutions move approximately correctly, but there is some damping. Among the
given values of r, there are none which give significantly better
error values, unlike the case for the explicit heat equation which had a spike
in error at 1/6.
05.12.04: Shewchuk has prepared some
notes on the conjugate gradient method, which we will cover in class.
05.07.04: This is approximately the dependance of error on the value of
r, for homework 3. Note the dip at r = 1/6.
05.07.04: New homework posted in the homework section.
05.05.04: The average grade on the midterm was 59.75; the median
grade was 67.5; both out of 100.
05.05.04: Here are some notes on iterative methods:
as
postscript
or
pdf
file.
This is redundant to § 5.2 of the book.
05.04.04: Here is a copy of the exam,
as postscript or pdf file.
You can also get the exam with answers,
as postscript or pdf file.
04.30.04: The exam is Monday May 03, 05:00pm in HSS 1305.
I plan on answering your questions during class, at 3:00pm on Monday.
At 4:00pm, I will be available for questions as well, either in the
class room, or in my office.
I have prepared an exam preparation sheet, which you can get as a
postscript or pdf file.
This review sheet consists of some problems which should look familiar, and
others which probably do not. You should expect the exam to be similarly
arranged, but quite a bit shorter. You may be expected to know some things,
derive some things, derive some things you know, and prove some things you
never knew and never derived.
Topics for the exam may include: PDEs, classification of PDEs, Taylor's
Theorem, wave equation, heat equation, transport equation, simple
discretization, error, stability, method of lines, as well as specific schemes
for specific PDEs: implicit, explicit, crank nicolson, and FTFX, FTBX, upwind.
You should be comfortable working with matrices and eigenthings, and be able to
perform Fourier analysis.
04.30.04: You should be thinking hard about your programming projects.
You should tell me which project you are doing before May 8th.
04.27.04: Here is some information about matlab/octave:
04.23.04: New homework posted in the homework section.
04.21.04: Here's a description of the funny
greek letters
we use in class. I still don't know how to draw a xi, though.
04.16.04: I have put together some project suggestions. You should
decide on your project some time in the next week. Please consult with
me regarding your project--at the very least I want to know that you have
selected a project and understand the details of what you are being
asked to do.
You can get the project descriptions as a
postscript or pdf file.
04.16.04: New homework posted in the homework section.
04.14.04: I have been looking for online alternatives to
the course notes. I like the following:
04.13.04: The second and final part of the course notes are
at AS Soft Reserves. Total damage: twelve dollars and change.
04.05.04: I stumbled onto a well-written
slideshow on spectral
methods. you might also be interested in one of the better
books on the topic.
maybe we will consider spectral methods in this class,
and these are good resources. don't worry if you do not quite understand
this material yet.
04.02.04: I am guessing the class will not be cancelled. I will hand
over the full notes to the soft reserves people to get copies made.
04.02.04: New homework posted in the homework section.
03.29.04: I will be posting information about the first homework here,
as soon as I can.
03.29.04: The first chapter of the course lecture notes should be
available at A.S. Soft Reserves after 10:30am, Wednesday March 31. Note this
is only one of six chapters of notes for this class. If the course is not
cancelled, I will make the other five chapters available there. We should know
whether the course is cancelled in the next two weeks.
03.29.04: You can get the syllabus as a
postscript
or pdf file.
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- Posted 04.02.04; Due Monday 04.11.04 From
§1.5 do exercises 1.1--1.12.
- Posted 04.16.04; Due Friday 04.23.04 From
§2.5 do exercise 2.1.
From §3.10 do exercises 3.1,3.5.
- Posted 04.16.04; Due Wednesday 04.28.04 From
§3.10 do exercise 3.2,3.3.
- Posted 04.23.04; Due Friday 04.30.04 Get the homework
as a
postscript or pdf file.
- Posted 05.07.04; Due Monday 05.17.04 Get the homework
as a
postscript or pdf file.
- Posted 05.18.04; Due Friday 05.28.04 Get the homework
as a
postscript or pdf file.
___________________________________________________________________________________
You can get the project descriptions as a
postscript or pdf file.
Projects and final report are due Friday June 4, 5pm.
___________________________________________________________________________________
Instructor: Steven E. Pav
Phone: 858 534 2126 (4-2126)
Email:
spav@ucsd.edu
Office: 5763 Applied Physics & Mathematics Building (APM)
Office Hours: tentatively: M 5:00p-5:50p, Tu 1:10p-2:00p, We 4:00p-4:50p
Meeting Times: MWF 3:00p-3:50p
Room: HSS 1315
Textbook: Numerical Treatment of Partical Differential Equations, and
Mathematics 172 Notes on the Finite Element Method, both by
Randolph E. Bank, Peter Rentrop, and Donald R. Smith. To be
made available from A. S. Soft Reserves.
You may also wish to consult The Mathematical Theory of Finite
Element Methods, by Susanne C. Brenner and L. Ridgeway Scott,
Partial Differential Equations : Analytical and Numerical Methods,
by Mark S. Gockenbach, and Finite Difference Schemes and
Partial Differential Equations, by John C. Strikwerda. I will try to
put some or all of these on reserve at the library.
Course Webpage:
http://scicomp.ucsd.edu/~spav/class/2004S-M172/
Final Exam: Monday June 7, 3:00p-6:00p
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Catalogue Description. 172. Numerical Partial Differential Equations. (4) Finite difference methods
for the numerical solution of hyperbolic and parabolic partial differential equations; finite difference and
finite element methods for elliptic partial differential equations.
Course Description. Scientists often model physical systems with partial differential equations
(“PDEs”). Analytic solutions exist only for the most elementary PDEs; the rest must be tackled
with numerical methods. These can roughly be broken into two types: the finite difference
and the finite element methods. The finite difference method approximates the solution of a
PDE at a number of points in space. The finite element method attempts to find the best
approximate solution to a PDE among some finite set of simple functions. In the end, both methods
require solution of a set of linear equations. After an introduction to PDEs in general, we will
look at each method, including theoretical and practical aspects, consistency, stability and
convergence.
Grading Policy. It is my belief that any grading scheme will be disagreeable to some student; the
best grading scheme one can hope for is one that is agreeable to the majority, and applies equally to all
students.
Grading in this class will be based upon performance in homeworks, on a programming project, and
two examinations. The final quarter grade is subdivided as follows: Homework: 30%; Project:
10%; Exams: 30% each. It is expected that the exams will be challenging, and grades will be
curved.
The dates and times for the exams are listed in this syllabus: The first exam is Monday, May 3, during
the discussion section at 5pm. The second exam is during the final exam period for the class, Monday
June 7, at 3pm. The second exam is not a comprehensive final.
If you have known conflicts with any of these exams, I encourage you to notify me immediately.
Legitimate, documented, excuses for missing an exam will be dealt with individually.
Homework. It is expected, and encouraged, that students will work together on the homeworks. This
saves time (yours and mine), builds leadership, and encourages cooperation. Each student must submit
their own homework, written in their own hand (please no printouts, photocopies or faxes). Please list on
your homework the names of the other students you worked with.
A number of the homework problems ask you to write a program in FORTRAN. You may do this if
you wish, but I encourage you to instead write the program in Matlab (or even better, the free Matlab
clone Octave). If you choose to write in Matlab, do not use Matlab’s finite difference toolkit or otherwise
“cheat” by using Matlab’s high-level functions. It should be clear from the wording of the
problem what you are supposed to program; if not, ask me. You may talk to one another about
programming assignments, but you should write your own programs. Please do not share
code.
Project. The project will consist of a longer programming assignment. You will be able to choose
from a limited number of different projects. Please do not consult one another for your project, and do not
share code.
Getting Help. I encourage you to attend my office hours. Unfortunately there is no TA for the
class.
Academic Integrity Students are expected to adhere to the University’s Policy on Integrity of
Scholarship, found in the UCSD general catalogue. Minimum punishment for cheating on a exam is a
score of zero on that exam.
Course Webpage. The course page, (http://scicomp.ucsd.edu/~ spav/class/2004S-M172/) will
include this syllabus and any updates, general announcements, handouts and other materials.
Course Schedule. The lecture schedule is tentative, but the exam schedule is exact. Section numbers
are those of Numerical Treatment of Partical Differential Equations, except those on FEM, which are from
Mathematics 172 Notes on the Finite Element Method.
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| | M Mar 29 | PDE review: §1.1 |
| week 1 | W Mar 31 | PDE review: §1.2 |
| | F Apr 02 | PDE review: §1.3 |
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| | M Apr 04 | PDE review: §1.4 |
| week 2 | W Apr 07 | FDM intro: §2.1 |
| | F Apr 09 | FDM intro: §2.2 |
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| | M Apr 12 | FDM intro: §2.3 |
| week 3 | W Apr 14 | FDM parabolic: §3.1 |
| | F Apr 16 | FDM parabolic: §3.1, 3.2 |
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| | M Apr 19 | FDM parabolic: §3.2, 3.3 |
| week 4 | W Apr 21 | FDM parabolic: §3.3, 3.4 |
| | F Apr 23 | FDM parabolic: §3.5 |
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| | M Apr 26 | FDM parabolic: §3.6 |
| week 5 | W Apr 28 | FDM parabolic: §3.8 |
| | F Apr 30 | FDM parabolic: §3.8, 3.9 |
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| | M May 03 | FDM hyperbolic: §4.1 |
| | M May 03 | 5:00pm: Exam 1 covering §1.1-1.4, 2.1-2.3, 3.1-3.6,3.8,3.9 |
| week 6 | W May 05 | FDM hyperbolic: §4.2 |
| | F May 07 | FDM hyperbolic: §4.2 |
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| | M May 10 | FDM hyperbolic: §4.5 |
| week 7 | W May 12 | FDM elliptic: §5.1 |
| | F May 14 | FDM elliptic: §5.2 |
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| | M May 17 | FDM elliptic: §5.3 |
| week 8 | W May 19 | FEM elliptic: §1.1 |
| | F May 21 | FEM elliptic: §1.2 |
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| | M May 24 | FEM elliptic: §1.3 |
| week 9 | W May 26 | FEM elliptic: §1.4 |
| | F May 28 | FEM elliptic: §1.5 |
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| | M May 31 | Memorial Day: no class |
| week 10 | W Jun 02 | FEM elliptic: §1.6 |
| | F Jun 04 | FEM elliptic: §1.7 |
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| finals | M Jun 07 | 3:00pm: Exam 2 covering §4.1,4.2,4.5,5.1-5.3,1.1-1.7 |
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