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Information on ndiff2-08,
Numerisk behandling av differentialekvationer II
Latest News
080526
Exam paper 080520 graded. The paper is pdf here
080516
Room for TODAY, 15.15--, 1537 (5th floor, Osquars B 2); Monday, May 19, 10-12, also 1537.
080513
- Lecture notes H-J Eqn etc.: here
- Room for Friday, 15.15 --, probably near my office; Room for Monday, May 19, not booked yet, but will be. Check the home page tomorrow evening!
080506
080416
- Extra lecture replacing cancelled apr. 10, TODAY 080416 15-17 in E32.
080328
- Lecture notes on well=posedness, etc. pdf here
- Some hints on differential equations, definitions, etc., pdf here
080303
- Lecture notes March 3 on reflections pdf here,
080228
- Extra Lab Fri Feb 28, 13-15, Yellow; Dag & Jesper available
for questions etc. MONDAY is DEADLINE HW2 !
080227
080225
- Lecture notes Feb. 25 here: pdf.
- Please study Leveque Ch 8 about Lax-Richtmyer stability on your own!
080218
080211
- Hint for the Lab 1 matrix here:pdf
080208
- The deadline for Lab 1 is moved up one week to Mon Feb 18.
- A solution with Dirichlet conditions for the time-dependent
problem is easier because the matrix
changes are then ONLY the 1/Dt contribution to the
diagonal. The change of BC, however, also invalidates the
simple solution to the "conservation" question.
Nevertheless, such a solution will be accepted. You may be asked later
also to do the Neumannn conditions, dependent on desired grade and performance
on other homework.
080204
- Updated notes for MG here pdf
080130
- The links to HW1 material are now active
- Briggs' notes , matlab coding hints, available
at student office.
Course start 080121
- New lecture plan, including deadlines
- Homework 1-4 and hints, downloadable below
- Lecture notes: Lecture notes L1&2, pdf here,
- Papers handed out Jan 21:
- matlab hints, will be available at student office.
- Briggs, "multigrid tutorial", pp. 1 - 46
Under construction 080116
About the Course
The course treats the numerical solution of differential
equations. It emphasizes partial differential equations (PDE)
solved by finite difference methods and finite volume schemes.
Well-posedness, stability and other properties of schemes for
hyperbolic systems of equations are a major concern, as well
as elliptic and parabolic equations.
The choice of boundary conditions has an impact on stability
and well-posedness, and will be discussed.
The goal of the course is to give students
- Understanding of the mathematical concepts, properties
and tools for analyzing differential equations and their discretizations, and
ability to carry out the manipulations and calculations required.
- Working knowledge and experience of implementing FD
schemes with various boundary conditions
- Experience of carrying out a complete solution of a computational
problem - formulation, analysis, method choice, implementation, validation,
and interpretation and presentation of results.
The theoretical part introduces model equations and Fourier - Continuous
as well as Discrete - techniques for the analysis of equations and schemes.
The theory is complemented by a set of homework, study problems, and computer
labs on the formulation, analysis, and solution of
model problems from engineering science.
The students are expected to have a solid background of calculus,
differential equations, and linear algebra; a basic course in
numerical analysis is required, as is familiarity with the NADA
computer environment and MATLAB.
Instructors
Dag Lindbo, Osquars B 2, floor 5, room 1527, dag at csc.kth.se, 08-7906927
Jesper Oppelstrup,
jespero@nada.kth.se.
Office hours: by agreement, and adapted to deadlines for homework.
Literature
LeVeque: Finite Volume Methods for Hyperbolic Problems
, Cambridge, 2002,
Other course materiel, such as
- homework problems,
- a set of examination questions
- additional material and reading hints,
will be
distributed on lectures and downloadable from this home page.
CSC student office DELFI
Oscars Backe 2, level 2, open Mo-Fr 9.45-11.30, Mo-Thu 12.45-14.15,
Tel: 790 8077.
Examination
To pass the student must
- Pass a written examination. (3 ects)
The exam will consist of a selection of the distributed examination questions.
- Solve the homework problems and projects. (4.5 ects).
A written report of good quality must be handed in for each of the
six (6) problems on the given deadlines.
You can find a latex file with a skeleton for a
report in the course archive.
Students may be asked to give a short oral presentation classroom-style
of (parts of) the solutions.
For homework and projects, students are encouraged to work
in groups of two. Each group needs only to hand in one report, but the
oral accounts are given individually. The grade on the course will be
based on the written examination, the homework and project solutions.
You do not need to register for the exam.
Homework
Downloads: HW1 pdf , Multigrid intro for HW1 pdf , M-files for HW1, .txt ,
HW2 pdf,
HW3 pdf,
HW4 pdf,HW5 pdf, preliminary, HW6_08 to be defined.
We will provide timely feedback, usually in the form of comments written
on a paper copy of the report. Grade and overall assessement will be
noted on the cover page. Reports will be handed back on lectures. If you
do not attend lectures, have a friend pick up your report.
You must hand in a report on the deadline. It can be incomplete, and/or
contain (serious) errors, in which case you may be asked to revise it.
The reports are graded F - A. The report for project/HW 1 does NOT
contribute to the final grade, and serves to indicate the relation
between grade and completeness.
How to hand in reports
Reports MUST have a cover page with author names, course code (DN2255) and
homework number, and instructor name (Dag Lindbo). The reports can be handed in
- e-mail to Dag as ps- or pdf-files
- e-mail to Dag that a paper version has been deposited in
(a) the Nada/CSC mailbox, bottom floor, Osquars B 2, or
(b) Dag's or Jesper's mail stop (floor 4, Osquars B.2)
The m-files for your code must be e-mailed to Dag on the deadline.
Legibility is paramount, details of formatting less so. Quite OK to cut & paste
paper plots with hand-written notes. Make sure you
- label axes correctly
- explain what the plots show
- combine plots so that comparisons are easy.
MERE SHEAVES OF MATLAB PLOTS, ONE TO A PAGE, WILL NOT BE ACCEPTED.
Code Review
(Semi-)Professional Matlab coding is part of the
handiwork of the trade. Project 1 m-files and one later report (TBD) will
be subjected to code review and feedback given. Material with style guidelines
and coding suggestions will be handed out on lecture 1.
Schedule
The schedule is available from KTH home page Time Edit "Schemagenerator".
Lecture content plans below.
DN225 Spring 08, Numerical Differential Equations II
Preliminary Lecture plan, DN2255 Spring 2008
Addresses:
D41 : Lindstedtsv. 17
D31,34 : Lindstedtsv. 5
E32,4V4Gul,
4V4Ora : Osquars B. 2
L32 : Dr Kristinas v. 30
Lecture plan, DN2255 Spring 2008
When Where What Ref.
=======================================================================
w 4 Mon 21 Jan 10 F1 D41 Intro., theory & num. methods ODEs From DN2225
Wed 22 Jan 13 F2 L32 Cons. laws, FV for Parabolic PDEs Ch.2.1-5,4.1-2
w 5 Mon 28 Jan 10 F3 D41 Multigrid Extra material
Thu 31 Jan 15 L1 4V4Gul
w 6 Mon 4 Feb 10 F4 D41 Hyperbolic conservation laws Ch.3
Thu 7 Feb 13 L2 4V4Gul
w 7 Mon 11 Feb 8 --- Deadline HW1: 2D heat eqn, Multigrid
Mon 11 Feb 10 F5 D41 Fin. Vol. for hyperbolic cons.laws Ch.4 and 6
Thu 14 Feb 15 L3 4V4Gul
w 8 Mon 18 Feb 10 F6 D41 BC for hyp.systems, well-posedness Ch.7, Extra
Thu 21 Feb 15 L3 4V4Gul
w 9 Mon 25 Feb 8
Mon 25 Feb 10 F7 D41 Convergence, Accuracy, Stability Ch.8
w10 Mon 3 Mar 8 --- Deadline HW2: Linear, ShalWat, L-F
Mon 3 Mar 10 F8 D31 More about von Neumann analysis
w11 ---
---
w12 ---
---
w13 ---
---
w14 Mon 31 Mar 8 --- Deadline HW3: Well-posed, L-F & L-W, dispersion
Tue 1 Apr 10 F9 D34 High resolution I Ch.6,10
Wed 2 Apr 10 L4 4V4Ora
w15 Tue 8 Apr 10 F10 E32 Nonlinear hyperbolic Ch.11
Wed 9 Apr 10 L5 4V4Ora
w16 Mon 14 Apr 8 --- Deadline HW4: Kynch, L-F & Godunov
Tue 15 Apr 10 F11 E32 High resolution II Ch.12
Wed 16 Apr 10 L6 4V4Ora
w17 Tue 22 Apr 10 F12 E32 Hyperbolic Problems in multiD Ch.18,19
Wed 23 Apr 10 L7 4V4Ora
w18 Mon 28 Apr 8 --- Deadline HW5: Hi-Res ShalWat
Tue 29 Apr 10 F13 E32 Boundary conditions in multiD Extra
Wed 30 Apr 10 L8 4V4Ora
w19 Tue 6 May 10 F14 D34 Non-reflecting BC. Extra
Wed 7 May 13 L9 4V4Ora
w20 Mon 12 May 8 --- Deadline HW6: To Be Defined
Tue 13 May 10 F15 E32 Projects, review
---
============================= =================================
w21 Tue 20 May 14:00-19, Exam E31-E35
Registration and "course join" in RES
You must register with your Sektions Kansli to take this course. Please do
so as soon as possible!. PhD students from other schools,
please contact the course responsible ASAP.
You must also, as soon as you have decided to
complete the course, register for participation in the CSC RES
system. Homework, examination grades, etc., will be recorded and available
to students ONLY in this way, and with some delay, in the web-based
system "Mina Sidor". The dialogue is in Swedish, so you may want
to ask a native Swedish speaker for assistance ...
In the CSC unix system, upon login , do
res checkin ndiff2-08
and
course join ndiff2-08
When you have finished the course, exit the registration by
course leave ndiff2-08
A course evaluation will be conducted via www from this home page, details
to appear here shortly.
Info directory
The course archive /info/ndiff2-07 will probably stay empty,
the stuff you need will be downloadable from this home page.
Upp till kursens hemsida.
Sidansvarig: Jesper Oppelstrup <jespero@nada.kth.se>
Senast ändrad 26 maj 2008
Tekniskt stöd: <webmaster@nada.kth.se>