# TMA4195 Mathematical Modelling - Fall 2015

Messages
The evaluation of the project work can be found in It's learning.
The solution to the exam can be found in It's learning.
All topics covered in class as well as the old exams are part of the curriculum for preparing to the exam. The content of the lectures is summarised at the page https://wiki.math.ntnu.no/tma4195/2015h/lectures, and we consider the old exams and the homework as good training for the exam. The exam is a collection of problems which you are asked to solve. The structure of the exam of this year is similar to what given in the Previous exams. See below for the permitted aids allowed to use at the exam.
At the exam you will be allowed to take with you: "Approved calculator, Rottman: Matematisk formelsamling." You will have to remember the main results learned during the course and know how to apply them in concrete cases (see Plan ) for the overview of the curriculum.
There was a mistake in the Poisson solver. This mistake concerns the boundary conditions. There is a new version available where it is fixed (if it is actually only a change in one line: line 70 in the new version).
I have added a short note on the Lax-Friedrichs flux approximation. Such approximation can be used when implementing the numerical method for the shallow water equation which is given in the paper of Bouchut et al.
The project description has been updated on 17/11 and contains now some more hints. If you have been working on these questions using a different approach than the one suggested by the hint, I would like very much to see it! There are different ways to answer to these questions and I am more interested in original work.
On Wednesday the help session will be from 14.15-16.00 at Nullrommet.
There was a mistake in the code solverPoissonMimetic.m : After the coordinates of the nodes were changed, the geometrical properties of the grid were not computed again. The version available on the project webpage is now updated.
The deadline for sending in the project reports has been moved to the 25th of November.
You can now get a printed copy of the compendium (including almost all the important teaching material used for the course) at the office of the Department of Mathematical Sciences, 7th floor central building 2. Eva Lien can help you with this.
Presentation of the project. We will use only one day for the presentations of the project, the 23rd of November. Those who cannot make it that day, can present the project to Anders and Elena on the 20th of Novermber in Elena's office 1346 Sentralbuilding 2. Please, send me an e-mail and let me know if you cannot be at the presentation on Monday 23rd. All groups should send me thier presentations on Monday 23rd at 11:30 at the latest.
The help session 08:15-10:00 on Thursday November 12 will be held at the computer lab Nullrommet.
Fixed sign mistake in project description (equation 2.4). Added the slides used for the presentation on Laplace solver for irregular grid
On Monday 9. November, at the start of session, I will go through the matlab code provided to solve the Laplace equation on irregular mesh and explain it.
The project description has been updated. Some more details have been added concerning the decoupling between pressure and the other variables, which serves as a basis for the derivation of a numerical scheme in the second section.
We have been informed that the MRST algorithm is apparently already installed at the computers in Matteland. In MATLAB command line the command is run '/global/etc/matlab/mrst/startup.m'
The project description is available.
The project groups. If there has been any misunderstanding (you are not on the list, mix up of groups etc) please contact Anders as soon as possible.
There has been a change of plan, the publication of the project text will be Monday the 2nd of November 2015
Dear students, Eva Lien at the office of our department, can arrange to get you a copy of the compendium by Harald Krogstad if you would like to buy one. It will take one week. So it would be best if you let her know as soon as possible if you want one, so that she has a rough idea of how many copies are necessary. Be advised that this compendium can contain sections which are not part of the curriculum, and might not contain some other material, which was actually used for the lectures. On the other hand, under Teaching material you will find electronic versions of everything you need to prepare for the exam and for the project.
21st of October. Please do not forget to review the techniques for solution of the Heat equation using the Fourier transform. Kreyszig (9th edition) chp. 12.6. This topic will be used but not explained in the lectures.
Exercise 5 (Supervision in class on the 26th of October between 12:15 and 14, regular supervision on the 28th. Deadline to hand in 28th of October)
Modeling project registration is now closed. If you have been unable to register please send Anders an e-mail as soon as possible.
Exercise set 5 is available. To be handed in October 28th.
Registration for project is now open. Registration deadline is October 18th.
I recommend to read Sections 1 and 2.1-2.4 of the note on "Models based on conservation principles" to prepare for the lecture on October 1st.
The teaching assistant has office hours on Wedensdays from 10 to 12 for those who are unable to go to the exercise sessions.
Exercise set 4 is available. This exercise is to be handed in October 7th.
Today September 16th: Guest lecture with Svenn Anton Halvorsen from TEKNOVA. Tomorrow, September 17th supervision of the exercises with Anders from 8:15 to 10 in F2.
16. September: Guest lecture with Svenn Anton Halvorsen from TEKNOVA (in place of the regular exercise class)
17. September 8-10 (Thursday) exercises on singular perturbation with Anders (not to be handed in)
21. September second exercise set to be handed in is published on the webpage
21. September meeting with reference group
28. September 12-14 supervision of the second exercise with Anders.
7. October deadline for the second exercise set.
14. October publication of the third exercise set (to be handed in).
26. October 12-14 supervision of the third exercise set
28. October deadline to hand in the third exercise set.
Exercise set 3 is available. This exercise is not to be handed in, but we strongly recommend you to solve the exercises anyway.
Solutions to Exercise set 1 available.
Today 7th of September 12-14 in EL1, there will be supervision of the exercise set 2 instead of the regular class.
Exercise set 2 has been updated. Some errors have been corrected.
Exercise set 2 is available. This exercise will count towards your grade. The deadline is set to Wedensday 09 September 2015 at 23.00. You may hand in your solution on e-mail to Anders.
Exercise set 1 is available. The solution of the first problem on Exercise set 1 is to be handed in to Anders at latest 15:00 Thursday August 27.
First class: August 17th 2015
Important dates
First lecture: Monday the 17th of August 2015 in EL1 12-14
Expression of interest for the project: deadline Monday October 18th, 2015
Publication of the project text: Monday the 2nd of November 2015
Project presentation to the students: Monday the 2nd of November 2015
Deadline to send in presentations: 23rd of November
Project presentations: 23rd of November
Deadline project report: 25th of November
Exam: 11th of December 2015 (written)

EL1 on Mondays and F2 on Thursdays for the regular classes, R10 on Wednesdays for the exercises classes

## Lecturer

Elena Celledoni, room 1346 Sentralbygg II.

## Teaching assistant

Anders Samuelsen Nordli, room 1050, Sentralbygg II.
Office hours: Wedensday 10-12.

## Project lecturer

Xavier Raynaud, raynaud (at) math.ntnu.no