TMA4212 Numerical solution of differential equations by difference methods - Spring 2023
Kont/Retake exam August 16 and 17, 2023
Oral exam on August 16 and 17, 2023. Room 1148, SB2 (Espen's office).
- To get a time slot for the exam:
- Email lecturer (Espen) as soon as possible and no later than August 7.
- The schedule and place for the exam:
- Emailed to you on August 14.
- The time slots may change (it will for many of you), but not the day.
- To keep your time slot:
- Confirm that you will attend your August 14 time slot…
- … by email no later than August 15.
The exam will be a standard oral exam, where you answer questions for about 40 min. Paper and black/whiteboard will be available.
PS: Since I will not answer emails during my vacation, it is safest to contact me before July 7.
Old messages
Welcome to TMA4212 NumDiff!
Messages
| Date | Title | Message |
|---|---|---|
| 27.06. | Kont/retake exam | |
| 12.06. | Grading | … completed. The result will appear in Studentweb and the grading document in Blackboard. \\ |
| 22.05. | Exam 20.05.2023 | Problems and solutions (corrected 12.06.2023) |
| 08.05. | Overall projects grades | The final overall grades (updated with the results deriving from the feedback session now concluded) for what concerns the projects is now available on Blackboard. |
| 28.04. | Office hours | Tuesday 16.05. 12:30-14:30 - Questions and answer session in EL1 Friday 19.05. 09:15-11:00 - Questions and answer session in EL1 |
| Exam | Exam in Inspera, handwritten solutions submitted for scanning (InsperaScan). Different problems will have different codes! Also note the following: - English: The exam problems will be given in English only. You may write you answers in Norwegian or English as you prefer, but I recommend English. - Aids: Calculator and Rottmann. In addition several course notes/chapters will be available in Inspera. See 'Course info' in the menu for more info. |
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| Final curriculum | See "Course info" in the menu. Note in particular the parts that are not always so well covered in the lecture note of Owren. |
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| Reference group | Last meeting 27.04. Short summary - see 'Reference group' in the menu. I would like to thank Amandus, Emil, and Ine for their work in the reference group. |
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| Student evaluation | Dear students! The Faculty of Information Technology and Electrical Engineering (IE) is sending out a questionnaire-based student evaluation for courses taught at IE. Please help us to improve our teaching by answering this survey in the course TMA4212 Numerical Solution of Differential Equations by Difference Methods https://nettskjema.no/a/333932 The survey closes on May 5. (You answer anonymously, but need to log in with Feide for safety reasons.)  |
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| 20.04. | Final lectures | Thursday 20.04.: Info. Exam problems from 2019. Tuesday 25.04.: Last lecture. Final info. Exam problems. |
| 18.04. | Project grades | The scores of Projects 1 and 2 are available on Blackboard with a (partial) feedback. (The group indicated on the pdf file is the same as the one assigned on ovsys.) If you have any questions or complaints about the result, contact Alessandro. Use the Fridays support hours 8:00-10:00 in R4 (or contact him by email alessandro.contri@ntnu.no). The deadline for questions/complaints for both Project 1 and 2 is 28/04/23. After that, the scores of the projects will be combined and transformed into letter grades. |
| 23.03. | Project 2 | Deadline on Sunday, see schedule for supervision. |
| Comments: - Computing integrals of errors numerically: Make sure to use an integration method (quadrature) that is 2nd order accurate or more. By quadrature, you introduce an additional error into the problem, and this error small compared to the FEM error. - Problem 2 (e): Change the data of this problem into the following: \[\alpha=1, \qquad b=100, \qquad\text{and}\qquad f=1.\] This should give a solution with a boundary layer near one of the boundaries, a region with rapidly changing solution. In this setup you can try to see if redistributing the nodes can give you smaller error than an equidistant grid. If no exact solution is known, compare the results with a very refined/accurate numerical solution. |
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| Week 13 (27.03. - 31.03.) | - Espen in Rome and MTFYMA excursion. - Physical lectures replaced by recordings from 2022. … OBS: Only one lecture for that week. - Homework: Study carefully the Panopto recording of the lecture from week 13 in 2022. - Handwritten lecture notes under 'Plan of Lectures'. |
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| Panopto week 13 | The recordings for week 13 2022 can be found here. See the lecture dated 29.03.2022. |
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| Reference group | Meeting no 2 today. See short summary under 'Reference group' in the menu. | |
| 20.03. | Project 2 comment | In problem 2 e) you have to solve the equation with homogeneous boundary conditions and the right hand side given. Since no exact solution is known, compare the results with a very refined solution. |
| 15.03. | Supervision project 2 | Changes in the schedule, check under 'Exercises and projects' in the menu. Please organise your work so that you can make use of the time slots available. |
| 14.03. | Physical lectures… | … this week. I am back from Germany, and we go back to physical lectures. |
| 03.03. | Todays lecture | Order of dissipation is the minimal \(2s\) such that the definition given in class holds, see updated handwritten lecture notes in 'Plan of Lectures' in the menu. |
| Week 10 | - Espen in Germany. (But I lecture nest week - week 9!) - Homework: Study carefully the Panopto recordings lectures from week 10 in 2022. Intro FEM, very relevant for the exam. - Handwritten lecture notes under 'Plan of Lectures'. - Tuesday 07.03.: No physical lecture. - Thursday 09.03.: Q&A session + coding of FEM, by Alessandro. - Start looking the 1d FEM jupyter notebook, but note that part of this code uses an assembly technique that will be discussed in week 11. - It is a good idea to start working on Project 2. |
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| Panopto week 10 | The recordings for week 10 2022 can be found here. See the lectures dated 08.03.2022 and 10.03.2022. |
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| Homework | Read yourselves: Von Neumann stability for Lax-Wendroff, the Leap frog method, and systems of hyperbolic PDEs - BO section 7. | |
| 27.02. | Exercise 4 | Available now. Hyperbolic problems. |
| Project 2 | Project 2 is available now in the "Exercises and projects" page. | |
| 23.02. | Project 1 | * I have clarified the rules, see 'Exercises and Projects' in the menu. * Fattening the boundary: If the boundary condition is given in terms of a globally defined function (polynomial, trigonometric functions etc), you can just use this function itself as the extension outside the domain. * Iterative methods: Can be used to avoid computing the coefficient matrices in Problem 2. But if you have not tested such methods before - I suggest you drop it! |
| 14.02. | Monotone/ Pos.Coeff./ Stab. w.r.t. R.H.S | See 'Curriculum' under 'Course info' for where to find definitions in my handwritten notes. See also 'Plan of Lectures'. |
| Reference group | First meeting yesterday. See 'Reference group' in the menu for a short summary. | |
| Homework: | Read carefully the slides from week 7, see 'Plan of Lectures' in the menu. | |
| 10.02. | Exercise 3 comments | Some clarifications following questions on Exercise 3: *The condition \(\sigma^2>r\) is assumed in all the text, so even for Backward Euler in point b). In the text, replace "is monotone" by "has positive coefficients" everywhere (3 occurrences). * In point c) to show stability (and then convergence using consistency) for the implicit schemes (Cranck-Nicholson and Backward Euler) use the trick of the comparison function as seen in class \(-L_h(V_m^n-C\phi)\leq 0\), you need to come up with a suitable \(\phi\). * In point e) your scheme is supposed to be second order in time and space, thus exact for second order polynomials in time and space. The example function given thus shouldn't give you a convergence profile, since the solution will be always exact (up to machine precision), use a different one if you want convergence plots (for example \(\sin(x)\cos(t), x^4(1+t^3)\) etc.). * In point f) what you have to do is simulate using the given initial conditions (European put/binary call); in this case no exact analytical solution can be constructed. Use then a very refined numerical solution for a large value of \(R\) (small \(h\) and \(k\), and remember the CFL condition!). |
| 06.02. | Project 1 publication | Project 1 is now out. Please contact Alessandro as soon as possible in case you are still missing a group (or you communicated you need a group but you haven't been reached back yet). See 'Exercises and projects' for more info. |
| 23.01. | Exercise 3 (mandatory) | Exercise 3 (compulsory!) is now available under the section "Exercises and projects". (PS: You need a group to submit it!) |
| Exercise/Project groups | Send an email to Alessandro with the members (with email addresses) of your group (in English please). If you don't have a group, send an email, and you will be assigned to a group. |
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| Jupyter notebook | … for week 4 and 5: Numerical solution and testing of the 1d heat equation (forward Euler in time) | |
| Homework | Test the jupyter notebook. | |
| 19.01. | Todays lecture | Neumann BVP: \(u+C\) solution no matter which \(\sigma_1, \sigma_2\). General linear ODEs: \(A_h\) not symmetric only if \(p\neq 0\) (const. not enough). In Rem. 5: \(q>0\) not needed (as condition for well-posedness of (GL)). |
| Notes from lectures | … will be posted weekly after the two lectures. See 'Plan of Lectures' in the menu. OBS: These are the handwritten notes I use in class, they are not polished and may contain some mistakes. Since I deviate slightly from the note of Owren when it comes to stability and convergence, by introducing the discrete maximum principle and monotone schemes, these notes can be useful for you. |
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| 17.01. | Todays lecture | Typo on the blackboard: Wrong: \(\Omega = \cup_{P\in Q_{P,h}}Q_{P,h}\). Correct: \[\Omega = \cup_{P\in G_h} Q_{P,h}\] |
| Exercise 3, 2 projects | Exercise 3 one out of two projects are mandatory! The 2 projects count for 40% of the final grade (20% each). You work in groups of up to 3 students. Each group submits solutions/reports in ovsys2. Check the info and schedule carefully, see 'Exercises and projects' in the menu. |
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| Reference group | Amandus, Emil, and Ine volunteered - thank you very much! Feedback on the course? Contact me or the reference group - 'Reference group' in the menu. |
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| Office hours | Questions about the course? Come and talk to me. Thursdays 14:30 - 15:00, in my office, room 1148 SB2. |
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| 12.01. | Jupyter notebook | … for week 2 and 3: Numerical solution and testing of the 1d Poisson problem How to run it? Take a look at 'Course Software Info' under 'Course info' in the menu. |
| Homework | Check and run the Jupyter notebook for week 2 and 3 (above). Read yourselves: Section 2 in BO. Most of it is known from before. |
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| Exercise 1 | Available now, supervision week 3. Problem 4 is super useful for later exercises and projects, especially the programming part. The programming part can be solved by modifying appropriately the Jupyter notebook for week 2 and 3 (above). |
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| Slides | used in lectures will be posted under 'Plan of Lectures' every week (see the menu). | |
| 04.01. | First lecture | Tuesday January 10, 12:15-14:00. |
| Exercise classes | Here you get help to solve exercises and projects. Programming and theory. Fridays 8-10. No exercise class in week 2. |
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| No recordings in 2023 | The lectures will not be recorded this semester, and previous recordings will not be available. The reason is the very low attendance of the lectures in Spring of 2022 - combined with a much higher attendance when recordings then were dropped in most courses in the Fall of 2022. We want more students on campus because we belive that most of you learn and socialise better here than at home. (It is also more fun to lecture when more students show up  ). Exceptions can be made for "studenter med krav på tilrettelegging." |
Lecturer:
- Office hours: Thursday 14:30 - 15:00, in my office, room 1148 SB2.
Teaching assistant:
- Alessandro Contri (alessandro [dot] contri [at] ntnu [dot] no)
- Office hours: TBA
Student assistants
- Bendik Skundberg Waade
- Christian Oppegård Moen
Lectures:
Exercises:
- Friday 08:15-10:00, R4