TMA4212 Numerical solution of differential equations by difference methods - Spring 2022

NTNU course description.

Oral exam on August 18, 2022. To get a time slot for the exam, contact Espen as soon as possible.

Problems and solutions

How to compute the grades: Grading instructions

OBS: THE FIRST GRADES (PUBLISHED IN JUNE) IN STUDENT WEB NOT CORRECT!

They corresponded to exam grades only and not the combined grades.

Update 07.07.: The correct grades are now in Inspera and FS, Student Web should updated automatically within 1-2 days (I have no way of checking this).

We need 2 assistents for 2023. If you are interested, contact me (Espen) by email.

We need assistents that are good programmers and can supervise on coding/implementational issues.

Expected work: About 50 hours (preparation for supervision, programming of parts of projects, and 20 hours of student supervision). You will be paid by IMF.

Messages

Date	Title	Message
24.05.	Project 3 solutions	Partial solutions are out now for Project 3.
23.05.	Update on exam aids	You are allowed to bring also Strikwerda chp 13 and 14 to the exam. The 2 chapters will also available in Inspera as PDF attachments.
20.05.	Solutions to projects	We plan to post some solution sketches for project 3, but no code. We do not have the capacity to post more solutions this semester. Next year we will restructure the exercises and project and provide more solutions.
19.05.	Project 3 and Final Grades	Evaluations for project 3 are out now, together with the overall final grades for the part regarding the project. You can find the latter under the table where all the project-related files are linked.
27.04.	Reference group	Final meeting, see 'Reference group' in the menu for a short summary.
22.04.	Exam in English	Since all the course material is in English, the exam problems will be given in English only. You may write you answers in Norwegian or English as you prefer, but I recomend English.
	Project2 evaluations	Evaluations for Project2 are out in the page "Exercises and projects". If you strongly disagree with the grade or encounter some points you would like to discuss please write Alessandro or fix an appointment with him.
21.04.	Todays lecture	… finished before I had concluded the stability argument.   The complete argument - and an explanation of how to use this and consistency to get error estimates and orders of the scheme - can be found in the lecture note for week 16. See "Plan of Lectures" in the menu. This lecture note is very relevant for this years exam… \\
20.04.	Lecture Thu 21.04.	Discussion of the curriculum, the exam, some exam problems.
	Lecture Tue 26.04.	Last lecture: Supervision of project 3.
	Finial curriculum	See "Course info" in the menu.
	Exam info	See "Course info" in the menu. Note in particular what you can and cannot bring to the exam - new update 20.04.2022!
	Project 3	Deadline: May 1st, 23:59 Supervision tomorrow (Friday) and next week (Tuesday and Friday). All info under ""Exercises and projects" in the menu. Even if you can not hand in project 3, you should do it as an exercise. It is part of the training of this course, part of the curriculum, and very relevant for the exam.
07.04.	Todays lecture	There was a (small) mistake in my lecture (announced during the lecture). Solution: To find \(\beta_k\), we need to minimize not \(\varphi(x_{k+1})\), but \[\varphi(x_{k+2})= \dots = x_{k+1} + \alpha_{k+1}(p_{k+1} +\beta_kp_k)=F(\beta_k)\] with respect to \(\beta_k\). With this change, all computations in class are correct. I have updated and posted my handwritten lecture notes.
	Homework	Read yourselves: Implementation of CG, Strickwerda chp. 14.3.
30.03.	Lecture tomorrow cancelled	I have too much work right now and need to cancel the lecture tomorrow, Thursday March 31. I will still lecture all the planned materiel in good time. (I have been efficient so far - so we are doing very well right now).
24.03.	Reference group	Meeting 2 held today, see "Reference group" in the menu for a short summary.
22.03.	Todays lecture	Cea's lemma and best approximation/projection was not completely precise. The proof of Cea's lemma implies that \[\|u-u_h\|_E\leq \inf_{v_h\in V_h}\| u-v_h\|_E,\] where \(\|v\|_E=\,<u,u>^{1/2}\) is the energy norm and \(<u,v>=\frac12\big(a(u,v)+a(v,u)\big)\) is an (equivalent) inner product on \(V\). Hence \(u_h\) is the best approximation of \(u\) in \(V\) with the norm \(\|\cdot\|_E\) which is equivalent to \(\|\cdot\|_V\): \[\alpha^{1/2}\|v\|_V\leq \|v\|_E \leq M^{1/2}\|v\|_V \qquad\text{for all}\qquad v\in V.\] I have updated the lecture notes to clarify these points.
17.03.	Todays lecture	I have added more details about the assembly process in the handwritten lecture notes, see "Plan of Lectures" in the menu.
	1d FEM jypnb	A simple Jupyter notebook doing assembly and solution of a 1d Poisson problem with P1 FEM, can be found in under "Week 11" in "Plan of Lectures" in the menu. Update: Now the link is working - check it out!
10.03.	Project 2	Is now published! Deadline March 27th. Supervision: Fridays 11.03., 18.03., 25.11. All info can be found under "exercises and projects".
03.03.	Homework	Read yourselves: Leap frog method, systems of hyperbolic PDEs - in BO section 7.
01.03.	Exercise 3	Now available, see "Exercises and projects" in the menu.
16.02.	Reference group	A short summary of meeting no 1 can be found under "Reference group" in the menu.
10.02.	Project supervision	Projects will be supervised in Exercise classes Fridays 08:15-10:00. We have two additional assistents to help you out in the project period - Ottar and Johannes. Note that here you can also get help with programming/implementation. Make good use of this possibility - and do not wait - start working now!
	Project groups	An excel file with the members of the different groups can be found in the section "Exercises and projects". In case of errors or missing components contact Alessandro.
	Project 1 info	Including schedule/supervision, see "Exercises and projects" in the menu. Read carefully. Project deadline: 27.02.2022.
07.02.	Exercise 2	Exercise 2 pdf and jupyter notebook have been updated with some hints/code. If download problems still occur refer to the updated link in Mattelab for the file "heat_forweuler.ipynb".
03.02.	Project 1	Project 1 has been published in page "Exercises and Projects". You have to work in groups of 3 students, and the groups must be registered. Send an email as soon as possible to Alessandro with the group members in your group (in English please). If you don't have a group, send an email, and you will be assigned to a group. Deadline for registration of groups: Wednesday 09.02.2022.
	About the projects	You can do up to 2 out of 3 projects, and each project counts for 20% of the final grade (max 40%). One must be passed in order to take the exam. For more info and supervision, see "Exercises and projects" in the menu.
	Office hours	Wednesdays 16:15-17:00 on Zoom: See blackboard for the zoom-link.
	Homework	a) Read about the \(\theta\)-method (BO sec. 4.2.5) and stability of this method (BO p. 55-56) b) Read BO sec 5.3 on Domain of dependence. c) Discretization of B.C. (BO sec. 4.4 - similar to 1d Poisson!)
27.02.	Todays lecture	Slides and handwritten notes available, see under "Plan of Lectures". The notes includes the end of the proof of max-norm-stability for (BE) that came after filming stopped.
	Exercise 2	Now available, see "Exercises and project" in the menu. Both theoretical and programming problems and an attached Jupyter notebook. Doing Exercise 1 and 2, will help you prepare for Project 1 (and the exam). Available help: Exercise classes Fridays and Mattelab forum.
	Physical exercise class	From tomorrow Friday 28.01, all exercise classes will be physical. Place: F6, time 8:15-10:00. The room capacity is very good, bring Laptops and ask about programming as well as theory.
20.01.	Hybrid teaching	Hybrid lectures from Tuesday 25.01. and onwards. Lectures in F6 and stream/recordings in Panopto. F6 capacity under 1 meter rule: 38. With 51 students in class, this is probably sufficient for everyone who wants to attend. No signup for the first lecture now. Streaming/recordings: The video-link can be found under "Course info" in the menu, and then "Lectures".
	Exercise class tomorrow Fri 8:15-10:00	On zoom and mattelab forum, links are found under "Exercises and projects" in the menu. Help available for programming and theory.
17.01	Problems with recordings	Some students report having access problems to the Zoom recordings. I have updated the settings and hope it works now. If it still does noe work, I have to refer you to my lecture notes (see below).
13.01.	Correction! to lec 1 and 2	I have made a mistake in the error analysis and need to redefine the matrix \(A_h\) and vector \(\vec F\) to fix it: \(A_h=\frac 1{h^2} \text{tridiag}\{-1,2,-1\}\) and \(\vec F= [f_1+\frac{g_0}{h^2}, f_2,\dots,f_{M-1}+\frac{g_1}{h^2}]\). I have corrected this mistake throughout the electronic notes and also tried to clarify the definition of stability more. The result can be found under "Week 2" in "Plan of Lectures" in the left menu.
	jupyter nb	A python code (jupyter notebook) for computing and testing the 1d Poisson problem can be found under "Week 2" in "Plan of Lectures" in the left menu.
	Homework	a) Read section 2 in the note of Owren (see "Course info" in the left menu). This is well-known material. b) Read carefully my corrected lecture notes mentioned above. c) Check and experiment with jupyter notebook mentioned above.
	Exercise 1	… was posted today, see "Exercises and project" in the left menu. It covers the first 2 weeks of the curriculum. You should work it out well to learn the course, including the programming part . It will be very helpful for you to do it before the first project.
10.01.	First Lecture	Tuesday 11.01.
	Digital teaching…	… the first two weeks. We will use Zoom. To participate in the lectures (realtime), use the info provided on the course page in Blackboard. If you have questions, use the chat or unmute yourself. The lectures will be recorded, and manually posted on Panopto once a week.
	Physical/hybrid teaching	From 25.01. (3rd week of teaching). The lectures will be recorded, and automatically uploaded to Panopto. More info will follow.
	Exercise classes	Here you get help to solve exercises and projects. Programming and theory help. No exercise class this week.
	Recorded lectures…	… can be found under "Course info" in the left menu.

• Espen R. Jakobsen (espen [dot] jakobsen [at] ntnu [dot] no)
• Office hours: Wednesday 16:15-17:00, in my office, room 1148 SB2.

• Alessandro Contri (alessandro [dot] contri [at] ntnu [dot] no)
• Office hours: Friday 10:00-12:00, on appointment by e-mail through Teams/Zoom, room 1144 SB2.

• Ottar Hellan
• Johannes Kolstø

• Tuesday 10:15-12:00, F6/digital
• Thursday 10:15-12:00, F6/digital

• Friday 08:15-10:00, F6/digital.