Weekly plans and update for week 39

Hi everybody, here comes a short update on last week and plans for this week.

Last week we discussed in more details the mathematics and physical cases of project 2, in particular we discussed in more detail the Jacobi method and how to scale our equations and convert a quantum mechanical system into a dimensionless equation which allows to reuse large parts of the code from part 2b. We discussed also unit tests. Here we would to emphasize that although we made demonstrations with the library catch++, see https://github.com/catchorg/Catch2, the important for us is to start thinking what can go rong and how can we test that our program is running correctly. This means actually trying to get a deeper understanding of what we are doing. Many of unit tests we can implement are thus related  to the algorithms we are implementing. Having analytical solutions is thus one of those examples which we should use in tests of our code. 

The material we discussed is covered in the lecture notes chapter 7  https://github.com/CompPhysics/ComputationalPhysics/blob/master/doc/Lectures/lectures2015.pdf as well as in the slides on eigenvalues, see for example http://compphysics.github.io/ComputationalPhysics/doc/pub/eigvalues/html/eigvalues.html

On Thursday this week, we will end our discussion of eigenvalue problems, discussing how to find the eigenvalues of a tridiagonal matrix in a more efficient way than using Jacobi's method, we will discuss Householder's method and finally Lanczos' iterative scheme. 

We will also say something about vectorization and compiler flags if we get time, else we discuss this topic on Friday.

On Friday, we start our discussion of ordinary differential equations. This will be relevant for project 3, which deals with developing a solver for the solar system. The differential equations material is covered in chapter 8 of the above lecture notes and the slides at 

http://compphysics.github.io/ComputationalPhysics/doc/pub/ode/html/ode.html

Else, at the lab sessions we continue with project 2.  Keep also in mind that the digital lab on Fridays from 14 to 16 (lab 9) is available. See the weekly schedule at https://www.uio.no/studier/emner/matnat/fys/FYS3150/h20/timeplan/index.html  There you find also the zoom links to the lectures and the labs.  Else, we remind you also that the labs on Fridays from 14 to 18 in room FØ434 are open to everybody (you just need to register your name when you arrive due to covid-19 tracking). 

Best wishes to you all,

Anders, Aksel, Kaspara, Maria, Morten, Rene' and Sebastian