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Live Jupyter Notebooks for Seismology
http://seismo-live.org
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A possible problem with the linear advection code #43

Open sangeethsimon2 opened 3 years ago

sangeethsimon2 commented 3 years ago

Hi Krischer, I was going through your code and found that in its present form, the code is specifically capable of only handling situations where the nodal DOF match with the quadrature points. However, this need not always be the case as you may know. For example, this code would break if I wanted to choose more quadrature points than the DOF, say to overintegrate the solution and obtain a non-diagonal (or exact) mass matrix. Given this issue, what additional modifications do you think has to be done to address this issue?

krischer commented 3 years ago

Heyhey,

I assume you mean the nodal DG advection code? I did not write that notebook but @swollherr did so I'm looping them in. While I realize that one could change the quadrature rule to use other points I'm really no numeric expert so I'll have to defer this question to someone else.

The main purpose of seismo-live in general is to educate people in various topics of seismology and related disciplines. If you can think of a modification to this notebook without adding a lot of complexity (or maybe even a new one) that would be great and we'd be glad to have it. In case you are looking for a usable production solution you are probably better of looking at tools like Fenics or potentially even a dedicated software for your purpose.

sangeethsimon2 commented 3 years ago

Hi Krischer,

I assume you mean the nodal DG advection code? - Yes. Since you have used the Lagrange polynomials, your construction falls into that category.

If you can think of a modification to this notebook without adding a lot of complexity (or maybe even a new one) that would be great and we'd be glad to have it. - Actually, the code can be extended. But for that, we need to pin down the math behind what to do for incorporating a generic number of quadrature points. I guess it has something to do with projection from the nodal DOF space to the required quadrature space, although I am not sure. If @swollherr replies and is interested in discussing this, we could try to fix it.

In case you are looking for a usable production solution you are probably better of looking at tools like Fenics or potentially even a dedicated software for your purpose. - I am new to this area as well and was trying to write my own code. I was skimming through various codes on GitHub when I came across yours and eventually took interest. Thats the story! But thanks for the pointers towards other codes.