Crank nicholson

[brmather]

Implement a Crank Nicholson scheme for the diffusion equation.

Uses the "theta rule":

• theta=0 : forward Euler
• theta=1: backward Euler
• theta=0.5 : Crank Nicholson

[lmoresi]

Do we want this to pass the benchmarks before merging or have it as a placeholder and develop around it ?

[brmather]

It's not ready to merge, but I quite like having the PR open so we have one place to comment on stuff that doesn't work.

[brmather]

The problem I see with taking the line integral is that the natural neighbours are unordered. They were ordered anticlockwise when we obtained the triangulation from Qhull but that's quite time consuming to do here. There is probably a better way to go about it, but I've been chasing this white rabbit too long that I've entered the matrix. I'd appreciate if @lmoresi or @rbeucher could take a look.

Ex7b-LinearDiffusion.txt (uploaded as a txt file)

[lmoresi]

Renka’s code claims that it does order the neighbour nodes. We used to resort them by distance but I don’t think we do that now. Any loop will do for the line integral so around the neighbours is OK - boundaries might be weird though. On 9 Jul 2020, 4:34 PM +1000, Ben Mather <notifications@github.com>, wrote: The problem I see with taking the line integral is that the natural neighbours are unordered. They were ordered anticlockwise when we obtained the triangulation from Qhull but that's quite time consuming to do here. There is probably a better way to go about it, but I've been chasing this white rabbit too long that I've entered the matrix. I'd appreciate if @lmoresi<https://github.com/lmoresi> or @rbeucher<https://github.com/rbeucher> could take a look. Ex7b-LinearDiffusion.txt<https://github.com/underworldcode/quagmire/files/4894888/Ex7b-LinearDiffusion.txt> (uploaded as a txt file) — You are receiving this because you were mentioned. Reply to this email directly, view it on GitHub<#36 (comment)>, or unsubscribe<https://github.com/notifications/unsubscribe-auth/ADABPIYTYYDNQHBCCAGBBSTR2VQHRANCNFSM4OUJPO3Q>.