Laplace's Equation of Electric Potential (Solved in Python)

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It turns out that a sequence of convolutions is the most efficient way to solve Laplace's equation in python. In this video I tackle a 3D problem: the potential between two (finite size) parallel plates.
Code:
github.com/lukepolson/youtube...
Discord:
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[@Nickname006]

Amazing stuff once again! Thanks for all the work you do. Your videos are great for refreshing my memory on the undergraduate physics course material while keeping me lured in with amazing tutorials on how to actually solve/model these problems in Python. I think we need more of this kind of teaching in universities! Everytime you post a video, I get this feeling that I have to watch it or I will be missing out.

[@_RTheBruce]

I remember this stuff from university from years ago. Needed a good refresher. This was better than perfect.

[@andresyesidmorenovilla7888]

Dude, this channel is totally underrated. Great work!!!

[@sinecurve9999]

Dirichlet (dir-i-klay)
Neumann (Noi-man)
Euler (oi-ler)

[@hsh7677]

I've been waiting for this!!
You rock!

[@er_lee7540]

Amazing work! Thanks a lot. You deserve much more subscribers.

[@mingshey]

Truly amazing lesson this is, as are your other videos! I could learn this method and apply to the case of a field cage, as is used in time projection chambers.

[@pauljansen8744]

Great video tutorials! I wish your channel was around when I was doing my PhD, it would definitely have saved me a lot of time. Also nice setup at the end of your video for introducing multi grid methods, are you planning a short follow-up on that?

[@fufaev-alexander]

Thank you so much for this awesome Python content! 😍

[@mandyokpoji8787]

Well done son.
Reckon you should model photons spatial distribution when carrying orbital angular momentum (quadro and octopole atomic transitions and that)

[@user-ld8oo4zd6t]

Dude you gave me the inspiration thanks!

[@lucatonin1742]

Thank you, your videos are really useful!

[@underfilho]

such a beautiful contour plot

[@AJ-et3vf]

awesome video! Thank you!

[@Maniclout]

Very nice 👌🏼

[@scoot_tv]

You should do a strong field approximation vid

[@mikekertser5384]

Great Video, as always!
Could you please make a video of Navier-Stokes eqn. solution for some simple case with some turbulent flow algebraic approximation?
May be von-Karman sheets for 2D case?

[@ShinjiCarlos]

I would appreciate it as well lol

[@brauliops]

Nice video!!. How you calculate the electric field once you solve the potential?

[@zaid2095]

will you do tutorials in different coordinate systems? for instance we may want to solve for prescribed potentials on spherical surfaces?

[@adamtaylor2142]

I had to have one of my students in a graduate class tell me it was dee·ruhsh·lay (Dirichlet).

[@MrPSolver]

Interesting... Guess this is what I'm going with for now on!

[@MikiSH]

Hi, is there an easy way to represent the electric vector field in the contour graph??

[@javierguallart8250]

It would be really helpful if you add chapters to the video

[@perjohankasper]

always great, shortminded as i am cam i find the notes on github?

[@MrPSolver]

Ya, link is in the description!

[@lionelmartinez6810]

Could you make a video explaining how to graph the electric field?How is the gradient of a matrix calculated? Thank

[@GeneralPet]

There is a small issue, the laplace/averaging function will give different results depending on the resolution/number of points. So increasing N has an effect on the potential. How can I fix that?

[@MrPSolver]

It shouldn't have that effect. Is that something you programmed and noticed?

[@ShinjiCarlos]

So nice, man!
I guess this method of solving boundary condition differential equations used is the relaxation method, right?

[@MrPSolver]

Exactly!

[@YeduKrishnan]

14:35

[@brobroo6154]

How can l transform his code to a jupyter code?

[@ShinjiCarlos]

There is no difference, bruh. There isn't such a thing as a Jupyter code. It is either Python-, Julia- or R-coded. Just copy and paste it in a Jupyter notebook, it will work fine ^^V
PS.: I managed even to use a computational algebra program called Cadabra (written in C/C++) inside it.

[@monkeyofwar6818]

Oh shit we upgraded to 4k quality, nice

[@drfredkin]

Schrodinger died in 1961!

[@akhilc8381]

Hey!! Mr. P solver can you make a video on PID controller

[@ralphwalters906]

Pronounced DUR-EE-SHLAY

[@alexplyushch7297]

no intro music 😞

[@ShinjiCarlos]

Thank God! \o/

[@alexplyushch7297]

@Del Squared - دل تربيع Some people enjoy, others can skip, you know ;)

[@ShinjiCarlos]

@@alexplyushch7297, sorry, man xD
I just wouldn't let the opportunity go, you know?

[@MrPSolver]

I'll be back, don't worry 😉

[@neuralwarp]

TL;DW