I was deterred from watching the video for the longest time because of the name of the channel, because I'm not studying Fluid Mechanics but honestly this is the best explanation of CG I found on youtube! You're really breaking it down into bits that are easy to understand and explain the relevant concepts from basics and built up on that. It only required attention but I finally understand it now. Thank you so much! :-)

Could not be more clear, thanks!

I really, really like your approach of explaining things. Like when you go through concrete examples with numbers instead of variables or explain physical meaning also circling back to the basics when needed, it makes it possible to understand this even for people like myself, who has very little experience if CFD solvers. Thank you very much.

The best explanation, anyone could ever find

what a great introduction to steepest descent method! Looking forward to your next lecture on CG and perhaps GMRES :D

A fantastic video mini series, I'm excited for the Part 2!

Best lecture I found on the Internet. Thank you so much. Now, I'm forwarding to the next lecture.

Great explanation to begin with gradient methods! Thank you for this video 😀

thank you for the clear instructions. You are more than a god to me

Great lecture, thanks so much. You took time to explain lots of things which other videos just stated.

Great effort, thanks

Wow, this was such an amazing explanation

Great video, helped me a lot. Big thanks to you!

Woooow! Very nice class! Please send the part 2!

Great work

I wish you had solved some examples, your explanation is great but hands on practice would really drill the method into my brain, specially that there is very few examples on youtube about those methods

Very nice class! Steepest gradient is a lot like gradient descent (used in neural networks).

So nice 🎉

Thank you Aidan, a great lecture! Currently I have encountered in my multi-phase magneto-hydrodynamics simulation using OpenFOAM convergence problems for the Poisson equation for the electric potential due to the presence of a low conductive phase. Algebraic multi grid (GAMG in OpenFOAM) was fast, but it stuck at low convergence level. Conjugated gradient (PCG in OpenFOAM) managed to converge (I need 1e-18 absolute tolerance at least), but it takes ~800 iterations. The great solution appeared to be a combo of PCG solver with GAMG preconditioner with Fast-DIC smoother. It allows to converge in 16 (only!) iterations. Would be nice to have some lecture on such hybrid approaches. Thank you in advance!

Really nice. I just implemented this algorithm (CG) for a problem I was working on, so it's really cool to see your take on it! Very detailed and beginner-friendly! Edit: why does it sometimes diverge? Maybe you can discuss that in the next lecture?

@wile9763

11 ай бұрын

CG methods are a member of a class of linear solvers called Krylov subspace methods. The iteration error of these methods can be shown to depend on the condition number of the matrix which is in turn determined by the eigenspectrum of the matrix. So, in short, if a linear system is sufficiently poorly conditioned, Krylov methods will diverge. Preconditioners are used to remedy this problem and represent a large area of interest in the literature.

@fluidmechanics101

11 ай бұрын

Exactly! Great response. I didn't want to get into condition number and pre-conditioners here, as I wanted to focus on actually understanding the method first. Hopefully I have succeeded!

@fzigunov

11 ай бұрын

@@wile9763 Thanks for the easy-to-understand response! This is also nice to know so I can improve my solver 🙂

@opencast1819

11 ай бұрын

@@wile9763 great answer! You can find some related experience in my comment above. Cheers!

Nice lecture, can you took about multiphase, vaporization and condensation ?

Hello, thank you very much for your video. However, in your video 34:20, you mentioned that all residuals point towards the global minimum. I would like to know, is this a special case or an inevitable situation? Because the residual equals the gradient,but the gradient does not necessarily point towards the global minimum.

These methods also solve the storage issue of sparse Matrix.. but how? Can someone please explain?

I find that u look like Sheldon

@fluidmechanics101

7 ай бұрын

😂😂

Promo_SM

There is better alternative to gauss seidel method. LUSGS method, gauss seidel method with approximate LU factorization.