Zizhou --

The Stokes (not NS) 2D lid-driven cavity example in Chapter 14 of my book focuses on algorithmic and parallel scaling relevant to your NS case. I look at block and multigrid preconditioner combinations that give good performance at high resolutions. (The runs shown in the text, done on my desktop, go up to 4 x 10^7 degrees of freedom.) See

https://github.com/bueler/p4pdes/tree/master/python/ch14

for the code, which includes some good solver-option combinations, and here for the book

https://my.siam.org/Store/Product/viewproduct/?ProductId=32850137

This may help a little, but as usual no magic bullets.

On Mon, Apr 12, 2021 at 7:01 AM Zizhou Huang <zizhou@nyu.edu> wrote:

To one whom it may concern,

I'm a PhD student at NYU. I'm working on a project on solving the Navier-Stokes equation with FEM, so I'm really interested in the amazing demo of solving the Navier-Stokes equation on the website. (https://www.firedrakeproject.org/demos/navier_stokes.py.html)

I modified the code to solve the 3d lid-driven cavity problem with a uniform grid of size 40x40x40, and found that it takes extremely long time and large memory. I had the same issue with my code of similar sizes, which uses Pardiso to solve the linear system. I'm wondering if fem is indeed unsolvable for a large problem like this? Do you have any experience to make it faster by changing the parameters in the linear solver?

Looking forward to hearing from you.

Best,
Zizhou
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