[Example] A stable fluid demo with sparse matrix

[Hanke98]

Related issue = #2906 #2792

In this pr, we show a stable fluid demo that solves Poisson's equations by using the sparse matrix. Thanks to the fast LLT factorization, this demo runs about 5x faster than the Jacobian iteration version on the CPU backend (on my 2019 MBP i7-9750H ).

My questions are here:

1. Is it possible to directly write the solution of the linear system to the taichi fields? For now, I have to first get the solution in numpy and then transfer it to the fields of pressure.
2. Should we integrate this demo and the original stable fluid example into a single one? (by adding some options like use_sp_mat)

@FantasyVR could you please help me to figure them out? Thanks in advance!

[CLAassistant]

All committers have signed the CLA.

[netlify]

✔️ Deploy Preview for jovial-fermat-aa59dc ready!

🔨 Explore the source changes: 9634819

🔍 Inspect the deploy log: https://app.netlify.com/sites/jovial-fermat-aa59dc/deploys/615c38cd2a06670008b651a8

😎 Browse the preview: https://deploy-preview-3081--jovial-fermat-aa59dc.netlify.app

[yuanming-hu]

Thank you!

Is it possible to directly write the solution of the linear system to the taichi fields? For now, I have to first get the solution in numpy and then transfer it to the fields of pressure.

We had some discussions about this before, and I believe ultimately we need a feature like this to avoid copying. We probably need to design a set of reasonable APIs to reshape the solution from 1D to 2D. For now, I think we can stick to the numpy solution :-)

Should we integrate this demo and the original stable fluid example into a single one? (by adding some options like use_sp_mat)

Sounds like a good idea!

[Hanke98]

/format

[yuanming-hu]

LGTM! Very cool!

[k-ye]

Is it possible to directly write the solution of the linear system to the taichi fields?

- @strongoier, FYI our type system work should take into account the ability to do zero-copy with other frameworks. NDArray is a glimpse of this direction :-)

[Hanke98]

/format