Small Step XPBD FEM Demo

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jak
Posts: 3
Joined: Mon Jun 07, 2021 5:12 am

Small Step XPBD FEM Demo

Post by jak »

Hi guys,

I've been working on a small step XPBD-based implementation of FEM off and on for the last several months, and I think I finally have something that someone might find interesting. Here's a WASM demo showing the current state of things: https://jak-xyz.github.io/xpbd-fem/. At some point I had delusions of grandeur of building an interactive walkthrough to show off the features, but unfortunately right now you're just presented with a wall of controls and an even bigger wall of text explaining them.

I think the two most interesting things about the demo are that it attempts to tackle incompressible FEM and it shows off higher-order elements (like quadratic quads/hexahedra). Until you peek at the demo this next sentence won't make too much sense, but the performance of the Sub energy function with Q4 and H8 element types seems promising. You can keep the number of steps/second pretty low and still maintain good stability and volume preservation, especially with 2-3 extra volume constraint passes.

Interestingly, I've found the WASM version running in Chrome to perform indistinguishably from native version. I have not attempted to add WASM SIMD support, but with an older version of the code I was getting a full 8x speedup with a trivial structure of arrays AVX2 implementation in a native build. The one issue I had to work around is that small step XPBD tends to require double precision floats and, in fact, single precision floats were insufficient for storing nodal position values. The constraints themselves, on the other hand, are calculated in normalized element space, which is not so sensitive, so the vast majority of calculations can be on regular floats.

The code is here: https://github.com/jak-xyz/xpbd-fem, though I abandoned all attempts at tutorializing anything, so it's probably only readable to someone with a pretty good handle on FEM to begin with. That said, someone implementing their own XPBD FEM may find it useful to look at the code for normalizing things like compliance and damping against element size.

In the not-too-distant future I intend to add support for higher-order triangle and tetrahedron element types. I may also investigate storing additional values than just positions per node. I briefly tried storing volume per node, and that fixed hourglassing in the fully integrated mixed energy function, but I didn't really dive into its performance characteristics, so I might do that later.

Finally, I'd like to give a shout out to Matthias Müller and his SIGGRAPH(?) 2008 course notes on linear, co-rotational FEM (https://cgl.ethz.ch/Downloads/Publicati ... enotes.pdf). I've attempted to learn about FEM several times in the past, but always bounced off. Coming from a game development background, this is still the clearest intro to FEM I've seen, and it was enough to let me get a toe-hold into the wider subject.
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