Physics Simulation Forum

Here (http://fem.xp3d.net/files/sketch_v102.pdf) you can download quick sketch of part of our recent research. We present a method of solving mixed linear complementarity problem with box constraints applied to a typical formulation of modern constraint-based dynamics simulator, which is easy parallelizable (hence will take benefit of modern GPUs) and has O(N) complexity, while showing better convergence than typical PGS solver.
That's early version of the sketch, so if you will find any errors or inaccuracies, please let us know.

Update #1:
http://code.google.com/p/realtime-deformations-fem/ is our public code repository where you can download the source code of demos presented in this thread. GPU version of the solver is tested on NVIDIA GeForce GTX260.

Update #2:
Example in "Applying the preconditioner" fixed.

Thanks for sharing. That is really grand of you! I will read it.

First reflection. I don't see any system with complementarity conditions among the test systems. What type of systems that imposes bounds on the multipliers or velocity have you considered? And are the results for that also just as positive as for purely holonomic systems.

Ah, sorry, forgot to describe such test case. Actually in this forum thread, there is demos of the method described, and on the screenshot there is FEM brick, attached to world via chain of ball-socket joints, lying on the floor (contact joints with friction - here is where limits introduced). Actually, method is surprisingly good even with quite tight box constraints (e.g. low friction) - can't really share the numbers now, but if you want, I'll try to do some measurements on the weekend.
Actually, floor which produces contacts with friction is switchable in FEM stress demo too (long stiff brick), and it touches the floor when bending, also not really affecting convergence vitally.
One more thing I wanted to add in terms of test cases. We also tested arbitrary FEM models (up to 4k tetras) - they were main source of ill-conditioned systems, but having double Jacobi preconditioner, solver is converging quite fast there too. Models were falling onto floor with friction too, btw

We forgot to attach link to our public code repository, fixing that.. Link is now in the first post of the thread.

I have a quick question. How many iterations would need for say a stack of five boxes?

Dirk, sorry, but we didn't implement complex CD in our test framework, so we can't really say anything about stacks now. Although my assumption is that it would need about 15 iterations anyway because of CG nature.

Hi XperienS!I am very interested in your work!but I cannot download the paper with link you provided([http://fem.xp3d.net/files/sketch_v102.pdf)! Also with the same problem in another thread(viewtopic.php?f=6&t=5468)
Could you fix the link ,Thank you very much!