Implicit integration in large simulation

[jorj]

hello, I am an animation student at bournemouth university in England, I am writing a material simulator for my final major project ( some preliminary results http://www.youtube.com/user/jorjpimm ). The final idea is to have elastic, plastic and tearing and breaking material characteristics, all generated automatically, from a triangular mesh. A lot like http://www.pixeluxentertainment.com/ and their DMM, but mine uses no FEA, just mass and springs.

But I have two problems, one i am currently still using a forward euler integrator, with stiff springs and a tiny time step, any help in a better integrator choice would be appreciated ( i hear a lot about RK4 in games, and my tutors are pushing backward euler.

My other problems is that with a large simulation and collisions and unpredictable things like this, how does one use an implicit integration solution, for example in RK4 i need several samples of f(x) at different points inside h, how do i solve for these timesteps without using an explicit integrator, and then going back and using an implicit one ( which surely undoes any good RK4 might do )

Any help would be greatly appreciated, thanks
- Jorj

 

[jvicens]

Pimm

Dear Jorj Pimm,

First of all, let me say that your project sounds very interesting and challenging. I can understand your concerns about the integrator choice and using an implicit integration solution. Here are some suggestions that may help you with your project:

1. Consider using a higher-order integrator like the Runge-Kutta 4 (RK4) method that you mentioned. This method is commonly used in games and can provide more accurate results compared to a forward Euler integrator. It may also allow you to use a larger time step, which can improve the performance of your simulation.

2. You mentioned that your tutors are pushing for a backward Euler integrator. While this method is more stable than a forward Euler integrator, it may not be the best choice for your project. Backward Euler is known to be less accurate than other integrators, especially for stiff systems like the one you are simulating. I would recommend discussing this with your tutors and explaining your concerns about using a backward Euler integrator.

3. Another option is to use a symplectic integrator, which is specifically designed for simulating systems with conservative forces (such as springs). This type of integrator can provide better energy conservation and stability compared to other methods. Some examples of symplectic integrators are the Verlet and Leapfrog methods.

4. As for your second problem, using an implicit integration solution, you can consider using a predictor-corrector method. This approach combines an explicit integrator (such as RK4) with an implicit integrator to improve the accuracy and stability of the simulation. It works by first predicting the position and velocity of the particles using an explicit integrator, and then using this information to correct the predicted values using an implicit integrator.

5. You can also look into using a time-stepping technique called adaptive time stepping. This approach adjusts the time step size based on the behavior of the system, allowing for a more efficient and accurate simulation. This can be especially useful for large simulations with unpredictable collisions.

I hope these suggestions will be helpful to you in your project. Good luck with your final major project!