# Implicit integration in large simulation

• jorj
In summary, it is important to carefully consider the integrator choice and explore different techniques such as symplectic integrators, predictor-corrector methods, and adaptive time stepping to improve the accuracy and stability of your 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

Last edited by a moderator:
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!

## 1. What is implicit integration in large simulation?

Implicit integration in large simulation refers to a numerical method used to solve differential equations in a large-scale simulation. It involves incorporating the effects of all variables, including those that are not explicitly known, into the simulation.

## 2. How does implicit integration differ from explicit integration?

Explicit integration only considers the effects of known variables, while implicit integration takes into account the effects of both known and unknown variables. This allows for more accurate and stable simulations, especially in cases where the system is highly nonlinear or has stiff differential equations.

## 3. What are the advantages of using implicit integration in large simulation?

Some of the advantages of implicit integration include greater stability, better accuracy, and the ability to handle stiff systems. It also allows for larger time steps, which can improve the efficiency of the simulation.

## 4. What are some common applications of implicit integration in large simulation?

Implicit integration is commonly used in many fields, including physics, engineering, and computer graphics. It is often used to simulate complex systems such as fluid dynamics, structural mechanics, and electromagnetics.

## 5. Are there any limitations to using implicit integration in large simulation?

While implicit integration has many advantages, it also has some limitations. It can be more computationally expensive than explicit integration, and it may require more advanced techniques to solve the resulting equations. In some cases, explicit integration may still be preferred for simpler or more linear systems.

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