On the impact of explicit or semi-implicit integration methods over the stability of real-time numerical simulations

Physics-based animation of soft or rigid bodies for real-time applications often suffers from numerical instabilities. We analyse one of the most common sources of unwanted behaviour: the numerical integration strategy. To assess the impact of popular integration methods, we consider a scenario where soft and hard constraints are added to a custom designed deformable linear object. Since the goal for this class of simulation methods is to attain interactive frame-rates, we present the drawbacks of using explicit integration methods over inherently stable, implicit integrators. To help numerical solver designers better understand the impact of an integrator on a certain simulated world, we have conceived a method of benchmarking the efficiency of an integrator with respect to its speed, stability and symplecticity.