Pre-computation Approach to Nonlinear Simulations of Deformable Objects
My research area involves building real-time interactive simulations of solid deformable objects. For example, liver tissue should defo1m realistically during a vi1tual surgery simulation. A virtual assembly simulation can catch airplane construction design flaws early on during the manufacturing process. Deformable objects are also useful in computer games, for example to model the motion of trees in the wind. Researchers in computational physics, mechanics, and applied mathematics have been developing algorithms for simulations of deformable objects for the past 40 years. However, the partial differential equations of solid continuum mechanics that govern deformations of physical objects are very involved and as such computationally demanding. Even on a modern computer, long computation times are necessary to simulate such systems. This effectively prohibits interactive simulations of objects with detailed geometry, because such simulations require the state of the system to be updated at very fast rates: for example, 30 times per second for quality visual feedback and 1000 times per second for quality force-feedback. It can easily take several seconds for traditional methods to compute one timestep of a simulation of a large model, such as a liver model with 15,000 elements. The goal of my research is to develop methods that require substantially less computation time, while at the same time sac1ificing as little accuracy as possible in the solution. An interesting question is the following: Given a fixed amount of computation time, what deformable object algorithm achieves the highest simulation accuracy (for a large class of deformable models)?