EAGER: IIS (G&V):Scalable High-Fidelity Solids Simulation

【摘要】物理模拟的底层算法需要进行根本性的改变，才能使物理模拟在资源受限的应用（如实时游戏或外科训练）中实现数量级的性能改进。本研究主要研究三个问题：帧率模拟、异步进化和多级求解器。帧率模拟的方法包括通过仔细的能量管理原则来确保稳定性，以解决稳定性和阻尼问题。特别注意系统中人工阻尼的数量，可以避免过度阻尼的模拟，这是一个限制现有技术可能的时间步长的问题。这样的帧率模拟器实现了下一步：开发一种异步进化方案，允许在高频运动区域采取小的时间步长，在其他地方采取大的时间步长。开发异步方案的其他尝试在采用大时间步长时遇到过大阻尼的困难。本研究围绕所提出的帧率模拟器研究一种异步方法，以缓解这一问题，因为阻尼的数量可以显式控制。最后，为了减少单个时间步骤的成本，我们正在使用多层方法来减少求解物理模拟典型的大型线性系统所花费的时间。多层方法有着悠久的历史，但对物理仿真界来说却是一个新概念。寻找合适的粗化和精化算子是多层方法的关键，尽管难以表述，但有可能在求解这些系统的收敛率方面产生渐近改进。正在研究的方法代表了一种与当前技术完全不同的方法，这项探索性研究旨在证明这种潜在变革的可行性。

AbstractFundamental changes in the underlying algorithms of physical simulation are needed to bring about the orders of magnitude improvement in performance required to bring physical simulation to resource-constrained applications such as real-time games or surgical training. This research is investigating three issues: frame-rate simulation, asynchronous evolution, and multilevel solvers. The approach to frame-rate simulation consists of ensuring stability by careful energy management principles to address both stability and damping. Paying special attention to the amount of artificial damping in the system enables one to avoid excessively damped simulations, a problem that limits the time step size possible with existing techniques. Such a frame-rate simulator enables the next step: developing an asynchronous evolution scheme that allows small time steps to be taken in regions of high-frequency motion and large time steps to be taken elsewhere. Other attempts at developing asynchronous schemes have difficulty with excessive damping when taking large time-steps. This research is investigating an asynchronous method around the proposed frame-rate simulator in order to alleviate this problem, as the amount of damping can be explicitly controlled. Finally, to reduce the cost of a single time step, we are using multilevel methods to reduce the time spent solving large linear systems typical of physical simulation. Multilevel methods have a long history, but they are new to the physical simulation community. Finding suitable coarsening and refinement operators are key to multilevel methods and, although difficult to formulate, have the potential to create asymptotic improvements in the convergence rates of solving these systems. The methods being investigated represent a radically different approach from current techniques and this exploratory research is seeking to demonstrate the feasibility of this potentially transformative change.