可调节能量的时间积分用于弹性动力学接触
Energy-Controllable Time Integration for Elastodynamic Contact
AI总结：
本文提出了一种可调节能量的时间积分方法A-search，用于弹性动力学接触问题，通过灵活控制能量耗散或保存，提升模拟的稳定性和视觉效果。
摘要：
弹性体的动态模拟是工程和计算机图形学中的长期任务。在图形学中，数值积分器如隐式欧拉法和BDF2因其在大时间步长下的稳定性而被偏好，但它们倾向于不可控地耗散能量。相比之下，辛方法如隐式中点法可以保守能量，但并不无条件稳定，且在中等刚度问题上会失败。为了解决这些限制，我们提出了一类适用于哈密顿问题的数值积分器，它们在线性问题上是辛的，但在非线性问题上具有更优越的稳定性。基于此，我们推导出一种新的可调节能量时间积分器A-search，这是一种对隐式欧拉法的简单修改，可以跟随用户指定的能量目标，从而在保持稳定性和物理真实性的同时，灵活地控制能量耗散或保存。我们的方法无缝地与屏障型能量相结合，并允许无反转和无穿透的保证，使其非常适合处理大变形和复杂碰撞。广泛的评估涵盖了广泛材料参数和场景，证明A-search倾向于保持低频运动的能量而非耗散，并在相似的总运行时间内，通过保持能量和产生更视觉上可取的模拟，优于传统方法如BDF2。
英文摘要：
Dynamic simulation of elastic bodies is a longstanding task in engineering and computer graphics. In graphics, numerical integrators like implicit Euler and BDF2 are preferred due to their stability at large time steps, but they tend to dissipate energy uncontrollably. In contrast, symplectic methods like implicit midpoint can conserve energy but are not unconditionally stable and fail on moderately stiff problems. To address these limitations, we propose a general class of numerical integrators for Hamiltonian problems which are symplectic on linear problems, yet have superior stability on nonlinear problems. With this, we derive a novel energy-controllable time integrator, A-search, a simple modification of implicit Euler that can follow user-specified energy targets, enabling flexible control over energy dissipation or conservation while maintaining stability and physical fidelity. Our method integrates seamlessly with barrier-type energies and allows for inversion-free and penetration-free guarantees, making it well-suited for handling large deformations and complex collisions. Extensive evaluations over a wide range of material parameters and scenes demonstrate that A-search has biases to keep energy in low frequency motion rather than dissipation, and A-search outperforms traditional methods such as BDF2 at similar total running times by maintaining energy and leading to more visually desirable simulations.
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