We construct a subspace simulator that adaptively balances solution improvement against system size. The core components of our simulator are an adaptive subspace oracle, model, and parallel time-step solver algorithm. Our in-time-step adaptivity oracle continually assesses subspace solution quality and candidate update proposals while accounting for temporal variations in deformation and spatial variations in material. In turn our adaptivity model is subspace agnostic. It allows application across subspace representations and expresses unrestricted deformations independent of subspace choice. We couple our oracle and model with a custom-constructed parallel time-step solver for our enriched systems that exposes a pair of user tolerances which provide controllable simulation quality. As tolerances are tightened our model converges to full-space solutions (with expected cost increases). On the other hand, as tolerances are relaxed we obtain output-bound simulation costs. We demonstrate the efficacy of our approach across a wide range of challenging nonlinear materials models, material stiffnesses, heterogeneities, dynamic behaviors, and frictionally contacting conditions, obtaining scalable and efficient simulations of complex elastodynamic scenarios.

中文翻译：

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交易空间：用于联系 Elastodynamics 的自适应子空间时间集成


我们构建了一个子空间模拟器，可以自适应地平衡解决方案改进与系统大小。我们模拟器的核心组件是自适应子空间预言机、模型和并行时间步长求解器算法。我们的时间步自适应性 oracle 持续评估子空间解决方案的质量和候选更新建议，同时考虑变形的时间变化和材料的空间变化。反过来，我们的自适应性模型与子空间无关。它允许跨子空间表示应用，并表示独立于子空间选择的不受限制的变形。我们将 oracle 和模型与定制的并行时间步求解器耦合在一起，用于我们丰富的系统，该求解器公开了一对用户容差，从而提供可控的仿真质量。随着容差的收紧，我们的模型收敛到全空间解决方案（预期成本会增加）。另一方面，随着容差的放宽，我们获得了输出绑定的仿真成本。我们展示了我们的方法在各种具有挑战性的非线性材料模型、材料刚度、异质性、动态行为和摩擦接触条件中的有效性，从而获得了复杂弹性动力学场景的可扩展和高效仿真。