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Spatial adaptive sampling in multiscale simulation

机译:多尺度模拟中的空间自适应采样

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In a common approach to multiscale simulation, an incomplete set of macroscale equations must be supplemented with constitutive data provided by fine-scale simulation. Collecting statistics from these fine-scale simulations is typically the overwhelming computational cost. We reduce this cost by interpolating the results of fine-scale simulation over the spatial domain of the macro-solver. Unlike previous adaptive sampling strategies, we do not interpolate on the potentially very high dimensional space of inputs to the fine-scale simulation. Our approach is local in space and time, avoids the need for a central database, and is designed to parallelize well on large computer clusters. To demonstrate our method, we simulate one-dimensional elastodynamic shock propagation using the Heterogeneous Multiscale Method (HMM); we find that spatial adaptive sampling requires only ≈50 × N~(0.14) fine-scale simulations to reconstruct the stress field at all N grid points. Related multiscale approaches, such as Equation Free methods, may also benefit from spatial adaptive sampling.
机译:在多尺度仿真的一种通用方法中,必须用精细尺度仿真提供的本构数据来补充不完整的宏观尺度方程组。从这些精细模拟中收集统计数据通常是压倒性的计算成本。我们通过在宏求解器的空间域上内插精细比例仿真的结果来降低成本。与以前的自适应采样策略不同,我们不会在精细规模仿真的输入的潜在非常高维空间上进行插值。我们的方法在时空上是本地的,无需中央数据库,并且旨在在大型计算机集群上很好地并行化。为了演示我们的方法,我们使用异质多尺度方法(HMM)模拟一维弹性动力冲击传播;我们发现,空间自适应采样仅需要≈50×N〜(0.14)精细模拟即可重建所有N个网格点的应力场。相关的多尺度方法(例如无方程式方法)也可能会受益于空间自适应采样。

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