Spatial adaptive sampling in multiscale simulation

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×^N0.14 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.