具有热涨落的流固系统的空间自适应随机多重网格方法
Spatially Adaptive Stochastic Multigrid Methods for Fluid-Structure Systems with Thermal Fluctuations
AI总结：
针对微观机械系统中弹性结构与溶剂流体之间的流体动力学相互作用及热涨落，提出基于多重网格的随机数值方法，实现空间自适应网格下的高效计算，复杂度为O(N log(N))。
摘要：
在微观机械系统中，弹性结构之间的相互作用通常由溶剂流体的流体动力学介导。在微观尺度上，弹性结构也受到热涨落的影响。基于多重网格开发了随机数值方法，能够有效计算存在壁面时的流体动力学相互作用以及热涨落。所提出的随机多重网格方法提供了有效的实空间数值方法，用于生成与统计力学一致的长程相关随机驱动场。该方法还允许使用空间自适应网格来解析流体动力学相互作用。数值结果表明，该方法在实际计算中具有O(N log(N))的计算复杂度。
英文摘要：
In microscopic mechanical systems interactions between elastic structures are often mediated by the hydrodynamics of a solvent fluid. At microscopic scales the elastic structures are also subject to thermal fluctuations. Stochastic numerical methods are developed based on multigrid which allow for the efficient computation of both the hydrodynamic interactions in the presence of walls and the thermal fluctuations. The presented stochastic multigrid approach provides efficient real-space numerical methods for generating the required stochastic driving fields with long-range correlations consistent with statistical mechanics. The presented approach also allows for the use of spatially adaptive meshes in resolving the hydrodynamic interactions. Numerical results are presented which show the methods perform in practice with a computational complexity of O(N log(N)).
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