Spatially adaptive stochastic numerical methods for intrinsic fluctuations in reaction-diffusion systems
Spatially adaptive stochastic numerical methods for intrinsic fluctuations in reaction-diffusion systems
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DOI：
10.1016/j.jcp.2010.01.012
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发表时间：
2010-03
期刊：
影响因子：
--
通讯作者：
P. Atzberger
中科院分区：
文献类型：
--
作者：
P. Atzberger
在微观力学系统中，弹性结构之间的相互作用通常是由溶剂流体的流体力学介导的。在微观尺度上，弹性结构也受到热波动的影响。建立了基于多重网格的随机数值计算方法，可以有效地计算壁面存在时的水动力相互作用和热波动。所提出的随机多重网格方法为生成符合统计力学的远程相关随机驱动场提供了有效的实空间数值方法。提出的方法还允许使用空间自适应网格来解决流体动力相互作用。数值结果表明，该方法在实际应用中是可行的，计算复杂度为O（N log(N)）。
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)).