In microscopic mechanical systems interactions between elastic structures areoften mediated by the hydrodynamics of a solvent fluid. At microscopic scalesthe elastic structures are also subject to thermal fluctuations. Stochasticnumerical methods are developed based on multigrid which allow for theefficient computation of both the hydrodynamic interactions in the presence ofwalls and the thermal fluctuations. The presented stochastic multigrid approachprovides efficient real-space numerical methods for generating the requiredstochastic driving fields with long-range correlations consistent withstatistical mechanics. The presented approach also allows for the use ofspatially adaptive meshes in resolving the hydrodynamic interactions. Numericalresults are presented which show the methods perform in practice with acomputational complexity of O(N log(N)).
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