摘要
We present a systematic study of homogenization of diffusion in random me- dia with emphasis on tile-based random microstructures. We give detailed examples of several such media starting from their physical descriptions, then construct the associated probability spaces and verify their ergodicity. After a discussion of material symmetries of random media, we derive criteria for the isotropy of the homogenized limits in tile-based structures. ~rthermore, we study the periodization Mgorithm for the numerical approxi- mation of the homogenized diffusion tensor and study the algorithm＇s rate of convergence. For one dimensional tile-based media, we prove a central limit result, giving a concrete rate of convergence for periodization. We also provide numerical evidence for a similar central limit behavior in the case of two dimensional tile-based structures.
We present a systematic study of homogenization of diffusion in random me- dia with emphasis on tile-based random microstructures. We give detailed examples of several such media starting from their physical descriptions, then construct the associated probability spaces and verify their ergodicity. After a discussion of material symmetries of random media, we derive criteria for the isotropy of the homogenized limits in tile-based structures. ~rthermore, we study the periodization Mgorithm for the numerical approxi- mation of the homogenized diffusion tensor and study the algorithm＇s rate of convergence. For one dimensional tile-based media, we prove a central limit result, giving a concrete rate of convergence for periodization. We also provide numerical evidence for a similar central limit behavior in the case of two dimensional tile-based structures.
基金
supported by the NSF grant DMS-0610013
