Graduate Thesis Or Dissertation
 

Hybrid Multiscale Methods with Applications to Semiconductors, Porous Media, and Materials Science

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https://ir.library.oregonstate.edu/concern/graduate_thesis_or_dissertations/t722hd56q

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  • In this work we consider two multiscale applications with tremendous computational complexity at the lower scale. First, we examine a model for charge transport in semicon- ductor structures with heterojunction interfaces. Due to the complex physical phenomena at the interface, the model at the design scale is unable to adequately capture the behavior of the structure in the interface region. Simultaneously it is computationally intractable to simulate the full heterostructure on the scale required near the interface. Second, we con- sider the problem of the simulation of fluid flow in a dynamically evolving porous medium. The evolution of the medium strongly couples the porescale flow solutions and the macro scale model, requiring a novel approach to communicate the porescale evolution to the macroscale without resorting to the intractable simulation of the fluid flow problem di- rectly on the porescale geometry. We formulate novel methods for these two applications in the multiscale framework. For the semiconductor problem we present iterative sub- structuring domain decomposition methods that decouple the interface computation from the macroscale model. For the fluid flow problem we develop a reduced order three-scale fluid flow model based on a spatial decomposition of the porescale geometry and the offline approximation of a stochastic process describing macroscale permeability paramaterized by the volume fraction of the evolved geometry.
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