Event Type:

Ph.D.Defense

Date/Time:

Tuesday, May 31, 2016 - 11:30 to 12:30

Location:

STAG 112

Guest Speaker:

Timothy Costa

Institution:

OSU Mathematics

Abstract:

In this work we consider two multiscale applications with tremendous computational overhead at the lower scale. First, we examine a model for charge transport in a heterostructure semiconductor. Due to the behavior 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 consider the problem of of the simulation of fluid flow in a dynamically evolving porous media. The evolution of the media strongly couples the porescale flow solutions and the macro scale model, requiring a novel approach to communicate the porescale evolution to the macrsoscale without resorting to the intractable simulation of the fluid flow problem directly on the porescsale geometry. We formulate novel methods for these problems in the multiscale framework. For the semiconductor problem we present iterative substructuring 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.