UC San Diego

This dissertation deals with multiscale and multi-physics mathematical modeling and global sensitivity analysis. Multiscale and multi-physics problems are ubiquitous in every eld of science and engineering. For example, micro- or even nano-scale material properties often in uence their large-scale properties, and microscopic interfaces between dierent materials affect bulk transport phenomena.

We develop and deploy methods of global (variance-based) sensitivity analysis to determine how, and to what degree, nano-scale characteristics of (nano)porous materials aect and give rise to bulk (Darcy-scale) properties.

We deploy stochastic multiscale algorithms to solve several problems of relevance in materials science and biology, and conduct rigorous sensitivity analysis and uncertainty quantication. In Chapter 2, we present a novel hybrid algorithm to ameliorate high

computational costs typical of multiscale, multi-physics simulations, and apply it to solve a chemotaxis-diusion-reaction problem. In Chapter 3, we report on our pore- and multi-scale simulations and perform a global (variance based) sensitivity analysis for uncorrelated input parameters. This chapter also contains results of our uncertainty quantication analysis for this multiscale problem, which is based on a (generalized) polynomial chaos expansion (gPCE). This UQ strategy can be used to identify a set of pore-scale characteristics for robust materials design. In Chapter 4, we introduce a novel graph-theoretic approach to conduct global sensitivity analyses in the presence of correlated inputs.