The investigator focuses on material models involving multiple coexisting scales, for which ad-hoc computational approaches frequently yield unsatisfactory results. Through a rigorous mathematical study, she finds effective parameters and approximations that are not otherwise obvious. She combines computational and analytic tools to produce novel techniques that can simulate and image composite materials. In particular, the study involves structures arising from photonic bandgap materials, geophysical inversion, and heterogeneous electrochemical surfaces. The investigator answers open questions about the interaction of small scale parameters, solution expansions at singularity surfaces, and the links between continuous and discrete inversion.
Often the behaviors of many material substances, whether geological deposits or designed electromagnetic materials, depend on interactions between components of the materials at different scales of length. The investigator studies problems of this sort, in which advances have an impact in the applications area as well as in mathematics. The new photonic simulation techniques aid in the development of the next generation of nano-scale materials and optical devices. The tailored computational approaches allow for more accurate geophysical prospecting. The investigator and collaborators also analyze models that further the fundamental understanding of certain electrochemical processes. Both graduate and undergraduate students benefit by participating in the project at appropriate levels.
