ABSTRACT (talk by Boo): Meta-materials have unique electromagnetic properties and possess transformative potential for optics. Electromagnetic waves are governed by a set of partial differential equations called Maxwell's equations. The material response to electromagnetic waves is modeled by constitutive laws. Accurate simulations of Maxwell's equations with dispersive constitutive laws can aid the design of such materials. However, materials with such unique electromagnetic properties often have nano-scale structures that pose a challenge in solving Maxwell's equations numerically due to the resulting high computational cost. We describe a novel numerical method enabled by Heterogeneous Multiscale Methods (HMM), designed to simulate Maxwell’s equations coupled with the constitutive laws efficiently. We also present an energy analysis and error analysis for this numerical method.

ABSTRACT (talk by Cowal): Traditional algorithms for CT reconstruction require measurements to be taken non-locally; imaging a small area of interest requires taking X-ray measurements through a much larger area. Algorithms for local and pseudo-local tomography allow for reconstructions using only measurements through a region of interest, but they require prior information about the subject or can produce lower quality reconstructions. In this talk, I'll present an algorithm that uses a small number of non-local measurements to greatly improve the accuracy of a local reconstruction. This method can be adapted to arbitrary scanning geometry.