Two talks

"Towards Optimal Design with Maxwell's Equations and HMM" by Wei Xi Boo from Oregon State University

and

"A mixed finite element approach to a flow vegetation root-soil model" by Nachuan Zhang Oregon State University

in STAG 113

Link  to AMC seminar. 

Absract: Wei Xi Boo presentation

We are interested in designing materials that have unique electromagnetic properties, for example, a material that does not absorb 5G signals. Electromagnetic waves like 5G signals are governed by a set of partial differential equations called Maxwell's equations. To describe the interaction of electromagnetic waves with materials, we couple Maxwell's equations with constitutive laws like the Lorentz model and Landau–Lifshitz model.

However, materials with such unique electromagnetic properties often have nano-scale structures. It poses a challenge to solve the particular solutions for Maxwell's equations numerically due to the computational cost. A numerical method for simulating Maxwell’s equations coupled with Heterogeneous Multiscale Methods for the constitutive laws will be presented.

Abstract Nachuan Zhang presentation

We consider a vegetation root-soil model which couples a Richards PDE in the soil domain and saturated flow in the root domain. A mixed finite element method is applied to obtain numerical solutions, and the well-posedness for its weak formulation and error estimates are studied. An equivalent cell-centered finite difference method is implemented in simulation. We provide numerical examples in 1D and 2D with different root domains, and study their convergence errors to validate our theoretical results.