Talk 1 Title: A Solution Method for Ordinary Differential Equations with Random Forcing
Speaker: Brian McKenzie
Abstract: We will discuss a method for solving odes with forcing functions involving random inputs. We will consider a certain change of basis involving generalized polynomial chaos (GPC) and demonstrate how this leads to a solution method using matrices constructed from the recurrsion coefficients of an orthogonal polynomial basis, while allowing us to avoid issues related to determining generalized Fourier coefficients via integration.
Talk 2 Title: Electromagnetic Relaxation Time Distribution Inverse Problems in the Time-Domain
Speaker: Megan Armentrout
Abstract: We consider wide bandwidth electromagnetic pulse interrogation problems for the determination of dielectric response parameters in complex dispersive materials. We couple Maxwell's equations with an auxiliary ODE modeling dielectric polarization. A problem of particular interest is to identify parameters in a standard polarization model (e.g., Debye) using time-domain electric field data. A larger class of materials (e.g., anomalously dispersive media) can be represented by assuming distributions of parameters (e.g., relaxation times). We present results for an inverse problem for the relaxation time distribution based on a least squares cost functional and utilizing generalized Polynomial Chaos in the forward problem.