February 9, 2017
Mathematics Colloquium Lecture 1xbet online sports betting . 9
Christina Frederick, Georgia Tech, will present "Multiscale Inverse Problems for Partial Differential Equations and Applications to Sonar Imaging" as part of the Mathematics Department Colloquium Lecture series at 2:30 p.m. Thursday, 1xbet online sports betting . 9, in 122 Cardwell Hall.
The abstract for the lecture is: A common objective in many data-driven sectors is to accurately describe intrinsic features of a complex process. This is a typical 1xbet online sports betting problem for finding parameters in a model from given data, for example determining coefficients in partial differential equations, or PDEs, from solution data. 1xbet online sports betting problems for PDEs pose daunting theoretical and computational challenges. For example, the classical 1xbet online sports betting conductivity problem posed by Calderon is severely ill-posed, even in the case of smooth, isotropic coefficients. The situation is worse when modeling heterogeneous materials such as composites, lung airways and vasculature, and sedimentary layers in the Earth’s crust. For a variety of reasons, including the high cost of simulations and uncertainty in the measurements, the models are often simplified by a smoothing or homogenization process. Using the analysis of 1xbet online sports betting conductivity problems, our results identify key parameters in highly oscillatory coefficients that withstand the loss of information due to homogenization. Multiscale methods for numerical homogenization are then used to efficiently predict the forward model while recovering microscale parameters. Ideas presented in this strategy can also be applied to solving 1xbet online sports betting problems in ocean acoustics that aim to characterize properties of the ocean floor using sonar data. Here, forward solvers incorporate simulations of Helmholtz equations on a wide range of spatial scales, allowing for detailed recovery of seafloor parameters including the material type and roughness. In order to lower the computational cost of large-scale simulations, we take advantage of a library of representative acoustic responses from various seafloor configurations.