Back to Departmental Colloquium: Fall 2013
Departmental Colloquium
Date: Thursday, Nov 7, 2013
Time: 4:00PM
Location: LCB 219
Malgorzata Peszynska
Oregon State University
Title |
Hybrid Models and Interfaces |
Abstract |
In various applications, the mathematical models based on traditional partial differential equations (PDEs), with their empirically determined coefficients, and associated traditional numerical approximations, are not sufficient to describe all the relevant dynamics and complexity. In the talk, we describe a few alternative, hybrid computational models, which combine traditional numerical PDEs with other computational methods from, e.g., statistical mechanics, and more broadly computational physics and geosciences. The new models account for complicated physics occuring at material interfaces in semiconductors, or rock-fluid boundaries in evolving porous media. Sometimes the interfaces are dynamically evolving, e.g., as in phase interfaces aarising due to phase transitions in methane hydrates, and sometimes they are artificial, such as in heterogeneous domain decomposition solvers for fluids. These new modeling approaches need to be analysed and validated. The former is the charge for computational mathematicians; we overview our recent analysis of these models and indicate the challenges, not the least of which is a substantial interdisciplinary nature of these projects. |
Dynamical Systems
Mathematical Biology