Spotlight: Computational and Data Science
Computational science encompasses modeling, analysis, simulation and related techniques applied to theoretical problems in science. With experimentation and theory, it has become indispensable to advance scientific knowledge. Data science allows people to extract insights from massive amounts of data to tell a story, provide solutions, and more. These are growing, multidisciplinary areas, and IIT College of Science has significant areas of expertise in them.
In applied mathematics, for example, Professors Shuwang Li and Xiaofan Li work on computational fluid dynamics, materials science and biological systems at different time and length scales. In particular, interdisciplinary multi-physics problems involve time-dependent free boundaries. Examples include modeling and computation of biomembranes, tumor growth, epitaxial thin film, ion channels, Hele-Shaw and Stokes flows, etc. They derive mathematical models and constitutive relations via an energy variation approach so that the resulting formulations, usually posed as a system of partial diﬀerential equations (PDEs) and corresponding boundary conditions, are consistent with fundamental laws of physics. Because the locations of the moving boundaries are not known a-priori, the solutions to the PDEs and the positions of the free boundaries must be determined simultaneously. Their main objectives are to investigate the nonlinear dynamics of free boundaries and to understand the underlying physics by (1) performing analytical and numerical studies of important constituent processes; (2) developing and applying state-of-the-art adaptive numerical methods to large-scale computation. Whenever possible, they like to work with experimentalists to calibrate and validate the mathematical models, and to test the model predictions.
Applied Mathematics Professors Greg Fasshauer, Fred Hickernell, and Lulu Kang develop numerical methods for i) approximating functions, ii) integrating functions, and iii) solving partial differential equations. The applications inspiring this research include computer-aided design and manufacturing (CAD/CAM), design of complex systems, financial risk management, and earth sciences. These problems involve several to several hundred variables. Efforts are on constructing algorithms that obtain the answer with the desired accuracy in as little time as possible. This includes discovering new ways to plan computational experiments, reduce the computational burden, avoid lethal round-off error, and estimate error reliably. Collaborators include scientists involved in imaging of the brain, design of manufacturing systems, nuclear reactor design, and wind energy.