Lecture series presentation to explore mathematical modeling
The Provost's Lecture Series continues on Friday, April 12, noon-2 p.m., with a presentation by Andrea Dziubek, assistant professor of applied mathematics, entitled "'Modern' Computational Mathematical Modeling in Teaching and Research." The presentation will be held in Donovan Hall Rm. G152. Dziubek earned a Ph.D. in Energy and Process Engineering from Berlin Institute of Technology, Germany, in 2006 and held teaching and research positions in Indiana at Rose-Hulman Institute of Technology and at Indiana University-Purdue University Indianapolis.
Abstract: Computational mathematical modeling is an excellent way for students and researchers to study the modeling of a problem and what effects its solution, for example how the solution depends on parameters or on the choice of boundary conditions. Of course, it is also important that the numerical methods approximate the model equations accurately enough and preserve the qualitative structure of the original equations, otherwise this could result in dangerous and costly situations. Historically, numerical methods such as finite element method were developed for simple (isotropic, homogeneous) fluids and materials, but advanced materials often show nonlinear stress stain relations and exhibit phenomena at multiple scales, which further motivates the need for new approaches in computational mathematical modeling.
Dziubek will show some of the problems she has worked on, such as condensation in a compact heat exchanger, red blood cell membranes, and retinal blood flow. Then she will discuss what can go wrong if the numerical methods are not preserving the structure of the original analytic equations, illustrated by an example of a numerical method which preserves the symplecticity of a Hamiltonian system. Finally, she will show some student projects.
The Provost's Lecture Series allows SUNYIT faculty to share their research interests and activities with colleagues and the community.