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Areas of Research

Members of the Department of Mathematics and Statistics are actively engaged in research in many areas of Mathematics and Statistics. While the research interests of some of the members crossover into different branches of mathematics, below is a general division of the research groups.

To learn more about past and ongoing math research, request the full Academic Genealogy of the Oakland University Department of Mathematics and Statistics and the Collaboration graphic among tenure-track faculty members here at any time in the period 2003-2012 from Denise Diebold through [email protected] or (248) 370-3431.

Combinatorics and Optimization
Mathematical Biology
Number Theory
Faculty Awards

Aycil Cesmelioglu
National Science Foundation award (2021)

"Collaborative Research: Development of Reduced Order Models for Poroelasticity and Related Problems"

Poroelasticity is a framework of continuum mechanics models for problems involving a porous elastic medium and a fluid flow. Poroelasticity problems have real-world applications such as hydrocarbon extraction in petroleum engineering, physiological processes such as the blood flow in the human body, groundwater contamination in environmental engineering, and modeling magma and mantle migration in geophysics. There is a real need to obtain high-resolution numerical solutions for the poroelasticity but these require large computational resources, even with theoretically optimal algorithms. This project will develop methods that can provide high accuracy solutions for large poroelasticity problems with feasible computational costs.

Nghia Tran
National Science Foundation award (2018)

"Collaborative Research: Second-Order Variational Analysis in Structured Optimization and Algorithms with Applications"

In this project, Prof. Tran focuses on developing advanced tools of mathematical analysis to investigate modern structured optimization problems and designing new efficient algorithms to solve them. These problems arise in different areas of science and engineering, including massive data analysis, machine learning, signal processing, medical image reconstruction, statistics, traffic networks, and operations research. Most of them share the irregular phenomenon of nonsmoothness or nonconvexity that challenges computation. His approach will be mainly based on a relatively young subfield of applied mathematics, variational analysis, which is naturally compatible with these nonsmooth and complex structures.

Dan Steffy
A research project funded by Ford (2018)

Anna Spagnuolo
National Science Foundation award (2007)

"Collaborative Research" NSF PetaApps: Storm Surge Modeling on Petascale Computers"

The goal of this project is to investigate the use of petascale computing to significantly advance the state-of-the-art in storm surge simulation, to accurately model flows at multiple, interacting scales, at resolution never before attempted, and to demonstrate that results from these simulations can be delivered in real-time to emergency managers. To achieve this goal will require the continued development and improved understand of the mechanisms involved in tightly coupled models of wind, waves, circulation and geomorphology, improvements in the description of the physical domain and adaptive resolution of all energetic flow scales, and investigation of accurate, robust and highly parallelizable numerical algorithms. Efficient implementation of these models on emerging petascale architectures will require utilizing the latest developments in parallel data management, real-time visualization, and programming tools. In this project, the PIs will develop high resolution, large-scale coastal inundation models coupled with regional-scale rainfall/runoff models. Robust and highly parallelizable algorithms will be investigated for solving these systems on petascale architectures. The models will be implemented on NSF Track 2 HPC systems currently under construction; furthermore, implementation of the models on novel hybrid architectures will also be explored.

Anna Spagnuolo
National Science Foundation SGER award (2006)

"Numerical Speedup Using Flowpaths"

Applications for computer simulations include many research areas such as weather prediction, tracking the location and concentrations of contaminants in groundwater, oil recovery, studying disease processes, designing experiments, and developing medications. In these and several other applications, it is desirable to achieve speedup of numerical code. Current work in speeding up numerical simulations has several disadvantages. Considering the various disadvantages of each method, project will develop methods that increases the speed and (1) does not require rewriting an existing algorithm, although could be improved even further by making minor coding modification, (2) does not require algorithms written in traditional languages to be rewritten in other language, (3) executes portions of the code in parallel but does not suffer from the overhead of either a single microprocessor or multi-processor architecture, and (4) does not require time and effort to engineer and implement a special circuit for different types of numerical algorithms. This work proposes to develop such a technology using flowpaths where, starting with a C (or potentially FORTRAN) description of a numerical algorithm, a compiler will generate an executable that can be downloaded and will run on the Power PC embedded in an FPGA with parallel flowpaths to speedup the bottleneck loops in the numerical algorithm automatically.

With such a speed-up, some simulations that require real-time execution that can not currently be achieved by a PC will be able to run at a higher speed and achieve a real-time pace. The success of this research will result in future investigation including deriving optimizations for the compiler and resulting circuits, improving numerical schemes for optimal implementation in hardware and enhancing the compiler to support other popular languages.

Department of Mathematics and Statistics

Mathematics and Science Center, Room 368
146 Library Drive
Rochester , MI 48309-4479
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phone: (248) 370-3430
fax: (248) 370-4184

Monday–Friday: 8:00–11:59 a.m. and 1:00–5:00 p.m.