# Research - Applied Mathematics

# Research Groups

The department's research efforts can be grouped into three broad areas, as delineated below. These areas have considerable overlap and several faculty consider themselves associated with more than one group. Beyond the areas listed below, a number of researchers from the department have major interdisciplinary connections to researchers from other departments across the campus. Indeed there are very prominent collaborations with the departments of Computer Science, Defense Analysis, Electrical and Computer Engineering, Mechanical and Aerospace Engineering, Meteorology, Oceanography, Operations Research, and Physics.

### Applied Analysis

Applied analysis is concerned with the interface between fundamental mathematical structures which rely on continuity and their use in the physical and social sciences. This research group has diverse interests that include asymptotic analysis, control theory, mechanics (fluid and orbital), and game theory. There are significant overlaps with the research group in Numerical Analysis/Scientific Computing.

Faculty Members in the Applied Analysis Group

Chris Frenzen

Wei Kang

Art Krener

Guillermo Owen

Clyde Scandrett

Current Postdoctoral Members in the Applied Analysis Group

Cesar Aguilar

Thomas Hunt

**View slides from the** *Computational Issues in Nonlinear Control***conference.**

### Numerical Analysis / Scientific Computing

Numerical Analysis/Scientific Computing is the study of theories, computational methods, numerical algorithms, and other tools required to practically solve mathematical models of problems from science and engineering in a fast, accurate, and efficient manner. The primary goal is the development of novel techniques and approaches to approximation and efficient computation that are at the heart of modern science. This research group is primarily focused on the numerical solution of partial and ordinary differential equations, numerical linear algebra, and approximation theory. There are very significant overlaps with the research group in Applied Analysis.

Faculty Members in the Numerical Analysis / Scientific Computing Group

Carlos Borges

Fariba Fahroo

Frank Giraldo

Jeremy Kozdon

Beny Neta

Lucas Wilcox

Hong Zhou

Current Postdoctoral Members in the Numerical Analysis / Scientific Computing Group

Eric Choate

Michal Kopera

Daniel Abdi

Andreas Mueller

### Discrete Mathematics

Discrete mathematics, sometimes called finite mathematics, is the study of mathematical structures that are fundamentally discrete, in the sense of not supporting or requiring the notion of continuity. Discrete mathematics is extensively used in a variety of critical applications such as cryptography, coding theory, combinatorics, network analysis, and search algorithms for the internet.

Faculty Members in the Discrete Mathematics Group

David Canright

Ralucca Gera

Thor Martinesen

Pante Stanica

### Research Collaboration

There is a very high degree of collaboration within the department can be seen in the following graph which shows links between all of our faculty who have published jointly.

An example of transformational acoustics, demonstrating near field bending of an incoming plane wave about an acoustically hard sphere at a ka value of approximately 5.2. Principal Investigator: Clyde Scandrett

Jablonowski-Williamson Baroclinic Instability: Pressure (left) and Temperature (right) at the surface for NSEAM with a grid point resolution equivalent to the spectral resolution T185 L24. Principal Investigator: Frank Giraldo

A few examples of Generalized Petersen graphs of skip 2, whose spectrum is now known. Principal Investigators: Ralucca Gera & Pante Stanica