Applied & Computational Mathematics
Applied and computational mathematics includes mathematics with a wide range of applications across the sciences. Specific research areas can be found in faculty descriptions below.
Selection of Specific Areas of Research
Researchers
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Nicole Abaid
Dr. Abaid's research focuses on networked dynamical systems. She studies diverse biological systems, ranging from animal groups to brain networks, to inspire novel results in mathematical modeling and control.
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Christopher Beattie
The principal research interests of Professor Beattie are in the areas of scientific computing and large scale computational linear algebra, with an emphasis on iterative Krylov methods. His primary focus is on model reduction of large scale dynamical systems with a goal of developing practical and rigorous computational algorithms for efficient manipulation and simulation of systems arising from physical models frequently described by systems of partial differential equations.
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Jeff Borggaard
Professor Borggaard studies the design and control of fluids. This includes computational fluid dynamics, control theory, optimization, sensitivity analysis, uncertainty quantification, and reduced-order models. In each case, the application of these research areas to partial differential equations that describe fluids are of interest.
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John Burns
Professor Burns' current research is focused on computational methods for modeling, control, estimation and optimization of complex systems where spatially distributed information is essential. This includes systems modeled by partial and delay differential equations. Recent applications include modeling and control of thermal fluids, design and thermal management systems and optimization of mobile sensor networks.
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Lauren M. Childs
Professor Childs develops and analyzes mathematical and computational models to examine biologically-motivated questions.
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Julianne Chung
Professor Chung's research interests include numerical methods and software for computing solutions to large-scale inverse problems, such as those that arise in imaging applications.
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Matthias Chung
Professor Chung's research concerns computational methods in the intersection of computational modeling, machine learning, data analytics with an emphasis on inverse problems. Driven by its application, he and his group develop and analyze efficient numerical methods for inverse problems. Applications of interest are, but not limited to, systems biology, medical and geophysical imaging, and dynamical systems.
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Mark Embree
Professor Embree studies numerical linear algebra and spectral theory, with particular interest in eigenvalue computations for nonsymmetric matrices and transient behavior of dynamical systems.
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Serkan Gugercin
Professor Gugercin studies computational mathematics, numerical analysis, and systems and control theory with a focus on data-driven modeling and model reduction of large-scale dynamical systems with applications to inverse problems, structural dynamics, material design, and flow control.
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Russell Hewett
Professor Hewett's research interests lie at the intersection of inverse problems, deep learning, and high-performance computing. His research is motivated by problems in science with extreme data and compute scales, for example geoscience and space physics. Research in these areas also involves developments in numerical differential equations, optimization, estimation, and statistics.
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Traian Iliescu
At the core of Professor Iliescu's research program is his vision of using both mathematics and computations to provide new knowledge on turbulent fluid flows dominated by coherent structures and create models with practical impact in engineering, climate modeling, and medicine. The ultimate goal of his research program is to transform turbulence modeling as we know it today and use mathematics, computations, physics, and data to discover general laws of turbulent fluid flows.
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Martin Klaus
Professor Klaus' research mainly concerns the spectral theory of linear operators and their connection with nonlinear evolution equations. This research has applications in the study of optical pulse propagation.
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Tao Lin
Professor Tao Lin's main research interest is the numerical analysis on computational methods related with differential equations. He designs new numerical methods and carry out their convergence analysis. His recent research focuses on immersed finite element (IFE) methods that can solve interface problems of partial differential equation with interface independent meshes. He is also working on applying IFE methods to interface inverse problems via the shape optimization methodology.
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Honghu Liu
Professor Liu's research focuses on the design of effective low-dimensional reduced models for nonlinear deterministic and stochastic PDEs as well as DDEs. Applications to classical and geophysical fluid dynamics are actively pursued. Particular problems that are addressed include bifurcation analysis, phase transition, surrogate systems for optimal control, and stochastic closures for turbulence.
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Eileen Martin
Dr. Martin is an assistant professor doing research focused on computational mathematics, particularly with applications to geosciences. Her interests include data-intensive high performance computing, signal processing, imaging science, inverse problems, and working with large-scale sensor networks collecting streaming data.
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Shu-Ming Sun
Professor Sun's research interests include the mathematical theory of fluid mechanics, the theory of partial differential equations, and applied nonlinear analysis.
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Peter Wapperom
Professor Wapperom conducts research in computational fluid dynamics of complex fluids. This involves the mathematical modeling and numerical simulation of the flow of polymeric liquids and fluids reinforced with rigid particles.
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Tim Warburton
Professor Warburton holds the John K. Costain Chair in the College of Science at Virginia Tech and is a faculty member of both the Department of Mathematics and the Computational Modeling and Data Analytics program. His research interests include developing new parallel algorithms and methods that are used to solve PDE based physical modes on the largest supercomputers.
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Layne T. Watson
Dr. Watson's research interests include numerical analysis; nonlinear programming; mathematical software; solid mechanics; fluid mechanics; image processing; parallel computation; bioinformatics.
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Pengtao Yue
Professor Yue works on the numerical simulation of flow problems with moving boundaries and complex rheology, including multiphase flow, viscoelastic fluids, dynamic wetting, and phase change phenomena.
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Lizette Zietsman
Professor Zietsman's research area covers the development and analysis of fundamental numerical algorithms arising in the study of stability, control and estimation of distributed parameter systems typical in structural control, fluid flow control, and thermal systems.
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Eric Ufferman
Collegiate Assistant Professor Ufferman teaches classes in both Computational Modeling and Data Analytics and Discrete Mathematics.
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Jason R. Wilson
Collegiate Assistant Professor Wilson teaches Math and CMDA classes. His research interests include large scale linear algebra, high performance computing, and the mathematical foundations of data science.
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Teshome Balkew
My research interest is on Optimal Control Theory, Operations Research, Data Analytics.
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Turker Topcu
Dr. Topcu works in the field of computational science. His research involves developing algorithms and codes to solve partial and ordinary differential equations to simulate quantum dynamical systems.
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