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.

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Selection of Specific Areas of Research

Computational Fluid Dynamics

Data Analytics

High Performance Computing

Inverse Problems

Modeling, Control & Optimization

Model Reduction

Numerical Linear Algebra

Numerical PDEs

Researchers

      • Nicole Abaid profile picture
      • 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.

      • Christopher Beattie profile picture
      • 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.

      • Jeff Borggaard profile picture
      • 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.

      • John Burns profile picture
      • 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.

      • Lauren Childs profile picture
      • Lauren M. Childs

        Professor Childs develops and analyzes mathematical and computational models to examine biologically-motivated questions.

      • Julianne Chung. Headshots for the Virginia Tech College of Science.
      • 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.

      • 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.

      • Mark Embree profile picture
      • 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.

      • Serkan Gugercin profile picture
      • 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.

      • Russell Hewett profile picture
      • 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.

      • 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.

      • 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.

      • Honghu Liu profile picture
      • 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.

      • Eileen Martin profile picture
      • 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.

      • Sho-Ming Sun profile picture
      • 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.

      • Timothy Warburton profile picture
      • 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.

      • Layne T. Watson profile picture
      • Layne T. Watson

        Dr. Watson's research interests include numerical analysis; nonlinear programming; mathematical software; solid mechanics; fluid mechanics; image processing; parallel computation; bioinformatics.

      • Pengtao Yue profile picture
      • 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.

      • 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.

      • Eric Ufferman

        Collegiate Assistant Professor Ufferman teaches classes in both Computational Modeling and Data Analytics and Discrete Mathematics.

      • 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.