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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.

Dr. Johnson teaching MATH 4625

Researcher Advisors for Applied & Computational Mathematics

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    Nicole Abaid profile picture
    Nicole Abaid , bio

    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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    Silmane Adjerid profile picture
    Slimane Adjerid , bio

    Professor Adjerid conducts research on developing new discontinuous finite element methods for solving partial differential equations.

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    Daniel Appelo profile picture
    Daniel Appelö , bio

    Professor Daniel Appelö is a numerical analyst with an interest in computational techniques for solving differential equations fast and accurately. He is excited about applications in acoustics, electromagnetics, fluids, and more recently in quantum computing.

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    Christopher Beattie profile picture
    Christopher Beattie , bio

    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.

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    Jeff Borggaard profile picture
    Jeff Borggaard , bio

    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 profile picture
    John Burns , bio

    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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    Paul Cazeaux's profile picture
    Paul Cazeaux , bio

    Professor Cazeaux's research deals with multiscale phenomena in mathematical physics and biology, with recent applications in quantum chemistry and condensed matter physics (2D materials).

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    Yingda Cheng profile picture
    Yingda Cheng , bio

    Professor Cheng's research areas are in scientific computing, applied mathematics and data-driven modeling and computation. She develops numerical methods for partial differential equations, particularly those in higher dimensional space. The application area of Professor Cheng's research includes fusion energy and semiconductor device modeling, to name a few.

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    Lauren Childs profile picture
    Lauren M. Childs , bio

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

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    Eric de Sturler  profile picture
    Eric de Sturler , bio

    Professor de Sturler's research focuses on numerical analysis for large-scale computational problems with an emphasis on fast solvers for linear and nonlinear systems, inverse problems and parameter estimation, optimization, and design, including iterative solvers and numerical linear algebra, randomization, stochastic methods, model reduction, and high performance computing with applications in computational mechanics, such structural optimization and computational fluid dynamics, tomography and image reconstruction, big data, computational physics, biology, and computer graphics.

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    Mark Embree profile picture
    Mark Embree , bio

    CMDA Program Director 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 profile picture
    Serkan Gugercin , bio

    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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    Traian Illescu profile picture
    Traian Iliescu , bio

    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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    Tao Lin profile picture
    Tao Lin , bio

    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 profile picture
    Honghu Liu , bio

    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 profile picture
    Eileen Martin , bio

    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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    Agnieszka Miedlar's profile picture
    Agnieszka Miedlar , bio

    Professor Miedlar conducts research in numerical analysis and scientific computing, with a focus on iterative solvers for large-scale linear systems and eigenvalue problems, and adaptive finite element methods (AFEMs).

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    Mirjeta Pasha's profile picture
    Mirjeta Pasha (starting Fall 2024) , bio

    Dr. Pasha is an Assistant Professor with research interests on high dimensional (tensor) data analysis, regularization for inverse problems, uncertainty quantification, and high-performance computing. She develops computationally efficient methods and algorithms to solve large-scale problems that arise from an extensive list of applications in data science, medicine, and engineering.

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    Michael A. Robert profile picture
    Michael A. Robert , bio

    Professor Robert builds and analyzes mathematical models to study biological phenomena. He is particularly interested in developing and exploring models to better understand how ecological, meteorological, anthropogenic, and evolutionary processes impact the emergence, spread, and control of infectious diseases.

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    Johann Rudi , bio

    Professor Johann Rudi's research is interdisciplinary and spans large-scale parallel iterative methods for nonlinear and linear systems, development and implementation of algorithms for high-performance computing (HPC) platforms, computational aspects of inverse problems, and quantification of uncertainties in the inferred parameters.

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    Sho-Ming Sun profile picture
    Shu-Ming Sun , bio

    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 , bio

    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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    Timothy Warburton profile picture
    Tim Warburton , bio

    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 profile picture
    Layne T. Watson , bio

    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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    Steffen Werner profile picture
    Steffen Werner , bio

    Professor Werner conducts research at the intersection of scientific computing and numerical linear algebra with particular focus on scientific machine learning, model order reduction, data-driven modeling, optimization and control of partial differential equations, matrix equations and mathematical software development.

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    Pengtao Yue profile picture
    Pengtao Yue , bio

    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 profile picture
    Lizette Zietsman , bio

    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.

Researchers of Applied & Computational Mathematics

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    Andrea Carracedo Rodriguez , bio

    Dr. Carracedo Rodriguez conducts research in numerical analysis, with a focus on efficiently building approximations to dynamical systems from data or via model reduction.

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    Eric Ufferman , bio

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

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    Gazi Mahmud Alam profile picture
    Gazi Mahmud Alam , bio

    Dr. Alam's research interests are focused on the development of methods and algorithms for solving control and inverse problems on quantum graphs.

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    Giuseppe Cotardo's profile picture
    Giuseppe Cotardo , bio

    Doctor Cotardo's research interest is in algebraic coding theory, with a focus on algebra, geometry, combinatorics, and their applications to the invariant theory of codes endowed with the rank metric.

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    Jason Wilson profile picture
    Jason R. Wilson , bio

    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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    John Burleson profile picture
    John Taylor Burleson , bio

    Instructor Burleson is currently engaged with teaching with an interest in computational fluid dynamics.

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    Jorge Reyes profile picture
    Jorge Reyes , bio

    Dr. Reyes' research involves the theoretical and computational study of fluid dynamics primarily based on the Navier-Stokes equations (NSE). These studies consist of the finite element analysis of numerical solutions for full-order models and the development of corresponding reduced order models (ROMs).

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    Lihong Zhao profile picture
    Lihong Zhao , bio

    Dr. Zhao is an applied mathematician interested in using mathematical models to advance health equity. She focuses on models involving partial differential equations and ordinary differential equations, utilizing techniques from dynamical systems, numerical analysis, and inverse problem methodology to answer questions in ecology and epidemiology.

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    Stanca Ciupe profile picture
    Nilton Garcia Hilares , bio

    Dr. Hilares' research interests lie in computational and applied linear algebra.

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    Petar Mlinarić profile picture
    Petar Mlinarić , bio

    Dr. Mlinarić conducts research in the field of model order reduction, in particular, structure-preserving and optimal methods.

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    Ping-Hsuan Tsai profile picture
    Ping-Hsuan Tsai , bio

    I am a postdoctoral associate working on developing data-driven reduced-order models for turbulent heat transfer applications. Particularly, focusing on developing stabilization strategies and error indicators for turbulent flows to be used in engineering routine and design analysis. In addition to turbulent flows, plasma physics is another application that I have been working on recently.

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    Shixu Meng's profile picture
    Shixu Meng , bio

    Dr. Meng’s research interests include computational and analytical methods for solving PDEs and inverse problems, and a major theme is on forward and inverse scattering problems. His most recent interest is on low rank methods and dimension reduction techniques.

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    Turker Topcu , bio

    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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    Ziqiang Li , bio

    Visiting Assistant Professor Dr. Li researches algorithms on the 2-sphere for the use of computational geometry, numerical methods, and analytical cartography. On the side, he studies flows in microfluidic systems.

Recently Retired Faculty