Numerical Partial Differential Equations

Research Advisors for Numerical Partial Differential Equations

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Slimane Adjerid , bio
Professor Adjerid conducts research on developing new discontinuous finite element methods for solving partial differential equations.
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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 , 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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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 , 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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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 , 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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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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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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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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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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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 , 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 in Numerical Partial Differential Equations

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John Taylor Burleson , bio
Instructor Burleson is currently engaged with teaching with an interest in computational fluid dynamics.
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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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Patrick Collins , bio
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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.