Tim Warburton is a Professor of Mathematics and currently holds the John K. Costain Faculty Chair in the College of Science at Virginia Tech.
His research interests include developing numerical methods for solving PDEs and optimizing their performance on accelerators and clusters.
Tim Warburton is affiliated with both the Department of Mathematics and the Program in Computational Modeling & Data Analytics Program at VT.
He is also affiliated with the Center for Efficient Exascale Discretizations funded by the Department of Energy.
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Nodal Discontinuous Galerkin Methods: Algorithms, Analysis, and Applications
Authors: Jan S. Hesthaven & T. Warburton
Overview: This book discusses a family of computational methods, known as discontinuous Galerkin methods, for solving partial differential equations. While these methods have been known since the early 1970s, they have experienced an almost explosive growth interest during the last ten to fifteen years, leading both to substantial theoretical developments and the application of these methods to a broad range of problems.
These methods are different in nature from standard methods such as finite element or finite difference methods, often presenting a challenge in the transition from theoretical developments to actual implementations and applications.
This book is aimed at graduate level classes in applied and computational mathematics. The combination of an in depth discussion of the fundamental properties of the discontinuous Galerkin computational methods with the availability of extensive software allows students to gain first hand experience from the beginning without eliminating theoretical insight.
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Overview of Courses
Computer Science Foundations for Computational Modeling & Data Analytics
CMDA 3634@VT: Undergraduate level survey of computer science concepts and tools that enable computational science and data analytics. Data structure design and implementation. Analysis of data structure and algorithm performance. Introduction to high-performance computer architectures and parallel computation. Basic operating systems concepts that influence the performance of large-scale computational modeling and data analytics. Software development and software tools for computational modeling.