Computational and Applied Mathematics
Home Page: Yulong Xing
Yulong Xing is a staff scientist for the computational mathematics group in the Computer Science and Mathematics division at the Oak Ridge National Laboratory, as well as a joint faculty assistant professor in the Department of Mathematics at the University of Tennessee.
He earned his Ph.D. in mathematics from Brown University in 2006 and studied high-order accurate numerical methods for hyperbolic conservation laws. He then spent three years at the Courant Institute, New York University, where he devoted his efforts to the area of multi-scale modeling and computation for complex geophysical flows.
Xing has authored and coauthored 22 papers in peer-reviewed journals, written a book chapter, co-edited a book volume in his field, co-organized several conferences in computational mathematics, and given many invited presentations, both nationally and internationally.
Xing’s research interests encompass the design, analysis, and implementation of accurate and efficient numerical methods for differential equations arising from physical problems. During the past few years, he has developed and analyzed high-order numerical algorithms — finite element discontinuous Galerkin, finite volume, and finite difference — that inherit certain properties of the underlying natural phenomena, such as the energy conservation and positivity of physical quantities, to achieve better numerical approximations. Descriptions of the specific topics he has been pursuing are provided below.
Shallow-water equations in storm-surge modeling and coastal engineering: These equations, which have a non-flat bottom topography, play a critical role in modeling and simulations of the flows in rivers and coastal areas, and have wide applications in ocean, hydraulic engineering, and atmospheric modeling. To address these modeling and engineering challenges, Xing’s research group has been developing efficient and robust numerical methods, with the goal of improving the predictive capability of hydrodynamic models for flooding in a complex coastal region.
Energy-conserving methods for wave-propagation problems: Wave-propagation problems arise in science, engineering, and industry, and they are significant to geoscience, petroleum engineering, telecommunication, and the defense industry. The energy-conserving property is one of the guiding principles for numerical algorithms, because it provides an accurate approximation. Xing’s research group has developed and analyzed high-order, energy-conserving discontinuous Galerkin methods for solving the wave equation.
Well-balanced methods for hyperbolic systems with source terms: Hyperbolic systems often involve source terms arising from geometrical, reactive, biological, or other considerations. These source terms have wide applications in various fields, such as chemistry, biology, fluid dynamics, astrophysics, meteorology, and others. The research group introduces well-balanced methods with the aim of precise preservation of some of these equilibrium solutions.
Multi-scale modeling and computation: Geophysical flows often involve complex multi-scale nonlinear systems. Developing multi-scale models for these systems is necessary to enable scientists to better understand how the energy cascades across different scales. Xing’s research group has proposed multi-scale models for complex geophysical flows such as those contained in the hurricane embryo and developed an efficient novel multi-scale algorithm to solve the flows.