Theodore B. Stowell University Professor
of Applied Mathematics
Room 317, 182 George Street
Phone: +1 401 863 2549
Phone 2: +1 401 863 2115
Ph.D., University of California at Los Angeles, 1986
Professor Shu has a variety of research interests including: numerical solutions of conservation laws and in general convection dominated problems using finite difference essentially non-oscillatory (ENO) methods and weighted ENO (WENO) methods, finite element discontinuous Galerkin methods, and spectral methods; numerical solution of Hamilton-Jacobi type equations; computational fluid dynamics; and numerical solution of equations appearing in semi-conductor device simulations.
Professor Shu received his B.S. degree in Mathematics from the University of Science and Technology of China, Hefei, in 1982. In 1986 he received his Ph.D. degree in Mathematics from the Mathematics Department of the University of California at Los Angeles with Professor Stanley Osher as his advisor. He then spent a year at the Institute for Mathematics and Its Applications (IMA) in University of Minnesota as a post doctoral fellow. Since 1987 he has been with the Division of Applied Mathematics, Brown University, as an Assistant Professor (1987-91), Associate Professor (1992-96), Professor (1996- ), and Chairman (1999-2005). In 1992 he received the NASA Public Service Group Achievement Award for the pioneering work in Computational Fluid Dynamics as part of the ICASE algorithm team. In 1995 he received the first Feng Kang Prize of Scientific Computing from the Chinese Academy of Sciences. Since 2004 he has been listed as an ISI Highly Cited Author in Mathematics by the ISI Web of Knowledge, Thomson Scientific Company.
Professor Shu is the Managing Editor of Mathematics of Computation, the co-Chief Editor of the Journal of Scientific Computing, and a member of the editorial boards of the Journal of Computational Mathematics, Communications in Applied Analysis, Acta Mathematicae Applicatae Sinica, Dynamics of Continuous, Discrete and Impulsive Systems, Series B, International Journal of Pure and Applied Mathematics, Computational Fluid Dynamics Journal, Methods and Applications of Analysis, Chinese Journal of Computational Physics, Science in China, Series A, Journal of Hyperbolic Differential Equations, International Journal of Numerical Analysis and Modeling, Pure and Applied Mathematics Quarterly, and Communications in Computational Physics, and a former editor of the SIAM Journal on Numerical Analysis. Between 1989 and 2002 he was a consultant at the Institute for Computer Applications in Science and Engineering (ICASE), NASA Langley Research Center. He has also been an Overseas Assessor of the Chinese Academy of Sciences (since 2001), a Guest Professor (since 1995) and a Changjiang Lectureship Professor (since 2000) of the Department of Mathematics of the University of Science and Technology of China, a Guest Professor of the School of Mathematics of Nankai University in China since 1996, a Guest Professor of Shanghai University in China since 1997, a Guest Professor of Yunnan Polytechnic University in China since 1999, a Guest Professor of the Southeast University in China since 2000, a Guest Professor of the Nanjing Aeronautic and Space University since 2001, and a guest professor of the Nanjing University since 2005.
Professor Shu's research activities are concentrated on the design,
analysis, implementation and application of high order nonlinearly
stable numerical schemes for solving convection dominated partial
One major type of such schemes is the class of WENO (weighted essentially non-oscillatory) finite difference and finite volume schemes. These are schemes with solutions which are high order accurate in smooth regions and at the same time produce sharp and non-oscillatory shock transitions. They are especially suitable for solving problems with both strong discontinuities and complex smooth regions structures, such as the problem of shock interacting with turbulence. Recent development in WENO schemes include the technique to handle negative linear weights, the design of WENO schemes for conservation laws and Hamilton-Jacobi equations on arbitrary unstructured meshes, multi-domain finite difference WENO schemes, Hermite type WENO schemes, anti-diffusive corrections to WENO schemes to sharpen contact discontinuities, well balanced WENO schemes, and residual distribution finite difference WENO schemes for steady state problems on nonsmooth meshes. Recent applications of WENO schemes include the simulation for the Boltzmann-Poisson system in semiconductor device simulations in one and two spatial dimensions and in two and three phase space dimensions, particle-fluid two phase flow problems, cosmology in astrophysics, high Mach number astrophysical jets with radiative cooling, nearly-incompressible, inviscid Taylor-Green vortex flow, shallow water equations, hyperbolic models for chemosensitive movement, multi-stage interaction of a shock wave and a strong vortex, multi-class traffic flow models, shock mitigation and drag reduction by pulsed energy lines, low-redshift cosmic baryon fluid on large scales, and Rayleigh-Taylor instability.
Another major type of such schemes in the class of discontinuous
Galerkin (DG) methods. These are finite element methods but with
important features borrowed from high resolution finite volume
methodology, such as exact or approximate Riemann solvers as
numerical fluxes, limiters to control spurious oscillations, and
strong stability preserving high order Runge-Kutta time
discretizations. The major advantages of the discontinuous Galerkin method include its local conservation, compact data communication and hence high parallel efficiency, flexibility of arbitrary h-p adaptivity while keeping nonlinear stability, and provable stability and error estimates for many complicated nonlinear convection dominated PDEs. Recent development in DG methods include the design of local discontinuous Galerkin methods for nonlinear wave equations involving higher spatial derivatives, such as the KdV type equations, the nonlinear Schroedinger equations, the Kuramoto-Sivashinsky equations and the Ito-type coupled KdV equations, and the Kadomtsev-Petviashvili and the Zakharov-Kuznetsov equations, the design of WENO and Hermite WENO limiters for discontinuous Galerkin method, the post-processing technique to enhance the order of accuracy, the design of discontinuous Galerkin method for Hamilton-Jacobi equations, the analysis of the discontinuous Galerkin and related methods such as the spectral finite volume method, the design of locally divergence-free discontinuous Galerkin methods for the Maxwell and MHD equations and in general structure preserving discontinuous Galerkin methods, error estimates for fully discrete Runge-Kutta discontinuous Galerkin method for nonlinear conservation law systems and for other nonlinear wave equations for smooth solutions, and the design of discontinuous Galerkin method based on non-polynomial approximation spaces. Recent applications of the discontinuous Galerkin method include aeroacoustic simulations, Maxwell equations and MHD, compactons, moment models in semiconductor device simulations, and shallow water equations.
Related research has also been performed in multi-scale methods, spectral methods for discontinuous problems with the emphasis on accuracy recovery techniques, Lax-Wendroff type time discretizations, and stable high resolution schemes for a hierarchical size-structured model in computational biology.
Fellow, Society for Industrial and Applied Mathematics (SIAM), May 2009.
SIAM/ACM Prize in Computational Science and Engineering (SIAM/ACM CSE Prize), February 2007.
ISI Highly Cited Author in Mathematics (http://isihighlycited.com/), ISI Web of Knowledge, Thomson Scienticc Company, 2004- .
First Feng Kang Prize of Scientific Computing, Chinese Academy of Sciences, Beijing, October 1995.
NASA Public Service Group Achievement Award for pioneering work in Computational Fluid Dynamics, NASA Langley Research Center, March 1992.
Managing Editor, Mathematics of Computation, 2/02- . Associate Editor, 93-01.
Chief Editor, Journal of Scientific Computing, 2/09- . Co-Chief Editor, 3/00-1/09.
Co-Chief Editor, Methods and Applications of Analysis, 1/08- . Member of Editorial Board, 00-07.
Member of Editorial Boards:
Journal of Computational Mathematics (12/93-)
Communications in Applied Analysis (2/95- )
Acta Mathematicae Applicatae Sinica (4/00- )
Computational Fluid Dynamics Journal (2/02- )
Science in China, Series A (1/03- )
International Journal of Numerical Analysis and Modeling (1/04- )
Pure and Applied Mathematics Quarterly (1/05- )
Communications in Computational Physics (1/06- )
Boletin de la Sociedad Espanola de Matematica Aplicada (1/08- )
SIAM Journal on Numerical Analysis (4/93-12/01)
Chinese Journal of Computational Physics (5/02-9/07)
Journal of Hyperbolic Differential Equations (1/04-12/08)