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Table of Contents
News |
Research in Computational
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| Finite Element Computations | Dynamical Systems |
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| Mathematical Biology | Reservoir Simulations |
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| Fluid Mechanics | Numerical Methods for ODEs |
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| Nonlinear Waves | Boundary Element Computations |
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| Foam Structure | Networks |
Professor Ajaev's research involves applications of asymptotic and perturbation as well as numerical methods for partial differential equations to various problems in fluid mechanics and crystal growth. Of particular interest are simulations of moving interfaces in systems with phase transitions by means of finite-difference and boundary-integral methods.
He collaborates with scientists at the University of California, Santa Barbara
and the Technical University of Darmstadt, Germany. His published work has appeared
in Annual Review of Fluid Mechanics, Journal of Fluid Mechanics, Physics of Fluids,
Physical Review E, Journal of Computational Physics, Numerical Heat Transfer,
Proceedings of the Royal Society A, Journal of Crystal Growth,
and Journal of Colloid and
Interface Science.
Bruce Ayati
Assistant
Professor (Ph.D. 1998, University of Chicago)
Professor Ayati's research focuses on numerical methods for partial differential equations, mathematical biology, and the interface between the two. Problems where the spatial behavior of a biological population is a manifestation of its physiological structure are of particular interest. Areas of application include tumor invasion, biofilm growth, bacterial colony development, and forest modeling.
Prior to joining the faculty at SMU, Prof. Ayati was a Senior Member of the
Technical Staff at The Aerospace Corporation where he supported the management
of the GPS satellite constellation. His research has appeared in SIAM Journal
on Numerical Analysis, Mathematics of Computation,
Journal of Mathematical Biology, Multiscale Modeling and Simulation,
Theoretical Population Biology, and Methodology
and Computing in Applied Probability.
Thomas W. Carr
Associate
Professor (Ph.D. 1993, Northwestern)
Professor Carr's research focuses on the dynamics of physical systems modeled by nonlinear ordinary and partial differential euqations. He uses local and global bifurcation theory, asymptotic analysis, and numerical simulation and continuation to study the system's behavior and parameter sensitivities. Of particular interest is the synchronization characteristics of coupled oscillators. Areas of application include laser instabilities, coupled electronic circuits and mathematical biology.
He collaborates with scientists at the U.S. Naval Research Laboratory and the
Free University of Brussels, Belgium. His research has appeared in Physical
Review A, Physical Review E, Physical Letters A, Chaos, Physica D, and
SIAM Journal of Applied Mathematics.
Zhangxin John Chen
Professor
(Ph.D. 1991, Purdue University)
Professor Chen's scientific research concentrates on numerical methods and the supporting mathematical analysis of the partial differential equations arising from the modeling and simulation of multiphase fluid flows in porous media and of semiconductgor devices. In his research, he relates the three basic features of applied mathematics for these applications: (1) formulation of the physical problems in terms of mathematical models, (2) theoretical analysis of the mathematical models, and (3) development and analysis of numerical methods for the mathematical models.
Professor Chen has consulted with Rush-Presbyterian - St. Luke's Medical
Center and has close contacts with Mobil Oil Company. He has had research grants
from the U.S. Army Research Office, the Department of Energy, and the National
Science Foundation. His work has appeared in Mathematics of Computation, SIAM
Journal on Mathematical Analysis, SIAM Journal on Applied Mathematics, SIAM
Journal on Numerical Analysis, SIAM Journal on Scientific Computing, Numerische
Mathematik, and Journal of Computational Physics.
Yeo-jin Chung
Assistant Professor
(Ph.D. 2002, University of California, Irvine)
Professor Chung's research activity has focused on nonlinear photonics, specifically, (1) analyzing both analytically and numerically the stochastic phenomena of electromagnetic field propagation in nonlinear random media, (2) numerical modeling of light propagation in photonic crystals, (3) optimizing and modeling of ultrashort high-power pulses in optical fibers. Currently, her research efforts involve a broader area, which includes (1) nonlinear dynamics of light in photonic crystals and nanophotonic devices; (2) error correction in noisy communication networks; and (3) developing efficient numerical method to model various aspects of highly distorted flow in fluid dynamics.
She has collaborated with the theoretical physics and experimental groups at Los Alamos National
Laboratory, and the Department of Mathematics at University of New Mexico, and the theoretical
physics group at Landau Institute in Russia. Her research has appeared in Journal of Nonlinear Science,
Optics Communications, Journal of Physics A: Mathematical and General, Physical Review E,
Optics Letters, Optics Express, and Nonlinearity.
Ian Gladwell
Professor
(Ph.D. 1970, University of Manchester)
Professor Gladwell works in a variety of numerical analysis and scientific computation research areas - including ordinary differential equation initial and boundary value problems, mathematical software, and parallel computing - with an emphasis on developing tools to assist scientists and engineers with large-scale computing problems. His research has involved scientific computation for sintering and grooving of materials, diffusion-convection equations, waves generated by a semi-infinite plate, and chromosome synapsis in grasses.
Recently, he has worked on use of symbolic software for aiding the numerical solution of singularly perturbed boundary value ordinary differential equations, parallel codes for almost block diagonal systems, variable step Runge-Kutta-Nystrom algorithms for special second-order systems, integration of Hamiltonian systems, parallelization of numerical integration, and wavelet collocation for boundary value problems. He has been working with faculty members at the University of Manchester, Emory University and the Colorado School of Mines, with members of the Numerical Algorithms Group, and with former SMU graduate students at the Johns Hopkins University, Texas Instruments, Oakland University, the University of New Hampshire, the Polish Academy of Sciences, University of Texas at Dallas, Texas Women's University and Collin County Community College.
Professor Gladwell was a faculty member at the University of Manchester, UK, before
joining SMU in 1987. He has consulted with Texas Instruments and with NAG, is Editor-in-Chief
of the ACM Transactions on Mathematical Software, and an Associate Editor of the IMA
Journal on Numerical Analysis and of Scalable Computing: Practice and Experience, and
is the editor and author of seven research monographs and special journal issues.
His recent research has appeared in journals such as ACM Transactions on Mathematical
Software, Applied Numerical Methods, SIAM Review, Parallel Computing, Journal of
Computational and Applied Mathematics, Computational Materials Science, International
Journal of Numerical Methods in Engineering, Numerical Linear Algebra and its Applications,
Philosophical Magazine (Series A), and Computers and Mathematics with Applications,
Journal of Crystal Growth, and SIAM Review.
Richard Haberman
Professor
(Ph.D. 1971, Massachusetts Institute of Technology)
Professor Haberman is the author of textbooks on ordinary and partial differential equations in science and engineering and on mathematical modeling in mechanical vibrations, population dynamics, and traffic flow. His research has involved various areas of physical applied mathematics: Hydrodynamic stability, solitons for nonlinear dispersive waves, slowly varying bifurcations in nonlinear ordinary differential equations, and transitions such as caustics and shocks in partial differential equations. His work usually involves singular perturbation techniques: the methods of matched asymptotic expansions (boundary layers) and multiple scales (averaging).
Recently, he has used dynamical systems and singular perturbation methods to analyze the trapping of light due to interaction of a nonlinear pulse with an optical defect. He has also introduced a separatrix map to study chaotic interactions of nonlinear waves in fiber optics.
His research has appeared in the last few years in journals such as SIAM Journals
of Applied Mathematics and Applied Dynamical Systems, Studies in Applied
Mathematics, Physica D, Chaos, and the Journal of Nonlinear Science.
Mogens Melander
Associate Professor (Ph.D. 1983, Technical Univeristy of
Denmark)
Professor Melander's current research focuses on fundamental issues in vortex dynamics and statistical fluid mechanics. His topics include vortex/boundary interactions in 2-D, morphology of vortex interactions in 2- and 3-D, identification fo underlying mechanisms, topological description of 3-D viscous flows in terms of global bifurcation analysis of the vorticity field (i.e., vortex line history), construction and analysis of shell models of turbulence, statistical behavior of ensembles of shell model solutions, and the transition to turbulence in shell models.
Professor Melander's research is problem-driven and thus employs tools from
classical and applied mathematics, numerical analysis, and scientific
computation. Concepts from dynamical systems play a central role. His
publications have appeared in the Journal of Fluid Mechanics, Physics of
Fluids, Physical Review Letters, Fluid Dynamics Research, Physica D, and
Physical Review E.
Peter Moore
Professor (Ph.D.
1988, Rensselaer Polytechnic Institute)
The primary focus of Professor Moore's research has been on developing adapative finite element methods for solving reaction-diffusion systems in one, two, and three space dimensions. Reaction-diffusion systems appear in a variety of applications. These include models in cardiac electrophysiology such as Fitzhugh-Nagumo, Ebihara-Johnston and Luo-Rudy I, combustion, catalytic surface reactions, and pattern formation. Adaptive methods have proved effective in solving such systems increasing the reliability, robustness and efficiency of standard methods.
Professor Moore was a faculty member of Tulane University for eleven years
before arriving at SMU. His published work has appeared in SIAM Journal on
Numerical Anaylsis, SIAM Journal of Scientific Computation, Journal of
Computational Physics, BIT, Physica D, Applied Numerical Mathematics,
Mathematical Biosciences and the Journal of Cardiovascual
Electrophysiology.
Takashi Nishikawa
Assistant Professor. (Ph.D. 2000, University of
Maryland)
Professor Nishikawa's research reflects his broad interest in different aspects of dynamical systems. His focus is either on developing mathematics for practical problems in nonlinear dynamical systems, or on applying existing mathematics to understand the dynamics of such systems. Examples include studying synchronizability of oscillator networks with scale-free interaction topology, developing an asymptotic theory for the continuity statistics designed to test existence of a functional relationship in time series, and describing the coalescence process of inertial particles advected by chaotic flows.
He has collaboration with scientists at Arizona State University, Los Alamos
National Laboratory, University of Săo Paulo, Brazil, and Eötvös University,
Hungary. His work has appeared in SIAM Journal of Applied Mathematics,
Physical Review Letters, Physical Review E, Chaos,
Nonlinearity, and Physics Letters A.
George Reddien
Professor
(Ph.D. 1971, Georgia Institute of Technology)
Professor Reddien has worked in various areas of numerical analysis such as numerical bifurcation theory, approximation theory, and boundry value problems. Particular problems he has studied include projection methods for two-point boundary value problems, collocation at Gauss points in optimal control, and the computation and characterization of turning points and other singularities.
He is the former managing editor of the SIAM Journal on Numerical
Analysis. His work has been published in Numerische Mathmatik,
Mathematics of Computation, Journal of Computers and Applied Mathematics,
International Journal of Numerical Analysis, and Transactions of the
American Mathematical Society, among others.
Douglas Reinelt
Professor
(Ph.D. 1983, California Institute of Technology)
Professor Reinelt's research involves mathematical modeling of applied physical problems and the development of solution techniques for these problems. Past problems he has examined include the motion of long bubbles in capillary tubes, fluid draining from a tube under the effect of gravity, and the shapes of bubbles and fingers as a fluid penetrates into a more viscous fluid.
His current research interests include foam flow, and the stability and variations of thin film thickness in coating flows. His foam research involves the development of theories that relate foam structure and the physical properties of the constituent phases and interfaces to macroscopic rheology. In the coating flow problem, he is investigating the instabilities that occur when a thin liquid film is deposited on a moving roller or cylinder. This problem is of particular interest to the printing and photographic industries, and other problems have applications in petroleum and geothermal energy production and manufacture of coatings and polymeric foams.
He recently has done research at the Laboratoire de Dynamique des Fluides Complexes at the Universite Louis Pasteur in Strasbourg, France, and has collaborated with colleagues in applied mathematics and fluid and thermal science at Sandia National Laboratories.
Some of his publications have appeared in the Journal of Fluid Mechanics,
Physics of Fluids, Journal of Colloid and Interface Science, and
International Journal of Multiphase Flow.
Lawrence Shampine
Betty
Clements Professor of Mathematics, (Ph.D. 1964, California Institute of
Technology)
Professor Shampine began working in numerical analysis just as it was emerging as a discipline and later helped start the subdiscipline of mathematical software. He joined SMU after a distinguished career at Sandia National Laboratories, where he was supervisor of the Numerical Mathematics Division. He is the author of several items of mathematical software used around the world and is a past president of the Association of Computer Machinery's (ACM's) Special Interest Group on Numerical Mathematics (SIGNUM). He has held numerous editorial positions and is an associate editor of the SIAM Journal on Numerical Analysis.
Much of his research has been directed toward more effective numerical solution of ordinary differential equations (ODEs). He is developing methods and software appropriate for graphical user interfaces. This work is being used for computer experiments in courses on ODEs and for scientific computation in the MATLAB environment.
He is the author of four books: Nonlinear Two-Point Boundary Value
Problems; Numerical Computing: An Introduction; Numerical Solution of Ordinary
Differential Equations: The initial Value Problem; and Numerical Solution
of Ordinary Differential Equations. His recent research has appeared in
journals such as Computers and Mathematics with Applications, SIAM Journal of
Numerical Analysis, SIAM Journal of Scientific and Statistical Computation,
Journal of Computational and Applied Mathematics, Applied Numerical Mathematics,
and Mathematics of Computation.
Johannes Tausch
Associate
Professor (Ph.D. 1995, Colorado State University)
Professor Tausch's research focuses on the numerical analysis of integral and partial differential equations. He has developed efficient numerical algorithms to solve problems that arise in Electromagnetics, Optics and Fluid Mechanics. Currently he is applying multiscale techniques to obtain sparse representations and preconditioners for integral operators on surfaces with complicated geometries.
He has collaborated with engineers to simulate the behavior of integrated circuits, micro-mechanical devices and photonic waveguides. His software has been used in industry to help the design of semiconductor lasers with optical gratings.
His work has appeared in Mathematics as well as Engineering publications, such as, SIAM Journal of Scientific Computing, Mathematics of Computation, Computing, Journal of Numerical Mathematics, Journal of Computational Physics, Computational Mechanics, Journal of the Optical Society of America A, IEEE Transactions on Microwave Theory and Technology, and IEEE Transactions on Computer-Aided Design.
Sheng Xu
Assistant
Professor (Ph.D. 2002, Cornell University)
Professor Xu's research interests center on the development of computational techniques for problems in fluid mechanics and aerodynamics, including biological flows with tissues or membranes, supersonic and hypersonic turbulence with shockwaves, flow control by passive means, and fluid dynamics of nature's flyers and swimmers. The present development focuses on the immersed interface method, which models solids in a fluid with singular forces and solves the fluid flow subject to the singular forces by incorporating jump conditions into numerical schemes. The method is currently used to study the wing pitch reversal and fore-hind wing interaction in dragonfly flight.
Prior to joining the faculty at SMU, Professor Xu worked for GE Energy on steam turbine aerodynamics. He also worked at Cornell University and Princeton University as a post-doctoral research associate. His published work has appeared in Journal of Computational Physics, SIAM Journal on Scientific Computing, Physics of Fluids, and Journal of Fluid Mechanics.
Yunkai Zhou
Assistant
Professor (Ph.D. 2002, Rice University)
Professor Zhou's research focuses on numerical linear algebra, scientific computing, and their broad range of applications; especially applications in material sciences and electrical engineering. He has developed algorithms that greatly improve the efficiency in solving large-scale eigenvalue problems arisen in density functional theory (DFT) calculations.
His current research includes extending the polynomial filtered subspace methods for generalized eigenvalue problems; improving/developing more efficient mixing-schemes for self-consistent field calculations; and extending the subspace techniques that have been successful for time-independent DFT to time-dependent DFT calculations.
His publications have appeared in Numerical Linear Algebra and Its Application, Physical Review Letters, Journal of Computational Physics, System and Control Letters, Journal of Applied Mathematics, and Computer Physics Communications.