computaTIonal and applied mathematics

Graduate Study in
Computational and Applied Mathematics (CAM)
and
Computational Engineering and Sciences (CES)
at The University of Texas at Austin

Providing Excellence in Interdisciplinary Education

The Computational and Applied Mathematics graduate program prepares students for the exciting field of computational and mathematical modeling. The use of mathematical modeling is growing rapidly, and it is used to simulate, for example, the remediation of contaminants in the groundwater, tidal surges in coastal environments, the evolution of black holes, the damage and failure of composite materials, corporate risk and financial management, and the human ear and vocal cords.

The CAM program is a challenging interdisciplinary program. It develops in each student competencies in three concentration areas:

Area A Applicable Mathematics;

Area B Numerical Analysis and Scientific Computation;

Area C Mathematical modeling of a natural, engineered, or other system;

Students complete advanced coursework in applied mathematics, computer science, and in the fields representing the application area of the modeling effort. These courses are taught by faculty in their respective disciplines within the college of natural sciences, engineering, or business. Since this program is inherently interdisciplinary, it is housed not within a single university department, but rather within the Institute for Computational Engineering and Sciences (ICES).

The CAM program is primarily a Ph.D. track program. The CAM program seeks and is composed of outstanding students committed to excellence, desiring expertise in multiple disciplines, and willing to take on new challenges by working alongside faculty involved in cutting edge research.

Producing Contributors to Research, Academia, and Technology

Those who have received a Ph.D. degree in Computational and Applied Mathematics have obtained various professional opportunities, developed rewarding careers, and have made significant contributions to research, academia, and technology.

Here are just a few examples:

	Dr. Timothy Walsh is currently a Senior Member of Technical Staff at Sandia National Laboratories. He works in the Department of Computational Solid Mechanics and Structural Dynamics. Dr. Walsh’s expertise in the field of computational and applied mathematics is allowing him to participate in many groundbreaking research activities at Sandia Laboratories. He is helping develop massively parallel solution techniques for strongly coupled structural acoustics. Also, he is specializing in A posteriori error estimators for eigenvalue analysis of elastic structures. Other important research area’s he is collaborating on is that of finite element methods for linear and nonlinear acoustics, and structural dynamics.
	Dr. Beatrice Riviere is an Assistant Professor in the Department of Mathematics at the University of Pittsburgh. She also devotes some of her time as a Ph.D. advisor and research advisor to both graduate and undergraduate students. Dr. Riviere teaches a variety of math classes that help students gain a solid foundation in the discipline of Computational and Applied Mathematics. Some of the graduate classes she teaches include: Numerical Solution of ODEs, Finite Element Method, Numerical Methods in Scientific Computing I and II, and lastly Advanced Scientific Computing III. She also teaches Matrix theory and differential equations as an undergraduate class. Throughout Dr. Riviere’s educational experience she has developed many research interests. Some of these research interests are: Numerical methods for solving partial differential equations – discontinuous Galerkin methods, and mixed finite elements. Error analysis and development of hp adaptive software for DG methods, Flow and transport in porous media, Multiphase flow. Incompressible flow – Stokes and Navier-Stokes equations. Viscoelastic fluids and solids, Acoustic and elastic waves, and Coupled problems.
	Dr. Robert Kirby is now developing a code generation system what will translate variational forms to parallel code for assembling associated matrices. He works jointly with Matt Knepley of Argonne National Laboratory on this endeavor. He is also devising techniques for generating optimized algorithms for computation of local finite element forms. Lastly, he is developing a general family of nonconforming triangular finite elements. All this is done while Dr. Kirby teaches as an Assistant Professor in Computer Science at the University of Chicago.
	Dr. Tarek Zohdi is an Associate Professor at the University of California – Berkeley. He teaches Mechanical Engineering. Dr. Zohdi is an intriguing researcher who is actively involved in Micro-structural/macro-property inverse problems involving optimization and design of new materials. Also, he is researching genetic algorithms, modeling and simulation of strongly coupled multified processes in multiphase systems, computational and statistical testing methods, modeling and simulation of aging and fatigue of solids, modeling and simulation of granular flow and particulate accretion and fragmentation, modeling and simulation of the dynamics of high-strengh fabric. Dr. Zohdi has one three very distinguished international awards. He has won the “Zienkiewicz Prize and Medal”. This prize is awarded once every two years to one post-graduate researcher under the age of 35. It is given by the Institution of Civil Engineers in London to commemorate the work of Professor O. C. Zienkiewicz, and it is contributed to the field of Numerical Methods in Engineering. Also, Dr. Zohdi has been awarded the “Best Paper of the Year 2001”. Awarded in London at the Lord’s Cricket Ground by the Literati Club for “Modeling and simulation of the decohesion of particulate aggregates in a binding matrix.” This paper was published in the Journal: Engineering Computations. The third award Dr. Zhodi has received is the “Junior Achievement Award of the American Academy of Mechanics.” This award is given once a year, to one post-graduate researcher, to recognize outstanding research during the first decade of a professional career. The award was presented in Washington D.C. at the annual ASME Winter Conference.
	Dr. Gunnar Martinsson is an Gibbs Instructor of Applied Mathematics in the Department of Mathematics at Yale University. He is presently teaching Applied Mathematics and conducting research at Yale. Dr. Martinsson is an active researcher in Numerical methods for partial differential equations, especially boundary equation methods combined with FMM fast solvers. He also has research interests in Computational Continuum Mechanics, especially techniques for problems with Micro-structure.
	Dr. Abani Patra is an Associate Professor teaching in the Mechanical Engineering Department at The State University of New York at Buffalo. He is undertaking research in the following areas: Adaptive hp Finite Element Methods, Parallel Iterative Solvers, Domain Decomposition and Preconditioners, Applications to Incompressible Flows and simulations of Biomechanical Systems and Geophysical Mass Flows.