Applied Mathematics and Scientific Computing
Our research and teaching activities focus on mathematical problems that arise in real-world applications. These require often the use of computing ressources for simulation, computation, data analysis, and visualization. Key problems are the numerical approximation of differential equations, and the solution of large systems of equations. The mathematical modeling of real-world phenomena and the design of modern numerical approaches require a solid theoretical background in functional analysis, differential equations, calculus of variations, probability theory, and graph-theory.
Faculty
Prince Chidyagwai works in the areas of numerical partial differential equations. He works on finite element methods, Discontinuous Galerkin methods and finite volume methods with applications to fluid flow and porous media flow. Recently he has been working on coupled models for free flow and porous media flow.
Yury Grabovsky's interests are in the area of Calculus of Variations, PDE, and applications to Continuum Mechanics. He has worked on the mathematical theory of composite materials, non-linear elasticity, and phase transitions in solids. His work on exact relations for effective tensors of polycrystalline composites has combined methods of modern algebra and PDE. His recent work includes a proof of Ball's conjecture in the Calculus of Variations.
Davit Harutyunyan has worked on the theory of micromagnetics which is itself a minimization problem of a non-convex and non-local energy. Currently he is working on elasticity problems, and in particular on shell buckling problems.
Benjamin Seibold's primary research fields are computational partial differential equations and numerical analysis. He works on meshfree and particle methods for fluid flow simulations, level set methods, traffic modeling, radiative transfer, and molecular dynamics simulations.
Daniel B. Szyld has worked on many aspects of numerical linear algebra and matrix computations, including eigenvalue problems, sparse matrix techniques, Schwarz preconditioning and domain decomposition, and Krylov subspace methods. He is the editor of several leading journals on applied and numerical linear algebra, and an editor-in-chief of the Electronic Transactions on Numerical Analysis.
Fei Xue's research interests include numerical linear algebra, matrix computations and scientific computing in general. Specifically, he is working on design and analysis of efficient inexact eigenvalue algorithms for large sparse matrices. He is also interested in Krylov subspace methods for the solution of linear systems and preconditioning techniques for saddle point problems.
Wei-Shih Yang's research interests are in the fields of probability theory, mathematical physics and mathematical finance. He has worked on phase transitions and critical phenomena in statistical mechanics, Gaussian and non-Gaussian random fields with applications to quantum field theory, percolation, Ising model, and self-avoiding random walks. His more recent work includes the following topics: quantum random walks with applications to quantum computing and ruin probability of risk processes.
Our department also has research activities in computational geometry and combinatorics. Please consult the website of the Geometry and Topology Group for more details.
Current Ph.D. Students
- Shimao Fan
- Meredith Hegg
- Stephen Shank
- Kirk Soodhalter
- Dong Zhou
Former Members
Former Faculty and Long Term Visitors
- Lahcen Laayouni (2010)
- Marlliny Monsalve (2009-2010)
- Sébastien Loisel (2006-2009)
- Smadar Karni (1995-1997)
- Vladislav Kucher (2008-2009)
- Jian-Guo Liu (1993-1997)
Former Ph.D. Students
- 2010: David Fritzsche
- 2008: Worku Bitew, Xiuhong Du, Abed Elhashash
- 2007: Mussa Kahssay Abdulkadir, Tadele Mengesha, Kai Zhang
- 2005: Chao-Bin Liu
- 2004: Hansun To
- 2001: Yan Lyansky, Jianjun Xu
- 2000: Yun Cheng, Judith Vogel, Cheng Wang
- 1999: Hans Johnston
For more information please consult the department's listing of recent Ph.D. graduates.
Research Profile
The Applied Mathematics and Scientific Computing group is active in a variety of research areas, such as:
- high order methods for partial differential equations
- computational fluid dynamics
- meshfree and particle methods
- level set approaches
- traffic flow modeling
- radiative transfer
- iterative solution of large linear systems
- numerical solution of eigenvalue problems
- solution of matrix equations
- modern Krylov subspace methods
- theory of composite materials
- non-linear elasticity and phase transitions
Recent Publications by the Group Members
- List of recent publications by the group members
- For links to preprints of the individual papers, please consult the respective faculty member's personal website (linked above).
Presentation about the Group
Reflecting the status in November 2010.
Seminar
- Seminar Applied Mathematics and Scientific Computing: Our weekly seminar enjoys a mix of talks by external guest speakers, and internal presentations by faculty members and graduate students.
Special Events
- Friday, 4 November 2011: Mid Atlantic Numerical Analysis Day. A conference on numerical analysis and scientific computing, for graduate students and postdocs from the Mid-Atlantic region. .
- Thursday, 8 July 2010: Temple Summer Minisymposium on Computational Mathematics.
Special Courses
- Mathematical Modeling Course: Students taking this course work in groups on solving problems that come from an industrial partner company or an external scientific researcher. Please check the course listing whether this course is offered in the near future.
Graduate Program and Courses
In the recent years, several graduate students have completed a Ph.D. or masters degree in the area of Applied Mathematics and Scientific Computing.
Information of about the graduate program in Mathematics can be found on the
Graduate Program website.
Students who are interested in specializing in Applied Mathematics and Scientific Computing can achieve a M.A. in Mathematics with Applied Concentration, as well as a Ph.D in Mathematics, with an advisor in the applied areas. In both cases, students are advised to take (many of) the courses listed below.
More detailed syllabi can be found on the
Course listing by the Graduate School of the College of Science and Technology.
The courses are not be taught every semester. Please check the website of the Department of Mathematics for the course schedule.
Central Courses
5043. Introduction to Numerical Analysis provides the basis in numerical analysis and fundamental numerical methods.
8013/8014. Numerical Linear Algebra I / II cover modern concepts and methods to solve linear systems and eigenvalue problems.
8023/8024. Numerical Differential Equations I / II present modern methods for the numerical solution of partial differential equations, their analysis, and their practical application.
9200/9210. Topics in Numerical Analysis I / II
focus on specialized topics relating to the faculties' research areas.
This includes a special
Mathematical
Modeling Course that we offer.
Theoretical Basis
In addition, we recommend courses that provide fundamental theoretical background.
8141/8142. Partial Differential Equations I / II provide a theoretical understanding of many of the equations considered in 8023/8024.
8200/8210. Topics in Applied Mathematics I / II focus on specialized topics relating to the faculties' research areas.
9005. Combinatorial Mathematics relates to many key problems in Scientific Computing, such as mesh generation, load balancing, and multigrid.
9041. Functional Analysis is a theoretical basis for many numerical approximation approaches, such as the finite element method.
9043. Calculus of Variations provides powerful tools for the theoretical study of dynamics, structural mechanics, and material properties.