Our research and teaching activities focus on mathematical problems that arise in real-world applications. This involves the mathematical modeling of physical, biological, medical, and social phenomena, as well as the effective use of current and future computing resources for simulation, computation, data analysis, and visualization. Key areas of research in our group are the modeling of bio-films and of materials, computational neuroscience, traffic flow modeling and simulation, the numerical approximation of differential equations, and the solution of large systems of equations. The faculty and students in our group conduct research on many cross-disciplinary projects, including collaborations with biology, medicine, computer science, and mechanical, electrical, and nuclear engineering. Students conducting research on the mathematical modeling of real-world phenomena and the design of modern computational approaches receive a broad education and training in differential equations, computational mathematics, fluid dynamics, applied analysis, and specialized courses on topics like computational neuroscience, calculus of variations, kinetic equations, and other areas. Hands on research opportunities with modern hardware are provided by the Center for Computational Mathematics and Modeling.
Members of the Group:
- Sophia Blakely, Graduate Student
- Henry Brown, Graduate Student
- Yury Grabovsky, Professor
- Isaac Klapper, Professor
- Noa Kraitzman, Research Assistant Professor
- Zachary M. Miksis, Research Assistant Professor
- Sean Gillian Queisser, Professor
- Benjamin Seibold, Professor
- Madison Shoraka, Graduate Student
- Daniel B. Szyld, Professor
- Jacob Samuel Woods, Graduate Student
- Nicole Zalewski, Graduate Student
In addition, a number of undergraduate student researchers are regularly involved in our research projects.
Former Members
Former Faculty, Postdocs, and Long-Term Visitors | Former Ph.D. Students |
|---|---|
Alberto Tenore (2021-2022) | 2022: James Rosado |
Qingguang Guan (2019-2022) | 2021: Abhijit Biswas |
Rabie Ramadan (2020-2021) | 2020: Joshua Finkelstein, Stephan Grein, Rabie Ramadan, Najmeh Salehi, Xinli Yu |
Faycal Chaouqui (2018-2021) | 2019: Yilin Wu |
2018: Jose Garay, Kathryn Lund | |
Shelby Stanhope (2016-2018) | 2015: Scott Ladenheim |
Dong Zhou (2014-2018) | 2014: Stephen Shank |
Sunnie Joshi (2012-2016) | 2014: Dong Zhou |
Shumo Cui (2015-2016) | 2013: Shimao Fan |
Jieyong Zhou (2014-2015) | 2012: Meredith Hegg, Kirk Soodhalter |
Andreas Aristotelous (2014-2015) | 2010: David Fritzsche |
Davit Harutyunyan (2011-2013) | 2008: Worku Bitew, Xiuhong Du, Abed Elhashash |
Prince Chidyagwai (2010-2013) | 2007: Mussa Kahssay Abdulkadir, Tadele Mengesha, Kai Zhang |
Fei Xue (2009-2012) | 2005: Chao-Bin Liu |
Lahcen Laayouni (2010) | 2004: Hansun To |
Marlliny Monsalve (2009-2010) | 2001: Yan Lyansky, Jianjun Xu |
Sebastien Loisel (2006-2009) | 2000: Yun Cheng, Judith Vogel, Cheng Wang |
Smadar Karni (1995-1997) | 1999: Hans Johnston |
Vladislav Kucher (2008-2009) | |
Jian-Guo Liu (1993-1997) | |
Research Profile
Applied Mathematics | Scientific Computing |
|---|---|
modeling and simulation of biological and medical applications | computational fluid dynamics and fluid-structure interaction |
traffic flow modeling, simulation, and experiments | high order methods for partial differential equations |
fluid dynamics and applications | iterative solution of large linear systems and modern Krylov subspace methods |
continuum mechanics | solving coupled problems on complex geometries |
mathematical neuroscience | numerical solution of eigenvalue problems and matrix equations |
radiative transfer and applications in radiotherapy | |
high-performance computing and supercomputing |
Resources
The Center for Computational Mathematics and Modeling provides opportunities for hands-on research with modern hardware, including robotics, virtual reality, and 3D printing. The center also provides resources and assistance to modeling activities both at the undergraduate and graduate level.
Seminar
Seminar Applied Mathematics and Scientific Computing (the link to the external website will appear): Our weekly seminar enjoys a mix of talks by external guest speakers, and internal presentations by faculty members and graduate students.
Mid Atlantic Numerical Analysis Day is a conference on numerical analysis and scientific computing for graduate students and postdocs from the Mid-Atlantic region.
Graduate Program and Courses
Applications to become a Ph.D. student are processed by the Department of Mathematics. Information of about the graduate program in Mathematics can be found on the Graduate Program website. Active Ph.D. students interested in Applied and Computational Mathematics are encouraged to approach the faculty listed above to discuss possible research and coursework directions. Examples for Ph.D. projects can be found here. Students who are interested in obtaining graduate-level expertise and training in Applied and Computational Mathematics can also achieve a M.S. in Mathematics with Applied Concentration. A M.S. degree can conclude with a M.S. thesis research project. Examples of suitable courses, for both Ph.D. and M.S. students are listed below (for more details, please see the description of Temple math courses). Some courses are not taught every semester. Please check the Temple University Schedule of Classes.
Central Courses
- 5043/5044. Introduction to Numerical Analysis I / II provides the basis in numerical analysis and fundamental numerical methods, and well as expertise in numerical methods for ordinary differential equations.
- 8007/8008. Introduction to Methods in Applied Mathematics I/II provides the student with the toolbox of an applied mathematician: derivation of PDEs, solution methods in special domains, calculus of variations, control theory, dynamical systems, asymptotic analysis, hyperbolic conservation laws.
- 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 are special courses in Numerical Analysis that focus on topics relating to our group members' active research areas. Examples include finite element method, discontinous Galerkin method, and computational methods for flow problems.
- 8200/8210. Topics in Applied Mathematics I/II are special courses that are offered by demand. Examples include Applied Mathematics in Neuroscience and Survey of Fluid Dynamics.
Theoretical Basis
In addition, the following courses can provide fundamental theoretical background.
- 8141/8142. Partial Differential Equations I / II provide a theoretical understanding of many of the equations considered in 8023/8024.
- 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.