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:

In addition, a number of undergraduate student researchers are regularly involved in our research projects.

Former Members

Former Ph.D. Students

Former Faculty, Postdocs, and Long-Term Visitors

Alberto Tenore (2021-2022)

Former Ph.D. Students

2022: James Rosado

Former Faculty, Postdocs, and Long-Term Visitors

Qingguang Guan (2019-2022)

Former Ph.D. Students

2021: Abhijit Biswas

Former Faculty, Postdocs, and Long-Term Visitors

Rabie Ramadan (2020-2021)

Former Ph.D. Students

2020: Joshua Finkelstein, Stephan Grein, Rabie Ramadan, Najmeh Salehi, Xinli Yu

Former Faculty, Postdocs, and Long-Term Visitors

Faycal Chaouqui (2018-2021)

Former Ph.D. Students

2019: Yilin Wu

Former Faculty, Postdocs, and Long-Term Visitors

Giordano Tierra Chica

Former Ph.D. Students

2018: Jose Garay, Kathryn Lund

Former Faculty, Postdocs, and Long-Term Visitors

Shelby Stanhope (2016-2018)

Former Ph.D. Students

2015: Scott Ladenheim

Former Faculty, Postdocs, and Long-Term Visitors

Dong Zhou (2014-2018)

Former Ph.D. Students

2014: Stephen Shank

Former Faculty, Postdocs, and Long-Term Visitors

Sunnie Joshi (2012-2016)

Former Ph.D. Students

2014: Dong Zhou

Former Faculty, Postdocs, and Long-Term Visitors

Shumo Cui (2015-2016)

Former Ph.D. Students

2013: Shimao Fan

Former Faculty, Postdocs, and Long-Term Visitors

Jieyong Zhou (2014-2015)

Former Ph.D. Students

2012: Meredith Hegg, Kirk Soodhalter

Former Faculty, Postdocs, and Long-Term Visitors

Andreas Aristotelous (2014-2015)

Former Ph.D. Students

2010: David Fritzsche

Former Faculty, Postdocs, and Long-Term Visitors

Davit Harutyunyan (2011-2013)

Former Ph.D. Students

2008: Worku Bitew, Xiuhong Du, Abed Elhashash

Former Faculty, Postdocs, and Long-Term Visitors

Prince Chidyagwai (2010-2013)

Former Ph.D. Students

2007: Mussa Kahssay Abdulkadir, Tadele Mengesha, Kai Zhang

Former Faculty, Postdocs, and Long-Term Visitors

Fei Xue (2009-2012)

Former Ph.D. Students

2005: Chao-Bin Liu

Former Faculty, Postdocs, and Long-Term Visitors

Lahcen Laayouni (2010)

Former Ph.D. Students

2004: Hansun To

Former Faculty, Postdocs, and Long-Term Visitors

Marlliny Monsalve (2009-2010)

Former Ph.D. Students

2001: Yan Lyansky, Jianjun Xu

Former Faculty, Postdocs, and Long-Term Visitors

Sebastien Loisel (2006-2009)

Former Ph.D. Students

2000: Yun Cheng, Judith Vogel, Cheng Wang

Former Faculty, Postdocs, and Long-Term Visitors

Smadar Karni (1995-1997)

Former Ph.D. Students

1999: Hans Johnston

Former Faculty, Postdocs, and Long-Term Visitors

Vladislav Kucher (2008-2009)

Former Faculty, Postdocs, and Long-Term Visitors

Jian-Guo Liu (1993-1997)

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

Giordano Tierra Chica

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

Scientific Computing

Applied Mathematics

modeling and simulation of biological and medical applications

Scientific Computing

computational fluid dynamics and fluid-structure interaction

Applied Mathematics

traffic flow modeling, simulation, and experiments

Scientific Computing

high order methods for partial differential equations

Applied Mathematics

fluid dynamics and applications

Scientific Computing

iterative solution of large linear systems and modern Krylov subspace methods

Applied Mathematics

continuum mechanics

Scientific Computing

solving coupled problems on complex geometries

Applied Mathematics

mathematical neuroscience

Scientific Computing

numerical solution of eigenvalue problems and matrix equations

Scientific Computing

radiative transfer and applications in radiotherapy

Scientific Computing

high-performance computing and supercomputing

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.