Applied Mathematics and Scientific Computation

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 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 mathematical modeling of real-world phenomena and the design of modern computational approaches require a broad background in differential equations, fluid dynamics, applied analysis, calculus of variations, functional analysis, probability theory, and other areas.

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Former Members

Former Faculty, Postdocs, and Long-Term VisitorsFormer Ph.D. Students
  • 2015: Scott Ladenheim
  • 2014: Stephen Shank
  • 2014: Dong Zhou
  • 2013: Shimao Fan
  • 2012: Meredith Hegg, Kirk Soodhalter
  • 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

Applied MathematicsScientific Computing
  • continuum mechanics and theory of composite materials
  • fluid dynamics and applications
  • modeling and simulation of biological and medical applications
  • modeling and simulation of traffic flow
  • non-linear elasticity and phase transitions
  • neuroscience modeling
  • computational fluid dynamics and fluid-structure interaction
  • high order methods for partial differential equations
  • iterative solution of large linear systems and modern Krylov subspace methods
  • meshfree, particle, and level set methods
  • numerical solution of eigenvalue problems and matrix equations
  • radiative transfer and applications in radiotherapy
  • high-performance computing and supercomputing

Recent Publications by the Group Members

Presentation about the Group

Reflecting the status in November 2010.


Special Events

Special Courses

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 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.

8007/8008. Introduction to Methods in Applied Mathematics I / II provides the student with the toolbox of an applied mathematician: derivation of PDE, solution methods in special domains, calculus of variations, control theory, dynamical systems, anymptotic 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.

8107. Mathematical Modeling for Science, Engineering, and Industry. See above for the description of this special course.

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. Recent example:

  • Finite Element and Discontinous Galerkin Methods

8200/8210. Topics in Applied Mathematics I / II are special courses that are offered by demand. Recent example:

  • Survey of Fluid Dynamics

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.

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.