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Students
Information for students wishing to work with me

I have many research projects waiting for the right student. You may be the right student if you are interested in any or all of:

  • Numerical analysis / numerical methods
  • Time-dependent hyperbolic PDEs
  • Shock waves
  • Wave behavior in periodic and random materials
  • Computational science
  • Massively parallel computing
  • Scientific software engineering
  • Global optimization

Most of my research focuses on numerical methods for time-dependent partial differential equations. I also work with methods for ODEs, because these are frequently used for the time-integration of PDEs. My work focuses on the analysis of the methods, their practical implementation, and their application to interesting problems. The application problems primarily involve nonlinear waves. I'm especially interested in applications with unique features that make it challenging to design good numerical methods.

To work with me, it is helpful to have some background in programming, numerical analysis, and/or differential equations. Optimization often plays a role in my work as well. Many other branches of mathematics may be relevant to particular projects; some examples include group theory, graph theory, and complexity theory. Typical projects may involve

  1. Devising new numerical methods for specific classes of differential equations (this may involve analysis and/or numerical optimization)
  2. Analyzing stability, accuracy, and efficiency of existing numerical methods
  3. Using numerical methods to understand interesting wave phenomena
  4. Developing software for numerical modelling
  5. Extending software to run efficiently on new architectures

Any of these is likely to involve a significant amount of both analysis and programming. If you have a strong background in some application area, that may also be helpful. If you are interested in working in my group, please stop by my office on the 4th floor of al-Khwarizmi to discuss potential projects, or e-mail me for an appointment. You may also with to read the guidelines for working in my group.