Research topics

I'm a member of the research group of Numerical Analysis and Mathematical modeling. At the moment I'm mainly involved in groundwater modeling, advection-diffusion problems and parameter estimation. To be more specific, I am/was involved in:

1. FEM in stationary groundwater problems compared with semi-analytical solution. For this Maple files where developed which theoretically calculate groundwaterflow, and a C++ programm K2dGrFlow, that was developed for my master thesis in Applied Informatics at the VUB (GASTI).
2. The dual-well or double well problem. A practical experimental setup revisited. This advection-diffusion problem is solved by a convenient domain transformation and operator splitting, which allows the hyperbolic and parabolic problem to be solved separately.
3. Nonlinear adsorption in the dual-well setting. The way to handle this is like above, but now we have a nonlinear hyperbolic problem (shocks and rarefaction waves), and a nonlinear diffusion problem.
4. Flux based method of characteristics, see Dr. P. Frolkovic's homepage. This is an easy and very quick method to solve linear hyperbolic problems. The method is proved to be TVD. My contribution is toward dimensional splitting.
5. Diffusion Annealing in collaboration with J. Barros of the Department of Metallurgy and Materials Science. Diffusion Annealing is a technique to enrich a steel with Si or Al. My contribution is toward the parameter estimation: the macro diffusion is determined from experiments. The aim is to predict with a very basic model the Si/Al profiles over a sheet after a certain time starting from a specific steel. No temperature dependencies for now.
6. Operator Splitting The mathematical technique used in some of the models. Mathematically challenging is to prove the convergence of a split problem to the original problem.
7. Adjoint or Costate Method A mathematical technique to determine the gradient of a functional by solving a dual problem. In our case, dealing with PDE, the dual problem is again a PDE. We apply this technique and show it's very powerfull in diverse settings.