## Research |

## Home Research Applied Math Seminar Teaching Movies Pictures CV |

- Broad interests in the Analysis and development of space and time discretizations for Partial Differential Equations (PDEs) with mathematically provable properties.
- More precisely: development of numerical methods that preserve essential 'structural properties' of the PDE. In particular: energy estimates, entropy inequalities, invariant sets, maximum/minimum principles, positivity properties, and asymptotic limits of the original PDE. My core interest lies in PDEs that preserve two or more of such notions of stability, in particular, when "Hilbert-space like" notions of stability are either non-applicable or unimportant. Check for instance the introduction of Step-69.
- PDE physical modeling: particular interest on electric charge transport modeling (from semi-conductor to gas-plasma), electron dynamics, and electromagnetism-matter interaction within the context of Continuum Physics. More often than not, revisiting the mathematical properties of pre-existing PDE models, or coming-up with a good model, is far more important than any hasty attempt to solve it numerically.

You can find more publications and their links to the respective journal papers in:

- My Google scholar
- My Research gate

- If you cannot download one of my papers online please do not hesitate to contact me in order to get a pre-print.
- If you need to discuss the content of one of my papers e.g.: Why did we write the paper? What were we trying to achieve? Why is certain statement true? etc, just shoot me an e-mail.
- If you are a Graduate student in any of the Engineering or Science programs (Astrophysics, Chemistry, Electrical Engineering, Geophysics, Mathematics, Physics, Mechanical Engineering, etc) that needs to develop a Numerical-PDE tool for his/her PhD thesis, we can always meet to discuss it. I really enjoy developing tools that could have an impact on the Applied Sciences.

Prospective Graduate Students:

Numerical Analysis and Scientific Computation of PDEs is vast area of research that involves many subdisciplines such as: Numerical Linear Algebra, Control of PDEs, Numerical Solution of PDEs in high-dimensions, and Hyperbolic Balance Laws among many others. In this sense, Texas Tech is a very exciting place to be right now. We have very diverse group of people working in Numerical Analysis of PDEs. Each one of us has a quite different set of skills. Therefore, if you are a prospective graduate student willing to apply to either MSc or PhD program at TTU, with a strong interest in the Numerical Analysis of PDEs, I would also consider taking a serious look at the webpages of my colleagues working in related topics: