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.
I have worked in ferrofluid models, purely electrostatic electron-gas models
(Euler-Poisson), and compressible ideal-MHD models, all of which represent
entirely different physical regimes. These are three pieces of representative work (research milestones): click
on each thumbnail to open the corresponding Arxiv link
You can find more publications and their links to the respective journal papers
in:
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:
