|Address:||Institut für Numerische Simulation|
Rheinische Friedrich-Wilhelms-Universität Bonn
Endenicher Allee 60
|Phone:||+49 (0)228 - 73-62383|
|Fax:||+49 (0)228 - 73-9015|
Applied and Computational Mathematics with a focus on the numerical solution of PDEs on surfaces. I use tools from Fluid Dynamics, Differential Geometry, Optimization, Numerical and Functional Analysis. I am also interested in High Performance Computing and have extensive experience in implementing numerical methods in a number of languages and environments.
My doctoral thesis is on the evolution of thin viscous films on curved surfaces (supervised by Martin Rumpf). It involves modeling the problem on curved geometries and studying the well-posedness of the resulting variational model. Moreover, the model is discretized in time, with the help of its gradient flow structure, and in space, via appropriate finite element spaces. The well-posedness and convergence of the discrete model is shown, and the associated numerical scheme is implemented and applied on subdivision surfaces. An alternative spatial discretization via Discrete Exterior Calculus has been presented in a separate publication.
My master thesis is on the evolution of electrically charged liquid droplets (supervised by Santiago I. Betelu, expanded in joint work with Marco A. Fontelos et al). The numerical method presented there is based on the Boundary Element Method. Coupled with a dynamically relaxed and adaptive mesh, we were able to resolve the formation of singular conical tips on the evolving surfaces in the case of supercritical electric charge. Deploying the code on a linux cluster, we were also able to compare the numerical results with experimental data (as can be seen above).
|1.||O Vantzos. On a variational model for thin viscous films on curved geometries, submitted, 2014. [pdf]|
|2.||O Vantzos. Thin viscous films on curved geometries, Dissertation, University of Bonn, 2014. [link]|
|3.||M Rumpf and O Vantzos. Numerical gradient flow discretization of viscous thin films on curved geometries, Mathematical Models and Methods in Applied Sciences, 23(05):917-947, 2013. [bib | DOI | pdf]|
|4.||C Eck, MA Fontelos, G Grün, F Klingbeil, and O Vantzos. On a phase-field model for electrowetting, Interfaces and Free Boundaries, 11(2):259-290, 2009. [pdf]|
|5.||MA Fontelos, U Kindelan, and O Vantzos. Evolution of neutral and charged droplets in an electric field, Physics of Fluids, 20(9):092110, 2008. [link]|
|6.||C Eck, MA Fontelos, G Grün, F Klingbeil, and O Vantzos. A phase field model in electrowetting and related phenomena, PAMM, 7(1):1151205-1151206, 2007. [pdf]|
|7.||SI Betelu, MA Fontelos, U Kindelan, and O Vantzos. Singularities on charged viscous droplets, Physics of Fluids, 18(5):1706, 2006. [pdf]|
|8.||O Vantzos. Mathematical modeling of charged liquid droplets: numerical simulation and stability analysis, MA thesis, University of North Texas, 2006. [pdf]|