Ph.D. Student

Contact me

I am a 3rd year Ph.D. student at the Max-Planck-Institut für Plasmaphysik
in Applied Mathematics, under the supervision of Éric Sonnendrücker.

**Email:**laura.mendoza@ipp.mpg.de**Website:**www.ipp.mpg.de/~mela**GoogleScholar:**my scholar page**Phone:**(+49) 89.3299.1178**Address:**Boltzmannstr. 2, Garching bei München, Deutschland

I was born in Strasbourg, France, but was raised in Guatemala city where I went to a French school. I did my undergraduated degree in the University of Strasbourg, where I obtained a bachelor degree in Mathematics with minor in Computer Science followed by a Master degree in Applied Mathematics specialized in Scientific Computing and Computer Science Security.

I am now a Ph.D. student at the IPP in Numerical Methods in Plasma's Physics. My research interests are applied mathematics and numerical analysis. Currently I am working on solving the Vlasov equation using the Semi-Lagrangian method in multiple patches.

The GYSELA code is a non-linear 5D global
gyrokinetic code which
performs flux-driven simulations to solve the gyrokinetic Vlasov equation
coupled with the Poisson equation. Its 3D spatial representation
is limited to circular toroidal geometry (r, theta, phi). Currently the poloidal
plane, a circular cross-section, is discretized with a polar mesh. Due to
the singularity of this mapping on its origin, the geometry is discontinuous
(with a hole in the center).

Thus our aim is to generalise GYSELA’s geometry definition using IGA so that any geometry, however complex, can be simulated by mapping one or multiple patches. We decided to study two different approaches to solve this problem: on the one hand, Non-Uniform Rational B-Splines (NURBS), which provide an exact representation of complex shapes; on the other hand, using a regular equilateral triangle mesh of hexagonal form on which we will work with Box-Splines.

The GYSELA code is one of many examples of why we need Semi- Lagrangian codes adapted to complex geometries. Other examples from plasma physics (and further goals) are the X-point, the scrape-off layer or edge plasma, 3D representation of a Tokamak and Stellarator, etc.

Thus our aim is to generalise GYSELA’s geometry definition using IGA so that any geometry, however complex, can be simulated by mapping one or multiple patches. We decided to study two different approaches to solve this problem: on the one hand, Non-Uniform Rational B-Splines (NURBS), which provide an exact representation of complex shapes; on the other hand, using a regular equilateral triangle mesh of hexagonal form on which we will work with Box-Splines.

The GYSELA code is one of many examples of why we need Semi- Lagrangian codes adapted to complex geometries. Other examples from plasma physics (and further goals) are the X-point, the scrape-off layer or edge plasma, 3D representation of a Tokamak and Stellarator, etc.

Realistic magnetic equilibrium and field aligned coordinates for high performance computing of gyrokinetic turbulence in tokamaks.

graduated with honors in 2012

With major in Scientific Calculus and minor in Computer Science Security

graduated with honors in 2010

With major in Applied Mathematics and minor in Computer Science

**Period:**Ferbruary - July 2012**Job type:**Internship**Supervisor:**Maxime Pierson

Optimization of the Bin Packaging Problem in 2D with polygons using genetics algorithms and exploring new solutions using evolutionary algorithms.

- Work in small groups of 2 to 4, as well as individual work;
- Worked on common optimization problems;
- Introduced to evolutionary algorithms;
- Develeoped a user-friendly application.

**Period:**June 2011 - August 2011**Job type:**Internship**References:**Fabrice Stalter

Determinate the risks linked to applications' development and their integration in an information system. Analyzed the best utilities to improve an information system's security level, specifically for a big organization like Strasbourg's Research Hospital.

- Work mostly done independently;
- Familiarization with the most common security's weakness;
- Integration and analyze of a big code;
- Development of security's application for I.S.

Third International Conference on Isogeometric Analysis (IGA 2015), Trondheim, Norway, June 2015, Beamer, IGA 2015 program.

Deutsche Physikalische Gesellschaft (DPG), Bochum, Germany, March 2015, Beamer, Abstract in DPG website, or Abstract as PDF.

NUMKIN workshop, Garching, Germany, October 2014, Beamer, Numkin.

CEMRACS Summer School, Marseille, France, August 2014, Beamer.

Theory Seminar, Ringberg, Germany, November 2014, Beamer, Film.

HEPP Seminar, Garching, Germany, June 2014, Beamer.

HEPP Colloquium at Strausberg, Germany, September 2013, Poster.

S. Eberhard, M. Ferreira, L. Mendoza et al., 26-th ECMI Modelling Week at Dresden, Germany, August 2012, Project Report.

Language Skills

For the last three years most of my programs have been developed in python. I have been using it daily since the start of my PhD.

I learned Fortran in school a few years ago and many libraries I use daily are developed in Fortran 90. Now most of the code I make during my PhD is in Fortran 2003.

I have programmed for a lot of time in C, from small projects to bigger ones, and I still come back to this language when I need to code something fast.

Even though I don't use them as often as I used to, although I am still very comfortable with oriented object programming.

Mathematical languages

I started using Matlab at the beginning of my thesis for short programs. Now I definitely know the basis but still have many things to discover. And I rather use other free and open source tools.

I feel quite at ease with these computational softwares. Some of my master projects were developed in Scilab and I recently developed a high order CENO method in Scilab. Scipy is my "go to" tool for all my symbolic computations.

During my master thesis I took several statistics courses in which we developed small programs in R. Even though I haven't really used them during my thesis I am sure I could get familiarized with them quite quickly.

My knowledge in SQL are pretty basics and are limited to a few weeks of classes during my Master diploma.

During my Ph.D. I have written a couple of scripts that I think could be useful to more than one person. So I put them online free to public access. Feel free to ask me any questions about them or to update them as you feel necessary. I have only chosen a couple to publish on this website but I should put some more in the near future. Finally, on my spare time I am working on an Android App that I hope I can realease by the end of this year.

**Doxygen headings python script**After coding for a library for a few months the library decided to add Doxygen documentation to every piece of code on the library. As I had already written a few thousands of lines of code, the task was terribly repetitive and time consuming. Thus, I decided to create a quick script that will add the headers to every function, subroutine and model. It has worked quite well and I was able to work more efficiently since I created it. The code is available at this site for Python versions < 3.0: Python Script, or here for Python versions >=3.0: Python3 Script.

**Correcting grammar in TeX files**I started writing (pieces of) my Thesis from the first year. Even if I think this was a great decision, I realized by the end of my thesis that what I wrote at the beginning was not always as well written as I would have hoped. Since my Thesis is 150+ pages divided into several files, the process of proof-reading was a nightmare. Furthermore, there are not that many tools to correct Grammar for LaTeX. I found a couple, but they all needed some kind of tweeking (convert LaTeX to PDF, html, plain text...) and since I used XeLaTex, it got even harder. Fortunately, I found a great web-app: Lyx-gc. The problem was that the result had many errors that weren't really errors and polluted my output file. So I created a small script to take out this errors. Is 100% adapted to my thesis, but I think someone could find it useful. You can get it here.