Laura Mendoza

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.

About me

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.

My Research

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.

Education

PhD in Numerical Methods for Plasma physics

Max-Planck Institut für Plasmaphysik,
started: November 2012,
supervisor: Eric Sonnedrücker.

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

Master degree in Applied Mathematics

University of Strasbourg,
graduated with honors in 2012

With major in Scientific Calculus and minor in Computer Science Security

Bachelor's degree of Mathematics

University of Strasbourg,
graduated with honors in 2010

With major in Applied Mathematics and minor in Computer Science

Work Experience

Master thesis

Quantup research laboratory

  • 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.

Computer science security Analyst Intern

Strasbourg's teaching hospital, Computer Science's department

  • 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.

Conferences and Papers

Conference Talks

Introducing the IGA approach in plasma physics

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

Modelling Vlasov equations on complex geometries using the Semi-Lagrangian scheme

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

Solving Vlasov-like equations using the Semi-Lagrangian scheme on a 2D hexagonal mesh

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

Solving the guiding center model using the Semi-Lagrangian scheme on a 2D hexagonal mesh (SelHex)

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

Seminars

Solving the Guiding Center model using the Semi-Lagrangian scheme on a 2D hexagonal mesh

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

Solving the Vlasov equation using the Semi-Lagrangian method on a hexagonal mesh

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

Posters

Solving the Vlasov equation using the Semi-Lagrangian method on multiple patches for the GYSELA code

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

Reports

Modelling of a storage water heater

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

Computer skills

Language Skills

Python

Excellent

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.

Fortran

Excellent

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.

C

Good

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.

Object Oriented (C++ / Java)

Excellent

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

Matlab

Good

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.

Scipy/ Scilab / Mathematica

Good

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.

R / Statistical computing

Good

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.

SQL

Excellent

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

Some code samples and scripts

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.