Jobs / Theses

Software Development Page (... always under construction ...)

Project: ReSSy (Regularity Structures Symbolic Computation Package)

Description: Symbolic manipulation package for dealing with regularity structures as introduced by M. Hairer in 2013/2014. Regularity structures are extremely useful when dealing with stochastic partial differential equations (SPDEs), in particular for defining suitable renormalized limits as solutions. However, many practical computations employing regularity structures can become incredibly cumbersome, even for relatively simple looking SPDEs. Hence, a symbolic manipulation software is called for. Due to the newly added layers of complexity and completely new formalism in the theory of regularity structures, it does not seem wise to force the calculations into a pre-existing symbolic package. Instead, the route pursued here is to glue existing algorithms to newly developed classes that can manipulate regularity structures as well as several associated objects.
Language: Python
Development: IMPORTANT - If you have a calculation that you want to do using regularity structures, then I am happy to try to code this calculation and extend the ReSSy package accordingly. The idea is that you send me a benchmark calculation that is checkable 'by hand'. Then you send me the calculation that you want to do which is a lot more cumbersome and I am going to extend ReSSy so that it can accomplish this job.
Current Release: v0.1 [please e-mail me to obtain a copy]

Project: DyGluS (Dynamics Gluing Scripts)

Description: Dynamical systems algorithms such as numerical continuation algorithms are a widespread tool in mathematics, engineering and almost all quantitative science applications. Several excellent software tools already exist; for example for continuation algorithms see AUTO, MatCont, COCO, pde2path, etc. However, the connection to cutting-edge numerical discretization codes and between different packages is still difficult, particularly for PDEs. Similar remarks apply for many other recent and emerging areas in dynamics systems. One goal of this project is to provide basic scripts to demonstrate how to glue codes for certain dynamics problems, e.g., using various PDE codes in tandem with numerical continuation and dynamics packages. The task is to develop for each project a set of scripts, which can be adapted to the need of each user; in particular, there is no aim for a comprehensive do-it-all tool but to build up a set of solutions, project-by-project. The time seems ripe to harness existing tools a lot more by gluing different packages within suitable high-level scientific computing languages.
Language: Python, Octave/MatLab, etc.
Development: ONGOING, released bit-by-bit
Current Release: v0.0 [still in base development]
* 2018-07:  Very basic Python scripts for 1D PDE integration
* 2018-11:  Basic Python script to integrate a 1D stochastic neural field