Master Thesis - A Parallel-in-time semi-Lagrangian finite element method for fluid dynamics

The Advanced time Integrators (ATI) research group, part of the Mathematics and Education Division of the Jülich Supercomputing Center (JSC), offers an interdisciplinary and dynamic research environment dedicated to advancing time integration techniques. Our team focuses on the development of innovative parallel-in-time integrators for a variety of applications, including fluid dynamics. With a strong commitment to open research practices and collaborative efforts, we encourage students and researchers interested in the intersection of computational science and engineering to join us. In this project, a parallel-in-time method for solving convection-dominated problems is proposed. The method combines the parallel spectral deferred corrections (SDC) for temporal discretization, semi-Lagrangian scheme for convection terms, and finite elements for geometry and boundary conditions. Numerical experiments should be performed to illustrate the method`s properties, highlighting its potential for tackling challenges in convection-dominated flows.

Your Job:

• Implement the semi-Lagrangian method for pure convection problems using FEniCSx ( FEniCSx: https://fenicsproject.org/download/ )
  
  
• Extend the code to solve convection-diffusion-reaction- and incompressible Navier-Stokes equations
  
  
• Integrate SDC into the code to enhance temporal accuracy
  
  
• Rewrite the project as an extension of the open-source framework pySDC to enable parallel time-stepping ( pySDC: https://github.com/Parallel-in-time/pySDC )
  
  
• Conduct rigorous verification of the method and implementation through convergence tests

Your Profile:

• Ongoing master`s degree in applied mathematics or computational engineering or a similar field
  
  
• Interest in scientific research and methodology
  
  
• Solid experience with numerical methods for solving partial differential equations, preferably in the context of spatial and/or temporal discretizations of convection-dominated equations
  
  
• Knowledge and experience in developing scientific software, preferably in python

Our Offer:

We work on the very latest issues that impact our society and are offering you the chance to actively help in shaping the change! We support you in your work with:

• Introduction to scientific research
  
  
• Professional supervision and support throughout the entire duration of the project
  
  
• Outstanding computing facilities at JSC
  
  
• Interdisciplinary collaboration on projects in an international, dedicated and collegial team
  
  
• Contribution to an open-source software platform with an international user community
  
  
• Opportunity for employment as a student assistant
  
  
• Flexible working hours as well as a reasonable remuneration
  
  
• Flexible work (location) arrangements, e.g. remote work in accordance with the supervisor
  

In addition to exciting tasks and a collaborative working atmosphere at Jülich, we have a lot more to offer: https://go.fzj.de/benefits


We welcome applications from people with diverse backgrounds, e.g. in terms of age, gender, disability, sexual orientation / identity, and social, ethnic and religious origin. A diverse and inclusive working environment with equal opportunities in which everyone can realize their potential is important to us.

https://www.fz-juelich.de/de/karriere/stellenangebote/2024M-110