PhD Student (f/m/d): Computational Methods for Cell Shapes and Elastic Materials – Numerical PDE Solvers on Complex Shapes
As a member of the Helmholtz Association of German Research Centers, the HZDR employs about 1,400 people. The Center's focus is on interdisciplinary research in the areas energy, health and matter.
The Center for Advanced Systems Understanding (CASUS) is a German-Polish research center for dataintensive digital systems research. We combine innovative methods from mathematics, theoretical systems research, simulations, data science, artificial intelligence, and computer science to provide solutions for a range of disciplines - materials science under ambient and extreme conditions, earth system research, systems biology and medicine, and autonomous vehicles. CASUS was jointly founded in August 2019 by the Helmholtz-Zentrum Dresden-Rossendorf (HZDR), the Helmholtz Centre for Environmental Research (UFZ), the Max Planck Institute of Molecular Cell Biology and Genetics (MPI-CBG), the Technical University of Dresden (TUD) and the University of Wroclaw (UWr). CASUS is located in the heart of Görlitz at the border between Germany and Poland. The CASUS start-up phase is hosted by the Helmholtz-Zentrum Dresden-Rossendorf and is financed by the Federal Ministry of Education and Research (BMBF) and the Saxon State Ministry for Higher Education, Research and the Arts (SMWK).
The CASUS Department of Systems Biology is looking for a PhD Student (f/m/d) excited about novel mathematical approaches to fundamental algorithms in scientific computing. Consideration of candidates will begin immediately and will continue until the position is filled. The employment contract is limited to three years. Location of work is Görlitz, remuneration is according to the German Civil Service Tariff and HZDR employment conditions. No tuition charged.
The Scope of Your Job
The project is embedded in a larger collaboration with MPI-CBG and TUD's Department of Mathematics and aims to exploit recent advances in high-dimensional interpolation problems with vastly improved computational performance and accuracy. Interpolation is at the heart of many applications in scientific computing. In particular, it allows us to derive polynomial level set parametrizations of non-flat manifolds. This fact shall be incorporated into the development of novel numerical solvers of PDE's on curved surfaces and complex shapes. You will work with experts in the field of mathematics to further develop the algorithmic foundations, and with colleagues from the other CASUS Departments in order to apply the new algorithms. Applications include, but are not limited to, discretizing active polar gel models of biological tissue dynamics and simulating deformations of synthetic materials.
Develop efficient polynomial-level-set parametrizations of complex shapes based on earlier work
Incorporate the parametrizations into existing finite element methods and mesh-free DC-PSE discretization of partial differential equations
Apply the results to numerical simulations of non-linear PDE's on complex shapes occurring in 3D bio- and synthetic-material mechanics
Implement the resulting algorithms in the parallel computing DUNE and OpenFPM frameworks
Publish your results in academic, peer-reviewed journals
Present your results at scientific meetings
Master's degree in mathematics, theoretical/computational physics, scientific computing or computational sciences
A solid background in computing and natural science
Programming skills in languages such as Python or C++
Experience in Functional Analysis, Differential Geometry and Numerical Analysis
Strong motivation to work in a collaborative and interdisciplinary environment
Excellent communication skills in English and in a professional context (presentation of research results at scientific meetings, colloquial discussions, writing of manuscripts).
- A vibrant research community in an open, diverse, and international work environment
- Scientific excellence and extensive professional networking opportunities
- The employment contract is limited to three years with the possibility of longer-term prospects
- Salary and social benefits in conformity with the provisions of the Collective Agreement TVöD-Bund
- 30 Vacation Days per year
- Company pension scheme (VBL)
- A good work/life balance for which we offer assistance in the form of:
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