Simon Praetorius

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Senior research and teaching associate

Name

Mr Dr. Simon Praetorius

Course coordination · Student supervision · Research

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Contact Information

Organization Name

Institute of Scientific Computing

Institute of Scientific Computing

Address work

Visiting address:

Z21, 235.1 Zellescher Weg 25

01217 Dresden

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work Tel.

I am a numerical mathematician working at the intersection of numerical analysis, geometric partial differential equations, and scientific computing. My research focuses on finite element methods for PDEs on surfaces and manifolds, in particular on the approximation of geometric quantities, geometrically constrained vector and tensor fields, and structure-preserving methods for geometric evolution equations. A second focus of my work is the development of reusable scientific software and finite element infrastructure, especially within the DUNE framework.

In teaching, I am particularly involved in programming and scientific computing at both Bachelor’s and Master’s level and supervise student projects and theses in numerical mathematics and scientific computing.

Personal academic website

Teaching

My teaching ranges from introductory programming in the Bachelor’s program to advanced scientific computing at Master’s level. A particular focus of my teaching is connecting mathematical and algorithmic concepts with their practical implementation in modern scientific software.

Current courses

• Programmieren – Grundlegende Konzepte — 1st semester Bachelor
  WS25/26, WS26/27
• Programmieren – Weiterführende Konzepte — 2nd semester Bachelor
  SS26
• Scientific Programming – Advanced Concepts — Master, C++
  WS26/27

More about teaching and previous courses

Student projects & theses

I regularly supervise Bachelor’s and Master’s theses as well as student research projects in numerical mathematics and scientific computing. Topics are often connected to current research and may range from mathematical and numerical analysis to computational experiments and the development of scientific software.

Currently available topics

• Curvature of discrete and higher-order curves (Bachelor’s thesis)
  Compare different curvature approximations on discrete and higher-order curves and investigate their accuracy and convergence.
• Stabilized finite-element approximation of curvature (Master’s thesis)
  Implement and investigate stabilized finite-element methods for the approximation of mean curvature and the shape operator.
• Lagrange multiplier methods for tangential vector fields (Master’s thesis)
  Study finite-element approximations of tangential vector fields on surfaces and investigate the interaction between discretization errors and multiplier parameters.
• Characterizing planar shapes with Minkowski tensors (Bachelor’s thesis)
  Investigate tensor-valued geometric measures for the characterization of planar shapes, including their invariance, eigenstructure, and numerical approximation.

If you are interested in one of these topics, or in a project related to finite element methods, geometric PDEs, numerical algorithms, or scientific computing, feel free to contact me. Topics can often be adapted to the background and interests of the student.

More information about student projects and supervision

Geometry-aware finite element methods

Surface finite-element methods approximate both a PDE and the curved surface on which it is posed. We investigate how errors in the discrete geometry enter the numerical method — and how the variational structure can lead to cancellations and unexpectedly high convergence rates. Learn more

Geometrically constrained surface fields

Vector and tensor fields on surfaces are subject to geometric constraints such as tangentiality, symmetry, fixed length, or head-tail symmetry. We develop and analyze finite-element methods that represent such constraints either exactly or through suitable numerical approximations. Learn more

Geometric evolution equations

In geometric evolution equations, curvature and other geometric quantities determine how the computational domain itself moves. We develop finite-element methods that accurately represent these quantities while preserving important structures such as energy dissipation or volume conservation. Learn more

Surface Minkowski tensors

Minkowski tensors characterize geometric properties and symmetries of shapes. We extend these tensor-valued shape descriptors to curved surfaces by incorporating the transport of geometric information across the surface. Learn more

Research

My research lies at the intersection of numerical analysis, geometric partial differential equations, and scientific computing. A central theme is the development and analysis of finite element methods that respect the geometric structure of the domain, the unknown fields, and the underlying evolution equations.

Current research focuses on geometry-aware finite element methods, geometrically constrained vector and tensor fields, and structure-preserving methods for geometric evolution equations. Closely connected to this work is the development of computational abstractions and scientific software for advanced finite element methods.

More information on my Research profile and current research areas.

Recent publications

Selected recent publications are listed below. A Complete publication list and preprints can be found on my personal academic webpage and on google scholar.

Publications

11 Entries

2024

• Active smectics on a sphereNestler, M., Praetorius, S., Huang, Z., Löwen, H. & Voigt, A., 8 May 2024, In: Journal of Physics: Condensed Matter. 36, 18, 13 p., 185001Electronic (full-text) versionResearch output: Contribution to journal > Research article
• Diffusion of tangential tensor fields: numerical issues and influence of geometric propertiesBachini, E., Brandner, P., Jankuhn, T., Nestler, M., Praetorius, S., Reusken, A. & Voigt, A., 1 Mar 2024, In: Journal of Numerical Mathematics. 32, 1, p. 55-75, 21 p.Electronic (full-text) versionResearch output: Contribution to journal > Research article

2023

• Influence of finite-size particles on fluid velocity and transport through porous mediaResidori, M., Praetorius, S., de Anna, P. & Voigt, A., 5 Jul 2023, In: Physical Review Fluids. 8, 7, 074501Electronic (full-text) versionResearch output: Contribution to journal > Research article
• Tangential Errors of Tensor Surface Finite ElementsHardering, H. & Praetorius, S., May 2023, In: IMA Journal of Numerical Analysis. 43, 3, p. 1543-1585, 43 p.Electronic (full-text) versionResearch output: Contribution to journal > Research article

2022

• Finite element discretization methods for velocity-pressure and stream function formulations of surface Stokes equationsBrandner, P., Jankuhn, T., Praetorius, S., Reusken, A. & Voigt, A., 5 Jul 2022, In: SIAM Journal on Scientific Computing. 44, 4, p. A1807-A1832, 4Electronic (full-text) versionResearch output: Contribution to journal > Research article

This information is provided by the FIS.

Scientific software

The development of reusable scientific software is an integral part of my research. I am a core developer of the DUNE and AMDiS finite element frameworks and contribute to their numerical and software infrastructure.

More about Scientific software and open-source projects.