NUMERICAL MATHEMATICS · GEOMETRIC PDES · SCIENTIFIC COMPUTING
Simon Praetorius
Senior Research and Teaching Associate at TU Dresden
I work on numerical methods and scientific software for geometric partial differential equations. My research combines the analysis and design of finite-element schemes with systematic computational experiments, mathematical modeling, and efficient, reliable implementations. I am particularly interested in how the geometry of computational domains and unknown fields can be represented accurately, and how geometric and variational structures can be preserved when these domains evolve. I develop these methods and reusable software abstractions within DUNE and AMDiS.
RESEARCH AREAS
Four connected directions
01
Geometry-aware finite-element methods
Accurate representations of curved domains, metric quantities, normals, curvature, and the shape operator.
02
Geometrically constrained fields
Finite-element spaces for tangential vector and tensor fields with interacting geometric constraints.
03
Structure-preserving geometric evolution
Geometric flows that retain relevant energy laws, conservation properties, and shape measures.
04
Scientific computing and finite-element software
Reusable abstractions in DUNE and AMDiS for advanced geometry and finite-element methods.