NUMERICAL MATHEMATICS · GEOMETRIC PDES · SCIENTIFIC COMPUTING
Simon Praetorius
Senior Research and Teaching Associate at TU Dresden
I develop and analyze finite-element methods for geometric partial differential equations. My work connects geometry-aware discretizations, constrained fields, structure-preserving evolution, and reusable scientific software in DUNE and AMDiS.
Email: contact@simon-praetorius.me
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
Finite elements for 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
Computational abstractions for advanced finite elements
Reusable abstractions in DUNE and AMDiS for advanced geometry and finite-element methods.