Simon Praetorius

Simon Praetorius © 2017, Simon Praetorius

Wissenschaftlicher Mitarbeiter

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Herr Dr. Simon Praetorius

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Institut für Wissenschaftliches Rechnen

Institut für Wissenschaftliches Rechnen

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Z21, 235.1 Zellescher Weg 25

01069 Dresden

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I'm a postdoc in the Insitute of Scientific Computing at the Technische Universität Dresden. End of 2015 I have finished my PhD about “Efficient Solvers for the Phase-Field Crystal Equation” supervised by Prof. Axel Voigt (TU-Dresden) and additionally reviewed by Prof. Steven M. Wise (The University of Tennessee).

Currently, I'm working on topics about Discrete Exterior Calculus, the Phase-Field Crystal equation, active matter and the evolution of surface vector and tensor fields.

Conferences and Events

Nov 29 - Dec 01, 2023 Workshop "Vector- and Tensor-Valued Surface PDEs"
Oct 06, 2023 Dune/AMDiS Hackathon
Sep 18 - 20, 2023 Dune Meeting 2023
Sep 04 - 08, 2023 ENUMATH2023: MS21 "Surface geometry approximation and vector-valued PDEs"

Curriculum Vitae

2023 - 2026 Principal investigator in the DFG research unit "Vector- and Tensor-Valued Surface PDEs"
2022 - today

Deputy equal opportunities officer of the faculty of mathematics.
2015 - today Postdoctoral researcher in the Institute of Scientific Computing at Technische Universität Dresden.
2020 Teaching award of the faculty of mathematics in the category "Nachwuchsvorlesung".

Sep - Dec 2018

 Research visit in the lab of Prof. Steven M. Wise at the University of Tennessee (Knoxville, TN, USA)
2016 Award for an excellent doctoral thesis: Georg-Helm-Preis 2016
2011 - 2015 Doctoral program in mathematics at Technische Universität Dresden. Title: summa cum laude.
March 2013 Research visit in the Isaac Newton Institute for Mathematical Sciences (Cambridge, UK).
2005 - 2011 Diploma study in mathematics (scientific computing) at Technische Universität Dresden. Grade: 1.3
Networks and Links
Visualization of a vector-field resulting from a vector diffusion process on a bunny-like manifold. © 2017, Simon Praetorius

Visualization of a vector-field resulting from a vector diffusion process on a bunny-like manifold.

Discrete Exterior Calculus (DEC) is a grid-based geometric discretization technique for differential/integral forms and exterior derivatives. The basic idea is to associate geometric entities of a grid with integral values, corresponding to integrals of discrete differential forms over these entities. Derivatives are defined in a way that follows Stokes low of integration. Mehr erfahren

Colloidal particles immersed in a fluid interacting with the fluid and with each other. © 2017, Simon Praetorius

Interacting colloidal particles immersed in a fluid.

Particles immersed in a fluid change the flowing behavior, due to hydrodynamic interactions. The fluid-structure interaction can be modeled in the simplest case with non-deformable (spherical) objects that induce an effective stress into the fluid. In a setup that is driven by a gradient flow, a corresponding stress tensor or volume force can be derived by thermodynamic considerations. Mehr erfahren

High-performance implementation of a discrete exterior calculus framework. © 2017, Simon Praetorius

Implementation of a discrete exterior calculus framework.

For a toolbox that can handle the discrete exterior calculus (DEC) discretization, a grid must be equipped with some additional data: geometric values, like volume and orientation of alle entities of all dimensions in the grid, and incidence and adjacency information between different entities. This allows to traverse neighbours and connected entities. Mehr erfahren

Interacting deformable objects, simulated on a highly parallel multi-core system. © 2017, Simon Praetorius

Interacting deformable objects, simulated on a multi-core system.

We study the interaction of many deformable cells, described by an active polar gel model. Therefore, an evolution of the cell manifold is coupled to internal vector field describing the polarization of cytoskeleton actin fibres. Activity in the direction of the net polarization and a steric interaction drives the system. Mehr erfahren

Defects in a polar liquid crystal film on a sphere. Colors indicate a polar order. © 2017, Simon Praetorius

Defects in a polar liquid crystal film on a sphere.

Liquid crystals are composed of anisometric molecules, like rods or plate-lets, and have orientational and translation order. They can be characterized in some sense as a liquid and in another sense as a solid. Forcing the molecules to locate at a fluid-fluid interface and align tagentially to this surface gives rise to interesting arrangements of the crystals. Mehr erfahren

Fluid penetration in paper structures driven by capillary forces. © 2017, Simon Praetorius

Fluid penetration in paper structures

In printing processes an amount of liquid is applied to the surface of a paper sheet. The water based solution is intended to be absorbed by the microscopic structure of the paper. Fluid penetration is thereby driven mainly by capillary forces resulting from an interplay between surface tension and a boundary wetting angle. Mehr erfahren

Coexistence of two phases - crystalline and liquid - within the phase-field crystal model in a three dimensional setup. © 2017, Simon Praetorius

Coexistence of two crystalline phases

The Phase-Field Crystal (PFC) model describes the evolution of a particle density of spherical colloidal particles in an overdamped limit, based on an expansion of the interaction part of a Hemlholtz free-energy. The lowest order PFC equation is given by a 6th order nonlinear PDE. Mehr erfahren

Surface Vector and Tensor Fields © Simon Praetorius

Surface Vector and Tensor Fields

The project focusses on the development of numerical schemes for vector and tensor fields on surfaces and to compare these methods to each other. Targeting stationary or evolving surfaces raises the question of which method to prefer in which context. The methods are then applied to applications involving vector fields, like surface fluid flow or polarization fields for surface activity. Mehr erfahren

Parametrization of geometric grid elements © Simon Praetorius

Software Development of Finite-Element Code

The development of the finite-element framework AMDiS - Adaptive Multi-Dimensional Simulations - is the focus of this project. This numerical software is created in the Institute of Scientific Computing around 2005 and since then developed in multiple directions. Since 2017 the framework AMDiS is rebased on the numerics environment Dune - the Distributed Unified Numerics Environment. Mehr erfahren

Research

Publications
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Software Projects
  • AMDiS — A Dune module reimplementing the legacy AMDiS framework
  • (legacy) AMDiS — Adaptive MultiDimensional Simulation, a Finite-Element framework implemened in C++
  • dune-curvedgrid — A meta-grid for dune grids mapping a flat geometry of elements to a curved geometry using dune-curvedgeometry
  • dune-curvedgeometry — Implementation of curved geometries by local-function parametrizations
  • dune-dec — A Dune Discrete Exterior Calculus module for the solution of (surface) partial differential equations
  • dune-vtk — File reader and writer for the VTK XML Format
  • dune-gmsh4 — File reader for the Gmsh MSH file format version 4.
  • tiny-la — Linear Algebra library for tiny (dense) matrices and vectors, using C++14 features and concepts-lite
  • mpi14 — A wrapper like Boost.MPI that provides high-level interfaces using C++14 features for the underlying MPI C-library

Teaching

Sommersemester 2024
Wintersemester 2023/24
Sommersemester 2023
  • So2023 Scientific Programming With C++ (OPAL)
  • Supervision of master thesis topics:
    • Overlapping Domain Decomposition Methods for the Efficient Solution of Partial Differential Equations
    • Code Generation for Finite Element Simulation: Interfacing AMDiS from Python
Wintersemester 2022/23
Sommersemester 2022
  • So2022 Scientific Programming With C++
  • Supervision of master thesis topics:
    • Periodic Boundary Conditions on non-periodic Meshes for Systems of PDEs: Methods, Implementation, Examples and Analysis
Wintersemester 2021/22
  • Scientific Programming - Object-Oriented Programming using Java
  • Supervision of master thesis topics:
    • Collective behaviour of active brownian particles by active VPFC modeling
    • Data exchange between independently refined grids and its application in multi-phase-field models
    • H2 (non)conforming Finite Elements for the DUNE framework
    • Machine Learning prediction models for functionality and performance parameters of semiconductor chips based on manufacturing datasets
Older lectures 2011 - 2021
  • AMDiS - Workshop
  • Math Ma WIA / SCCOMP: Large sparse linear systems: concepts & implementation
  • Math Ma WIA: Programming Languages in Scientific Computing
  • Scientific Programming with C++
  • Scientific Programming - Object-Oriented Programming using Java
  • Tutorial of numerics of partial differential equations and finite element method
  • Seminar of modelling and simulation
  • Tutorial of basics in numerical mathematics 2
  • Tutorial of basics in numerical mathematics 1
  • Tutorial of mathematics III for electrical engineers
Research projects and thesis topics 2019 - 2021
  • Restoration of Binary Images Using the Cahn-Hilliard Equation
  • Defect-tracking in Active Smectics
  • Modellvergleiche des maschinellen Lernens zur automatischen Applikation von Sitzpersonalisierungsfunktionen
  • Modelling Seminar: Fluid particle dynamics

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Letzte Änderung: 01.07.2023