Simon Praetorius

© 2017, Simon Praetorius

Postdoctoral research fellow

Name

Dr. Simon Praetorius

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Contact Information

Address work

Visitor Address:

Willersbau, B219 Zellescher Weg 12-14

01069 Dresden

work Tel.

+49 351 463-34432

simon.praetorius@​tu-dresden.de

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 fields. See also Selected Projects.

Direct Links

• Selected Projects and M.Sc. topics
• Teaching in current and previous semesters

Curriculum vitae

© 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. Learn more

© 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. Learn more

© 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. Learn more

© 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. Learn more

© 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. Learn more

© 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. Learn more

© 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. Learn more

© 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. Learn more

© 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. Learn more

Publications

Software Projects

• AMDiS — Adaptive MultiDimensional Simulation, a Finite-Element framework implemened in C++
• dune-dec — A Dune Discrete Exterior Calculus module for the solution of (surface) partial differential equations
• dune-amdis — A Dune module reimplementing the AMDiS framework
• 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 2019

• Large sparse linear system

Sommersemester 2018

• PDEs & Manifolds: Implementation aspects

Wintersemester 2017/18

• Lecture / Tutorial to Scientific Programming - Advanced Concepts

Sommersemester 2017

• Large sparse linear systems: concepts & implementation

Older lectures 2011 - 2016

• AMDiS - Workshop
• Math Ma WIA: Scientific Programming - Large sparse linear systems: concepts & implementation
• Lecture / Tutorial on Scientific Programming - Advanced Concepts
• 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