Numerische Mathematik in den Anwendungen
- Kontakt:
- Prof. Dr. Thomas Richter
- Universität Magdeburg
Institut für Analysis und Numerik
Universitätsplatz 2
39106 Magdeburg
thomas.richter@ovgu.de
Telefon 0391-67-57162
Fax 0391-67-48073
- Sprechstunde:
- in der vorlesungsfreien Zeit nach Vereinbarung
- Gebäude 2, Raum 16b
Aktuelles
- Mathematik
IngenieurIn - Mathematik mit Technikauswahl (Artikel in der Volksstimme, externer link)
- Konferenz
- PeC3 Peruvian Conference on Scientific Computing
Lehrveranstaltungen
Sommer 2021
- Vorlesung
- Algorithmische Mathematik II
- Vorlesung
- Numerische Methoden für partielle Differentialgleichungen
- Proseminar
- Numerik im Lehramt
- Seminar
- Analysis and Numerics for Partial Differential Equations
- Oberseminar
- Numerische Analysis
- Vorlesung
- Algorithmische Mathematik I
- Vorlesung
- Numerische Methoden für gewöhnliche Differentialgleichungen
- Seminar
- Numerische Aspekte des maschinellen Lernens (geeignet für Bachelor)
- Seminar
- Mathematics and Numerics of Deep Neural Networks for Physical Simulations (Master)
- Oberseminar
- Numerische Analysis
- Vorlesung
- Algorithmische Mathematik II
- Vorlesung
- Einführung in die Numerische Mathematik
- Vorlesung
- Numerische Methoden der Strömungsmechanik
- Oberseminar
- Numerische Analysis
- Seminar
- Mathematische Methoden der Klimamodellierung
- Gastdozentin
- Dr. Carolin Mehlmann, MPI für Meteorologie Hamburg
- Simulation und Optimierung von Strömungsvorgängen unter Extrembedingungen. Gemeinschaftsprojekt mit Prof. Dr. Turek (TU Dortmund) und Prof. Dr. Vexler (TU München) finanziert durch das BMBF
- Optimalsteuerung und Parameterschätzung bei Fluid-Struktur Wechselwirkungsproblemen. Projekt im Juniorprofessorenprogramm des Landes Baden-Württemberg
- Fluid-Struktur Interaktionen in Eulerschen Koordinaten
- Modellierung und Simulation von Plaque-Wachstum in Blutgefäßen. Twinning-Projekt der Exzellenz-Initiative Heidelberg
- Mechano-Chemische Effekte in der biologischen Musterbildung
-
Einfuehrung in die Numerische Mathematik - Begriffe, Konzepte und zahlreiche Anwendungsbeispiele,
ISBN 978-9-662-54177-7, Springer, 2017. -
Fluid-structure Interactions. Models, Analysis and Finite Elements,
Vol. 118 of Lecture Notes in Computational Science and Engineering, ISBN 978-3-319-63969-7, Springer, 2017. -
Fluid-Structure Interactions,
Radon Series on Computational and Applied Mathematics, ISBN 978-3-11-049425-9, De Gruyter, 2017. -
Using a deep neural network to predict the motion of under-resolved triangular rigid bodies in an incompressible flow,
submitted, 2021.
[ preprint ] -
Structure Preservation for the Deep Neural Network Multigrid Solver,
submitted, 2020.
[ pdf ] -
A neural network multigrid solver for the Navier-Stokes equations,
submitted, 2020.
[ preprint ] -
A locally modified second-order finite element method for interface problems,
submitted, 2020.
[ preprint ] -
Error estimation and adaptivity for differential equations with multiple scales in time,
submitted, 2020.
[ preprint ] -
An unfitted Eulerian finite element method for the time-dependent Stokes problem on moving domains,
submitted, 2020.
[ preprint ] -
LocModFE: Locally modified finite elements for approximating interface problems in deal.II,
submitted, 2019. -
Adaptive time-step control for a monolithic multirate scheme coupling the heat and wave equation,
BIT Numerical Mathematics, 2021.
[ preprint ] -
Parallel time-stepping for fluid-structure interactions,
Mathematical Modelling of Natural Phenomena, 2021.
[ preprint ] -
An averaging scheme for the efficient approximation of time-periodic flow problems,
Computers and Fluids, Vol. 214, 2021.
[ preprint ] -
Falling balls in a viscous fluid with contact: Comparing numerical simulations with experimental data,
Physics of Fluids, 2021.
[ preprint ] -
A finite element / neural network framework for modeling suspensions of non-spherical particles. Concepts and medical applications,
Vietnam Journal of Mathematics, 2021.
[ preprint ] -
Settling of spherical particles in the transitional regime,
International Journal of Multiphase Flow, Vol. 138, p.103589, 2021.
[ preprint ] -
Axisymmetric Stokes flow due to a point-force singularity acting between two coaxially positioned rigid no-slip disks,
Journal of Fluid Mechanics, Vol. 904, p.A34, 2020.
[ preprint ] -
On the Impact of Fluid Structure Interaction in Blood Flow Simulations,
Vietnam Journal of Mathematics, https://rdcu.be/ceo0t, 2021.
[ preprint ] -
A goal oriented error estimator and mesh adaptivity for sea ice simulations,
Ocean Modeling, Vol. 154, No. 101684, 2020.
[ preprint ] -
Low-rank Linear Fluid-structure Interaction Discretizations,
ZAMM, Vol. 100, No. 11, 2020.
[ preprint ] -
A Newton multigrid framework for optimal control of fluid-structure interactions,
Optimization and Engineering, 2020.
[ preprint ] -
A parallel Newton multigrid framework for monolithic fluid-structure interactions,
Journal of Scientific Computing, Vol. 82, No. 2, 2020.
[ preprint ] -
Efficient approximation of flow problems with multiple scales in time,
SIAM Multiscale Modeling and Simulation, Vol. 18, No. 2, p.942–969, 2020.
[ preprint ] -
Finite Element Error Estimates on Geometrically Perturbed Domains,
Journal of Scientific Computing, Vol. 84, No. 30, 2020.
[ preprint ] -
Second order pressure estimates for the Crank-Nicolson discretization of the incompressible Navier-Stokes Equations,
SIAM J. Numer. Anal., Vol. 58, p.375–409, 2020.
[ preprint ] -
Numerical benchmarking of fluid-rigid body interactions,
Computers and Fluids, Vol. 193, 2019.
[ preprint ] -
Quasi-random discrete ordinates method for neutron transport problems,
Annals of Nuclear Energy, Vol. 113, p.275–282, 2019. -
Efficient computation of time-periodic solutions of partial differential equations,
Viet. J. Math., Vol. 46, No. 4, doi=10.1007/s10013-018-0314-y, p.949–966, 2018. -
Post-Turing tissue pattern formation: Advent of Mechanochemistry,
PLOS Computational Biology, 2018.
[ preprint ] -
A Finite Element Multigrid-Framework for Discretizing Sea Ice Dynamics,
Journal of Computational Physics, Vol. 348, p.847–861, 2017.
[ preprint ] -
A modified global Newton solver for viscous-plastic sea ice models,
Ocean Modeling, Vol. 116, p.96–107, 2017.
[ preprint ] -
An ALE approach to mechano-chemical processes in fluid-structure interactions,
I. J. Num. Meth. Fluids, Vol. 84, No. 4, p.199–220, 2017.
[ preprint ] -
Beyond Turing: Mechanochemical pattern formation in biological tissues,
Biology Direct, Vol. 11, No. 22, 2016.
[ preprint ] -
A Monolithic Geometric Multigrid Solver for Fluid-Structure Interactions in ALE formulation,
Int. J. Num. Meth. in Engrg., Vol. 104, No. 5, p.372–390, 2015.
[ preprint ] -
Mathematical modeling and simulation of the evolution of plaques in blood vessels,
J. of Math. Biology., Vol. 72, p.973–996, 2016.
[ preprint ] -
Second order time-stepping for parabolic interface problems with moving interfaces,
ESAIM Math. Mod. Num. Anal., Vol. 51, p.1539–1560, 2017.
[ preprint ] -
Long-term simulation of large deformation, mechano-chemical fluid-structure interactions in \ALE\ and fully Eulerian coordinates ,
Journal of Computational Physics , Vol. 321, p.874 – 891, 2016.
[ preprint ] -
A Posteriori Error Estimation for the Fractional Step Theta discretization of the incompressible Navier-Stokes equations,
Comp. Meth. Appl. Mech. Engrg., Vol. 288, p.45–59, 2015.
[ preprint ] -
Variational Localizations of the Dual Weighted Residual Method,
Journal of Computational and Applied Mathematics, Vol. 279, p.192–208, 2015.
[ preprint ] -
A locally modified parametric finite element method for interface problems,
SIAM J. Numer. Anal., Vol. 52, No. 5, p.2315–2334, 2014, doi=10.1137/130919489.
[ preprint ] -
Goal-Oriented Error Estimation for the Fractional Step Theta Scheme,
Comp. Meth. Appl. Math., Vol. 14, p.203–230, 2014.
[ preprint ] -
Towards a Complete Numerical Description of Lubricant Film Dynamics in Ball Bearings,
Computational Mechanics, Vol. 53, p.239–255, doi=10.1007/s00466–013–0904–1, 2014. -
Optimal Control and Parameter Estimation for Stationary Fluid-Structure Interaction Problems,
SSC, Vol. 35, No. 5, p.B1085–B1104, doi=10.1137/120893239, 2013. -
Modeling and computing of deformation dynamics of inhomogeneous biological surfaces,
SIAM J. Appl. Math., Vol. 73, No. 5, p.1768–1792, doi=10.1137/120885553, 2013. -
Efficient numerical realization of discontinuous Galerkin methods for temporal discretization of parabolic problems,
Numerische Mathematik, Vol. 124, No. 1, p.151–182, 2013.
[ preprint ] -
A Fully Eulerian Formulation for Fluid-Structure-Interaction Problems,
JCP, Vol. 233, p.227–240, 2013.
[ preprint ] -
Goal oriented error estimation for fluid-structure interaction problems,
CMAME, Vol. 223-224, p.28–42, 2012.
[ preprint ] -
Implementation of REDIM reduced chemistry to Model an Axisymmetric Laminar Diffusion Methane/Air Flame,
Combustion Theory and Modelling, Vol. 15, No. 3, p.299–323, 2011.
[ preprint ] -
Sorting Mechanisms and Communication in Phase Separating Coupled Monolayers,
Journal of Physical Chemistry B, Vol. 115, No. 40, p.11739–11745, doi=10.1021/jp204127g, 2011. -
Optimal microstructures. Drag reducing mechanism of riblets,
J. of Math. Fluid Mech, Vol. 14, No. 3, p.429–447, 2011.
[ preprint ] -
Parallel multigrid method for finite element simulations of complex flow problems on locally refined meshes,
Numerical Linear Algebra with Applications, Vol. 18, p.615–636, doi=10.1002/nla.744, 2011. -
Finite Elements for Fluid-Structure Interaction in ALE and Fully Eulerian Coordinates,
Computer Methods in Applied Mechanics and Engineering, Vol. 199, p.2633–2642, doi=10.17485/ijst/2015/v8i1/84240, 2010. -
A posteriori error estimation and anisotropy detection with the dual weighted residual method,
Int. J. Numer. Meth. Fluids, Vol. 62, No. 1, p.90–118, 2010.
[ preprint ] -
An Adaptive Homotopy Multi-grid Method for Molecule Orientations of High Dimensional Liquid Crystals,
Journal for Computational Physics, Vol. 255, p.2069–2082, doi=10.1016/j.jcp.2007.03.009, 2007. -
Solutions of 3D Navier-Stokes benchmark problems with adaptive finite elements,
Computers and Fluids, Vol. 35, No. 4, p.372–392, 2006.
[ preprint ] -
Stabilized finite elements for 3-D reactive flows,
Int. J. Numer. Meth. Fluids, Vol. 51, p.981–999, 2006.
[ preprint ] -
An accurate Eulerian approach for fluid-structure interactions,
in: Fluid-Structure Interactions. Modeling, Adaptive Discretization and Solvers, Radon Series on Computational and Applied Mathematics, De Gruyter, to appear 2017.
[ preprint ] -
On time discretizations of fluid-structure interactions,
Multiple Shooting and Time Domain Decomposition Methods. Springer, 2015, pages=377-400.
[ preprint ] -
An Adaptive Finite Element Method for Fluid-Structure Interaction Problems Based on a Fully Eulerian Formulation,
Fluid-Structure Interaction II, Modelling, Simulation, Optimization. , No. 73, p.159–192Springer, 2010. -
A Study of Shark Skin and its drag reducing mechanism,
Advances in Mathematical Fluid Mechanics: Dedicated to Giovanni Paolo Galdi on the Occasion of his 60th Birthday. , p.271–286Springer, 2010.
[ preprint ] -
Numerical Simulation of Fluid-Structure Interaction Based on Monolithic Variational Formulations,
Comtemporary Challenges in Mathematical Fluid Mechanics. World Scientific, 2010. -
Mesh and model adaptivity for flow problems,
Reactive Flows, Diffusion and Transport. Springer Berlin Heidelberg, 2006, pages=47-75. -
Solving Multidimensional Reactive Flow Problems with Adaptive Finite Elements,
Reactive Flows, Diffusion and Transport. , p.93–112, doi=10.1007/978–3–540–28396–6_5Springer Berlin Heidelberg, 2007. -
Parallel multigrid on locally refined meshes,
Reactive Flows, Diffusion and Transport. Springer Berlin Heidelberg, 2006, pages=77-92. -
The candy wrapper problem - a temporal multiscale approach for pde/pde systems,
Numerical Mathematics and Advanced Applications - Enumath 2019. Springer, 2019.
[ preprint ] -
A Low-rank Approach for Nonlinear Parameter-dependent Fluid-structure Interaction Problems,
Numerical Mathematics and Advanced Applications - Enumath 2019. Springer, 2020.
[ preprint ] -
Linear Low-Rank Parameter-Dependent Fluid-Structure Interaction Discretization in 2D,
PAMM - Proc. Appl. Math. Mech. - Annual 89h Meeting of the International Association of Applied Mathematics and Mechanics. , 2018. -
An accelerated Newton method for nonlinear materials in structure mechanics and fluid mechanics,
Numerical Mathematics and Advanced Applications - Enumath 2017. , Vol. 126, p.345–353Springer, 2018.
[ preprint ] -
Parallel iterative finite element procedure with dwr mesh adaptation to simulation transport problems in x-y geometry,
25th International Conference on Transport Theory. , submitted 2017. -
Discretization of Parabolic Problems on Moving Domains with Moving Interfaces,
Oberwolfach Reports. , Vol. 55Mathematisches Forschungsinstitut Oberwolfach, doi= 10.4171/OWR/2015/55, 2015. -
Eulerian Techniques for Fluid-Structure Interactions - Part I: Modeling and Simulation,
Numerical Mathematics and Advanced Applications - Enumath 2013. , Vol. 103, p.745–753Springer, 2015.
[ preprint ] -
Eulerian Techniques for Fluid-Structure Interactions - Part II: Applications,
Numerical Mathematics and Advanced Applications - Enumath 2013. , Vol. 103, p.755–762Springer, doi=10.1007/978-3-319-10705-9_75, 2015.
[ preprint ] -
Fluid-Structure Interactions in Fully Eulerian Coordinates,
PAMM - Proc. Appl. Math. Mech.. , Vol. 10, p.827–830, 2012. -
Anisotropic Finite Elements for Fluid-Structure Interactions,
Numerical Mathematics and Advanced Applications 2011, Proceedings of ENUMATH 2011. , p.63–70Springer, 2013.
[ preprint ] -
A fully Eulerian formulation for fluid-structure-interaction problems with large deformations and free structure movement,
V. European Conference on Computational Fluid Dynamics. , 14-17 June, 2010. -
On Drag computations of rough surfaces: modeling, simulations and model reduction by applying homogenization,
V. European Conference on Computational Fluid Dynamics. , 14-17 June, 2010. -
Discontinuous Galerkin as Time-Stepping Scheme for the Navier-Stokes Equations,
Modeling, Simulation and Optimization of Complex Processes. , p.271–282Springer, 2012. -
Stabilized adaptive finite elements for laminar burner in 3-d,
Eccomas CFD Proceedings. , 2006. -
Local projection stabilization for the Stokes system on anisotropic quadrilateral meshes,
Enumath Proceedings 2005. , p.770–778Springer, 2005. -
Fluid-Structure Interactions in ALE and Fully Eulerian Coordinates,
PAMM. , Vol. 10, No. 1, p.487–488, 2010. -
Fluid-Structure Interactions in Fully Eulerian Coordinates,
PAMM. , Vol. 12, p.487–488, 2012. -
Falling balls in a viscous fluid with contact: Comparing numerical simulations with experimental data,
Zenodo, 2020.
[ preprint ] -
An implementation of a locally modified finite element method for interface problems in deal.II,
Zenodo, 2018.
[ preprint ] -
A Low-rank Method for Parameter-dependent Fluid-structure Interaction Discretizations With Hyperelasticity,
arXiv, 2020.
[ preprint ] -
On the implementation of a locally modified finite element method for interface problems in deal.II,
arXiv, 2018.
[ preprint ] -
A Fully Eulerian Formulation for Fluid-Structure Interaction Problems,
urn:nbn:de:bsz:16-opus-132158, 2012. -
Goal-oriented error estimation for fluid-structure interaction problems,
urn:nbn:de:bsz:16-opus-132144, 2012. -
A monolithic multigrid solver for 3d fluid-structure interaction problems,
urn:nbn:de:bsz:16-opus-121834, 2011. -
Solutions of 3D Navier-Stokes benchmark problems with adaptive finite elements,
SFB 2004-44, 2004. -
Einführung in die Numerische Mathematik,
Universität Heidelberg, 2012, 2014.
[ link ] -
Numerische Methoden für gewoehnliche und partielle Differentialgleichungen,
Universität Heidelberg, 2010. -
Numerische Methoden für partielle Differentialgleichungen,
Universität Heidelberg, 2011.
[ link ] -
Numerische Methoden in der Stroemungsmechanik,
Universität Heidelberg, 2014.
[ link ] -
Numerical methods for fluid-structure interactions,
Universität Heidelberg, 2010, 2012. -
Introduction to the finite element library Gascoigne 3d,
University of Heidelberg, 2012.
[ link ] -
Parallel Multigrid Method for Adaptive Finite Elements with Application to 3D Flow Problems,
PhD thesis, University of Heidelberg, URN: urn:nbn:de:bsz:16-opus-57433, 2005.
[ preprint ] -
Funktionalorientierte Gitteroptimierung für die Finite Elemente Methode,
Diploma thesis, University of Heidelberg, 2001.
[ preprint ]
Winter 2020/21
Sommer 2020
Gruppe

Members
Students
Jonas Herbert
Jochewed Schmeck
Nils Margenberg
Manuel Liebchen
Former Members
Dr. Felix Brinkmann
SAP AG
Dr. Stefan Frei
Universität Konstanz
Dr. Carolin Mehlmann
Max-Planck Institut für Meteorologie Hamburg
Ina Schüssler
FAU Erlangen-Nürnberg
Florian Sonner
FAU Erlangen-Nürnberg
Dr. Yifan Yang
SAP AG
Research
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Conferences and Workshops
Software
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