Numerical Analysis of
Partial Differential Equations
Coupled Multiphysics Problems

Professor Thomas Richter
Fully coupled simulation of an incompressible flow around an elastic obstacle. Computations with adaptive finite elements.

Numerical Methods for Partial Differential Equations

Kontakt:
Prof. Dr. Thomas Richter
Universität Erlangen-Nürnberg
Department Mathematik, AM3
Cauerstraße 11
91058 Erlangen
richter@math.fau.de

News

Group

Head

Secretary

Members

Students

Patrik Böttcher
Goal-oriented adaptivity for turbulent flows
Martin Molnar
Stabilization Techniques for Flow Problems on Moving Domains
Hans Schmidt
A Splitting Solver for Compressible Flows
Judith Stein
Numerical Simulation of Thermal Viscoelastic Flows
Tobias Sturm
Intitial Guesses for BDF Discretization of Nonlinear Problems

Former Members and Students

Former Members and Students

Carolin Mehlmann
Numerical Simulation of Sea-Ice Models
Tobias Siekmann
Vanka-Smoothers for Complex Flow Problems
Florian Sonner
Multigrid Solvers for Fluid-Structure Interactions
Sohely Sharmin
Finite Elements on Curved Boundaries
Anna Seitz
2014
Diplom-Arbeit
Varianten des Teilschritt-Theta Verfahrens
Sandra Schurdack
2013
Bachelor-Arbeit
Varianten des Schießverfahrens
Georg Luft
2013
Bachelor-Arbeit
Gemischte Ansätze für die Plattengleichung
Philipp Siehr
2013
Bachelor-Arbeit
Residuenbasierte Stabilisierung der Stokes-Gleichungen
Matthias von Laer
2013
Diplom-Arbeit
Numerische Analyse von Fluiden mit druckabhängiger Viskosität
Ina Schüssler
2013
Diplom-Arbeit
Adaptive Steuerung von Stabilisierungsparametern bei der Finite-Elemente Methode
Carolin Mehlmann
2012
Bachelor-Arbeit
Glättungseigenschaften bei der Black-Scholes Gleichung
Sebastian Bäum
2012
Bachelor-Arbeit
Asymptotische Fehlerentwicklung bei der FEM
Florian Sonner
2012
Bachelor-Arbeit
Varianten der LPS-Methode
Patrick Böttcher
2012
Bachelor-Arbeit
Vergleich von linearen Mehrschittmethoden und Extrapolationsverfahreb
Judith Stein
2012
Bachelor-Arbeit
Adaptive dG(1) und dG(2)-Verfahren für das Lorentz-System
Felix Brinkmann
2012
Diplom-Arbeit
Inverse Probleme in der medizinischen Operationsplanung
Sven Heberle
2012
Diplom-Arbeit
Effiziente Löser für die instationären Navier-Stokes Gleichungen
Julia Innig
2011
Diplom-Arbeit
A priori Abschätzungen für die Stokes-Gleichungen mit Slip-Randbedingung auf krumm berandeten Gebieten
Niels Mernke
2011
Diplom-Arbeit
Mehrgitterglätter auf anisotropen Gittern
Julia Geider
2011
Diplom-Arbeit
Vergleich von Ansys CFX und Gascoigne 3d: Instationäre Strömungsvorgänge
Tobias Neff
2011
Diplom-Arbeit
Vergleich von Ansys CFX und Gascoigne 3d: Wärmeübergänge
Simon Dörsam
2011
Bachelor-Arbeit
Adaptive dG-Zeitdiskretizierung
Felix Fehrenbach
2011
Diplom-Arbeit
Fluid-Struktur Interaktionen in Eulerschen Koordinaten
Hans Schmidt
2011
Bachelor-Arbeit
Approximation der Plattengleichung

Research

  • 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

Publications

Journals

  1. M. Mercker, F. Brinkmann, A. Marciniak-Czochra and T. Richter,
    Beyond Turing: Mechanochemical pattern formation in biological tissues,
    Biology Direct, accepted, 2016.
  2. Y. Yang, T. Richter, W. Jaeger, M. Neuss-Radu,
    An ALE approach to mechano-chemical processes in fluid-structure interactions,
    I. J. Num. Meth. Fluids, submitted, 2015.
  3. T. Richter,
    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 ]
  4. Y. Yang, W. Jaeger, M. Neuss-Radu, T. Richter,
    Mathematical modeling and simulation of the evolution of plaques in blood vessels,
    J. of Math. Biology., Vol. 72, p.973–996, 2016.
  5. S. Frei, T. Richter,
    Second order time-stepping for parabolic interface problems with moving interfaces,
    ESAIM Math. Mod. Num. Anal., submitted, 2016.
  6. S. Frei, T. Richter, T. Wick,
    Long-term simulation of large deformation, mechano-chemical fluid-structure interactions in ALE and fully Eulerian coordinates,
    J. Comp. Physics, submitted, 2015.
  7. D. Meidner and T. Richter,
    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 ]
  8. T. Richter and T. Wick,
    Variational Localizations of the Dual Weighted Residual Method,
    Journal of Computational and Applied Mathematics, Vol. 279, p.192–208, 2015.
    preprint ]
  9. S. Frei and T. Richter,
    A locally modified parametric finite element method for interface problems,
    SIAM J. Numer. Anal., Vol. 52, No. 5, p.2315–2334, 2014.
    preprint ]
  10. D. Meidner and T. Richter,
    Goal-Oriented Error Estimation for the Fractional Step Theta Scheme,
    Comp. Meth. Appl. Math., Vol. 14, p.203–230, 2014.
  11. S. Knauf, S. Frei, T. Richter and R. Rannacher,
    Towards a Complete Numerical Description of Lubricant Film Dynamics in Ball Bearings,
    Computational Mechanics, Vol. 53, p.239–255, 2014.
  12. T. Richter and T. Wick,
    Optimal Control and Parameter Estimation for Stationary Fluid-Structure Interaction Problems,
    SSC, Vol. 35, No. 5, p.B1085–B1104, 2013.
  13. M. Mercker, A. Marciniak-Czochra, T. Richter and D Hartmann,
    Modeling and computing of deformation dynamics of inhomogeneous biological surfaces,
    SIAM J. Appl. Math., Vol. 73, No. 5, p.1768–1792, 2013.
  14. T. Richter, A. Springer and B. Vexler,
    Efficient numerical realization of discontinuous Galerkin methods for temporal discretization of parabolic problems,
    Numerische Mathematik, Vol. 124, No. 1, p.151–182, 2013.
  15. T. Richter,
    A Fully Eulerian Formulation for Fluid-Structure-Interaction Problems,
    JCP, Vol. 233, p.227–240, 2013.
    preprint ]
  16. T. Richter,
    Goal oriented error estimation for fluid-structure interaction problems,
    CMAME, Vol. 223-224, p.28–42, 2012.
    preprint ]
  17. P. Konzen, T. Richter, U. Riedel and U. Maas,
    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.
  18. M. Mercker, T. Richter and D. Hartmann,
    Sorting Mechanisms and Communication in Phase Separating Coupled Monolayers,
    Journal of Physical Chemistry B, Vol. 115, No. 40, p.11739–11745, 2011.
  19. E. Friedmann and T. Richter,
    Optimal microstructures. Drag reducing mechanism of riblets,
    J. of Math. Fluid Mech, Vol. 14, No. 3, p.429–447, 2011.
  20. M. Kimmritz and T. Richter,
    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, 2011.
  21. T. Richter and T. Wick,
    Finite Elements for Fluid-Structure Interaction in ALE and Fully Eulerian Coordinates,
    Computer Methods in Applied Mechanics and Engineering, Vol. 199, p.2633–2642, 2010.
  22. T. Richter,
    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 ]
  23. P. Lin and T. Richter,
    An Adaptive Homotopy Multi-grid Method for Molecule Orientations of High Dimensional Liquid Crystals,
    Journal for Computational Physics, Vol. 255, p.2069–2082, 2007.
  24. M. Braack and T. Richter,
    Solutions of 3D Navier-Stokes benchmark problems with adaptive finite elements,
    Computers and Fluids, Vol. 35, No. 4, p.372–392, 2006.
    preprint ]
  25. M. Braack and T. Richter,
    Stabilized finite elements for 3-D reactive flows,
    Int. J. Numer. Meth. Fluids, Vol. 51, p.981–999, 2006.

Book Chapters

  1. T. Richter and T. Wick,
    On time discretizations of fluid-structure interactions,
    Multiple Shooting and Time Domain Decomposition Methods, 2015.
    preprint ]
  2. R. Rannacher and T. Richter,
    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.159–192, 2010.
  3. E. Friedmann, J. Portl and T. Richter,
    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.271–286, 2010.
  4. T. Dunne, R. Rannacher and T. Richter,
    Numerical Simulation of Fluid-Structure Interaction Based on Monolithic Variational Formulations,
    Comtemporary Challenges in Mathematical Fluid Mechanics, 2010.
  5. M. Braack and T. Richter,
    Mesh and model adaptivity for flow problems,
    Reactive Flows, Diffusion and Transport, 2006.
  6. M. Braack and T. Richter,
    Solving Multidimensional Reactive Flow Problems with Adaptive Finite Elements,
    Reactive Flows, Diffusion and Transport, p.93–112, 2007.
  7. R. Becker, M. Braack and T. Richter,
    Parallel multigrid on locally refined meshes,
    Reactive Flows, Diffusion and Transport, 2006.

Conferences and Workshops

  1. S. Frei and T. Richter,
    Discretization of Parabolic Problems on Moving Domains with Moving Interfaces,
    Oberwolfach Reports, Vol. 55, DOI: 10.4171/OWR/2015/55, 2015.
  2. S. Frei, T. Richter and T. Wick,
    Eulerian Techniques for Fluid-Structure Interactions - Part I: Modeling and Simulation,
    Numerical Mathematics and Advanced Applications - Enumath 2013, Vol. 103, p.745–753, 2015.
    preprint ]
  3. S. Frei, T. Richter and T. Wick,
    Eulerian Techniques for Fluid-Structure Interactions - Part II: Applications,
    Numerical Mathematics and Advanced Applications - Enumath 2013, Vol. 103, p.755–762, 2015.
    preprint ]
  4. T. Richter,
    Fluid-Structure Interactions in Fully Eulerian Coordinates,
    PAMM, p.827–830, 2012.
  5. T. Richter,
    Anisotropic Finite Elements for Fluid-Structure Interactions,
    Numerical Mathematics and Advanced Applications 2011, Proceedings of ENUMATH 2011, p.63–70, 2013.
    preprint ]
  6. T. Richter,
    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.
  7. E. Friedmann and T. Richter,
    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.
  8. T. Richter,
    Discontinuous Galerkin as Time-Stepping Scheme for the Navier-Stokes Equations,
    Modeling, Simulation and Optimization of Complex Processes, p.271–282, 2012.
  9. M. Braack and T. Richter,
    Stabilized adaptive finite elements for laminar burner in 3-d,
    Eccomas CFD Proceedings, 2006.
  10. M. Braack and T. Richter,
    Local projection stabilization for the Stokes system on anisotropic quadrilateral meshes,
    Enumath Proceedings 2005, p.770–778, 2005.
  11. T. Richter and T. Wick,
    Fluid-Structure Interactions in ALE and Fully Eulerian Coordinates,
    PAMM, Vol. 10, No. 1, p.487–488, 2010.
  12. T. Richter,
    Fluid-Structure Interactions in Fully Eulerian Coordinates,
    PAMM, Vol. 12, p.487–488, 2012.

Preprints

  1. T. Richter,
    A Fully Eulerian Formulation for Fluid-Structure Interaction Problems,
    urn:nbn:de:bsz:16-opus-132158, 2012.
  2. T. Richter,
    Goal-oriented error estimation for fluid-structure interaction problems,
    urn:nbn:de:bsz:16-opus-132144, 2012.
  3. T. Richter,
    A monolithic multigrid solver for 3d fluid-structure interaction problems,
    urn:nbn:de:bsz:16-opus-121834, 2011.
  4. M. Braack and T. Richter,
    Solutions of 3D Navier-Stokes benchmark problems with adaptive finite elements,
    SFB 2004-44, 2004.

Lecture Notes

  1. T. Richter and T. Wick,
    Einführung in die Numerische Mathematik,
    Universität Heidelberg, 2012, 2014.
    link ]
  2. T. Richter,
    Numerische Methoden für gewoehnliche und partielle Differentialgleichungen,
    Universität Heidelberg, 2010.
  3. T. Richter,
    Numerische Methoden für partielle Differentialgleichungen,
    Universität Heidelberg, 2011.
    link ]
  4. T. Richter,
    Numerische Methoden in der Stroemungsmechanik,
    Universität Heidelberg, 2014.
    link ]
  5. T. Richter,
    Numerical methods for fluid-structure interactions,
    Universität Heidelberg, 2010, 2012.
  6. T. Richter,
    Introduction to the finite element library \textscGascoigne 3d,
    University of Heidelberg, 2012.
    link ]

Theses

  1. T. Richter,
    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 ]
  2. T. Richter,
    Funktionalorientierte Gitteroptimierung für die Finite Elemente Methode,
    Diploma thesis, University of Heidelberg, 2001.
    preprint ]

Journals

  1. T. Richter,
    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 ]
  2. S. Frei and T. Richter,
    A locally modified parametric finite element method for interface problems,
    SIAM J. Numer. Anal., Vol. 52, No. 5, p.2315–2334, 2014.
    preprint ]
  3. T. Richter,
    A Fully Eulerian Formulation for Fluid-Structure-Interaction Problems,
    JCP, Vol. 233, p.227–240, 2013.
    preprint ]
  4. T. Richter,
    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 ]

Book Chapters

  1. T. Richter and T. Wick,
    On time discretizations of fluid-structure interactions,
    Multiple Shooting and Time Domain Decomposition Methods, 2015.
    preprint ]

Conferences and Workshops

Preprints

Lecture Notes

Theses