Numerische Mathematik in den Anwendungen
Partielle Differentialgleichungen und komplexe Multiphysik-Probleme

Professor Thomas Richter
Gekoppelte Simulation einer inkompressiblen Strömung um ein elastisches Hindernis. Adaptive Finite Elemente.

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

Group

Members

Felix Brinkmann
06221 54-14115
Uni Heidelberg
Carolin Mehlmann
0391-67-52633
G02-15a
Dr. Piotr Minakowski
0391-67-52633
G02-15a
Roman Weinhandl
0391 6110-472
MPI / S2.14

Students

Leopold Lautsch
DG-Diskretisierung der Meereis-Dynamik
Jonas Herbert
Multiraten-Zeitdiskretisierungen
Lisa-Marie Manke
Schnelle Löser für partielle Differentialgleichungen
Nils Margenberg
Parareal-Verfahren für Fluid-Struktur Interaktionen

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

Books

  1. T. Richter and T. Wick,
    Einfuehrung in die Numerische Mathematik - Begriffe, Konzepte und zahlreiche Anwendungsbeispiele,
    ISBN 978-9-662-54177-7, Springer, 2017.
  2. T. Richter,
    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.
  3. S. Frei and B. Holm and T. Richter and T. Wick and H. Yang (Eds.),
    Fluid-Structure Interactions,
    Radon Series on Computational and Applied Mathematics, ISBN 978-3-11-049425-9, De Gruyter, 2017.

Journals

  1. T. Richter and W. Wollner,
    Efficient computation of time-periodic solutions of partial differential equations,
    submitted, 2017.
    preprint ]
  2. F. Brinkmann, M. Mercker, T. Richter and A. Marciniak-Czochra,
    Post-Turing tissue pattern formation: Advent of Mechanochemistry,
    submitted, 2017.
  3. C. Mehlmann and T. Richter,
    A Finite Element Multigrid-Framework for Discretizing Sea Ice Dynamics,
    Journal of Computational Physics, Vol. 348, p.847–861, 2017.
    preprint ]
  4. C. Mehlmann and T. Richter,
    A modified global Newton solver for viscous-plastic sea ice models,
    Ocean Modeling, Vol. 116, p.96–107, 2017.
    preprint ]
  5. M. Mercker, F. Brinkmann, A. Marciniak-Czochra and T. Richter,
    Beyond Turing: Mechanochemical pattern formation in biological tissues,
    Biology Direct, Vol. 11, No. 22, 2016.
    preprint ]
  6. 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, Vol. 84, No. 4, p.199–220, 2017.
    preprint ]
  7. 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 ]
  8. 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.
    preprint ]
  9. S. Frei, T. Richter,
    Second order time-stepping for parabolic interface problems with moving interfaces,
    ESAIM Math. Mod. Num. Anal., Vol. 51, p.1539–1560, 2017.
    preprint ]
  10. S. Frei, T. Richter and T. Wick,
    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 ]
  11. 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 ]
  12. 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 ]
  13. 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, doi=10.1137/130919489.
    preprint ]
  14. 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.
    preprint ]
  15. 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, doi=10.1007/s00466–013–0904–1, 2014.
  16. T. Richter and T. Wick,
    Optimal Control and Parameter Estimation for Stationary Fluid-Structure Interaction Problems,
    SSC, Vol. 35, No. 5, p.B1085–B1104, doi=10.1137/120893239, 2013.
  17. 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, doi=10.1137/120885553, 2013.
  18. 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.
    preprint ]
  19. T. Richter,
    A Fully Eulerian Formulation for Fluid-Structure-Interaction Problems,
    JCP, Vol. 233, p.227–240, 2013.
    preprint ]
  20. T. Richter,
    Goal oriented error estimation for fluid-structure interaction problems,
    CMAME, Vol. 223-224, p.28–42, 2012.
    preprint ]
  21. 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.
    preprint ]
  22. 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, doi=10.1021/jp204127g, 2011.
  23. 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.
    preprint ]
  24. 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, doi=10.1002/nla.744, 2011.
  25. 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, doi=10.17485/ijst/2015/v8i1/84240, 2010.
  26. 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 ]
  27. 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, doi=10.1016/j.jcp.2007.03.009, 2007.
  28. 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 ]
  29. M. Braack and T. Richter,
    Stabilized finite elements for 3-D reactive flows,
    Int. J. Numer. Meth. Fluids, Vol. 51, p.981–999, 2006.
    preprint ]

Book Chapters

  1. T. Richter and S. Frei. In S. Frei and B. Holm and T. Richter and T. Wick and H. Yang (Eds.),
    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 ]
  2. T. Richter and T. Wick. In T. Carraro and M. Geiger and S. Körkel and R. Rannacher (Eds.),
    On time discretizations of fluid-structure interactions,
    Multiple Shooting and Time Domain Decomposition Methods. Springer, 2015, pages=377-400.
    preprint ]
  3. R. Rannacher and T. Richter. In H.J. Bungartz and M. Mehl and M. Schafer (Eds.),
    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.
  4. E. Friedmann, J. Portl and T. Richter. In R. Rannacher and A. Sequiera (Eds.),
    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 ]
  5. T. Dunne, R. Rannacher and T. Richter. In G.P. Galdi and R. Rannacher (Eds.),
    Numerical Simulation of Fluid-Structure Interaction Based on Monolithic Variational Formulations,
    Comtemporary Challenges in Mathematical Fluid Mechanics. World Scientific, 2010.
  6. M. Braack and T. Richter. In W. Jäger and R. Rannacher and J. Warnatz, doi=10.1007/978-3-540-28396-6_3 (Eds.),
    Mesh and model adaptivity for flow problems,
    Reactive Flows, Diffusion and Transport. Springer Berlin Heidelberg, 2006, pages=47-75.
  7. M. Braack and T. Richter. In W. Jäger and R. Rannacher and J. Warnatz (Eds.),
    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.
  8. R. Becker, M. Braack and T. Richter. In W. Jäger and R. Rannacher and J. Warnatz, doi=10.1007/978-3-540-28396-6_4 (Eds.),
    Parallel multigrid on locally refined meshes,
    Reactive Flows, Diffusion and Transport. Springer Berlin Heidelberg, 2006, pages=77-92.

Conferences and Workshops

  1. T. Richter and C. Mehlmann,
    An accelerated Newton method for nonlinear materials in structure mechanics and fluid mechanics,
    Numerical Mathematics and Advanced Applications - Enumath 2017. Springer, 2018.
    preprint ]
  2. P.H. de Almeida Konzen, E. Sauter, F.S. de Azevedo and T. Richter,
    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.
  3. S. Frei and T. Richter. In K. Deckelnick and C.M. Elliot and R. Kornhuber and J.A. Sethian (Eds.),
    Discretization of Parabolic Problems on Moving Domains with Moving Interfaces,
    Oberwolfach Reports. , Vol. 55Mathematisches Forschungsinstitut Oberwolfach, doi= 10.4171/OWR/2015/55, 2015.
  4. 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.745–753Springer, 2015.
    preprint ]
  5. 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.755–762Springer, doi=10.1007/978-3-319-10705-9_75, 2015.
    preprint ]
  6. T. Richter,
    Fluid-Structure Interactions in Fully Eulerian Coordinates,
    PAMM - Proc. Appl. Math. Mech.. , Vol. 10, p.827–830, 2012.
  7. T. Richter. In A. Cangiani and R.L. Davidchack and E. Georgoulis and A.N. Gorban and J. Levesley and M.V. Tretyakov (Eds.),
    Anisotropic Finite Elements for Fluid-Structure Interactions,
    Numerical Mathematics and Advanced Applications 2011, Proceedings of ENUMATH 2011. , p.63–70Springer, 2013.
    preprint ]
  8. T. Richter. In J.C.F. Pereira and A. Sequeira (Eds.),
    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.
  9. E. Friedmann and T. Richter. In J.C.F. Pereira and A. Sequeira (Eds.),
    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.
  10. T. Richter. In H.G. Bock and H.X. Phu and R. Rannacher and J.P. Schlöder (Eds.),
    Discontinuous Galerkin as Time-Stepping Scheme for the Navier-Stokes Equations,
    Modeling, Simulation and Optimization of Complex Processes. , p.271–282Springer, 2012.
  11. M. Braack and T. Richter. In Wesseling et. al. (Eds.),
    Stabilized adaptive finite elements for laminar burner in 3-d,
    Eccomas CFD Proceedings. , 2006.
  12. M. Braack and T. Richter. In B. de Castro et al. (Eds.),
    Local projection stabilization for the Stokes system on anisotropic quadrilateral meshes,
    Enumath Proceedings 2005. , p.770–778Springer, 2005.
  13. T. Richter and T. Wick,
    Fluid-Structure Interactions in ALE and Fully Eulerian Coordinates,
    PAMM. , Vol. 10, No. 1, p.487–488, 2010.
  14. 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 ]