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Matthias Augustin

Former Postdoctoral Researcher

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Position:    Former Postdoctoral Researcher
E-mail: augustin -at- mia.uni-saarland.de
(please replace anti-spam -at- by @)


Research Interests
  • PDEs in Image Processing
  • Radial Basis Functions
  • Pseudodifferential Operators

Publications

    Books

  1. M. Augustin:
    A Method of Fundamental Solutions in Poroelasticity to Model the Stress Field in Geothermal Reservoirs.
    Lecture Notes in Geosystems Mathematics and Computing
    Birkhäuser, Basel, 2015.

    Book Chapters

  1. M. Augustin, S. Eberle, M. Grothaus:
    An overview on tools from functional analysis.
    In W. Freeden, M. Z. Nashed (Ed.): Handbook of Mathematical Geodesy. Birkhäuser, pp.165-199, 2018.

  2. M. Augustin, W. Freeden, H. Nutz:
    About the importance of the Runge-Walsh concept for gravitational field determination.
    In W. Freeden, M. Z. Nashed (Ed.): Handbook of Mathematical Geodesy. Birkhäuser, pp.517-560, 2018.

  3. M. Augustin, W. Freeden:
    A survey on classical boundary value problems in physical geodesy.
    In E. Grafarend (Ed.): Encyclopedia of Geodesy. Springer, published online 2016.

  4. M. Augustin, C. Blick, S. Eberle, W. Freeden:
    Disturbing potential from gravity anomalies: from globally reflected Stokes boundary value problem to locally oriented multiscale modeling.
    In E. Grafarend (Ed.): Encyclopedia of Geodesy. Springer, published online 2016.

  5. M. Augustin, W. Freeden:
    Geodetically relevant finite point-set method (FPM).
    In E. Grafarend (Ed.): Encyclopedia of Geodesy. Springer, published online 2016.

  6. M. Augustin, R. Umla, M. Lücke:
    Convection structures of binary fluid mixtures in porous media.
    In W. Freeden, Z. Nashed, T. Sonar (Eds.): Handbook of Geomathematics, Second Edition. Springer, New York, pp.751-778, 2015.

  7. M. Augustin, M. Bauer, C. Blick, S. Eberle, W. Freeden, C. Gerhards, M. Ilyasov, R. Kahnt, M. Klug, I. Michel, S. Möhringer, T. Neu, H. Nutz, A. Punzi:
    Deep geothermal reservoirs: Recent advances and future perspectives.
    In W. Freeden, Z. Nashed, T. Sonar (Eds.): Handbook of Geomathematics, Second Edition. Springer, New York, pp.1547-1629, 2015.

    Conference Papers

  1. M. Augustin, J. Weickert, S. Andris:
    Pseudodifferential inpainting: The missing link between PDE- and RBF-based interpolation.
    In J. Lellmann, M. Burger, J. Modersitzki (Eds.): Scale Space and Variational Methods. Lecture Notes in Computer Science, Vol. 11603, 67-78, Springer, Cham, 2019.

    Journal Papers

  1. V. Daropoulos, M. Augustin, J. Weickert:
    Sparse Inpainting with smoothed particle hydrodynamics.
    SIAM Journal on Imaging Sciences, Vol. 14, No. 4, 1669-1704, November 2021.
    Also available as arXiv:2011.11289 [eess.IV], revised August 2021.

  2. M. Augustin:
    On the role of poroelasticity for modeling stress fields in geothermal reservoirs.
    International Journal on Geomathematics, Vol. 3, 67-93, April 2012.

  3. M. Augustin, W. Freeden, C. Gerhards, S. Möhringer, I. Ostermann:
    Mathematische Methoden in der Geothermie.
    Mathematische Semesterberichte, Vol. 59, 1-28, April 2012.

  4. M. Augustin, A. Caiazzo, A. Fiebach, J. Furhmann, V. John, A. Linke, R. Umla:
    An assessment of discretizations for convection-dominated convection-diffusion equations.
    Computer Methods in Applied Mechanics and Engineering, Vol. 200, 3395-3409, November 2011.

  5. R. Umla, M. Augustin, B. Huke, M. Lücke:
    Three-dimensional convection of binary mixtures in porous media.
    Physical Review E, Vol. 84, 056326, November 2011.

  6. M. Augustin, R. Umla, B. Huke, M. Lücke:
    Stationary and oscillatory convection of binary fluids in a porous medium.
    Physical Review E, Vol. 82, 056303, November 2010.

  7. R. Umla, M. Augustin, B. Huke, M. Lücke:
    Roll convection of binary fluid mixtures in porous media.
    Journal of Fluid Mechanics, Vol. 649, 165-186, April 2010.

    Preprints

  1. T. Alt, K. Schrader, J. Weickert, P. Peter, M. Augustin:
    Designing Rotationally Invariant Neural Networks from PDEs and Variational Methods.
    arXiv:2108.13993 [cs.LG], August 2021.

  2. T. Alt, K. Schrader, M. Augustin, P. Peter, J. Weickert:
    Connections between Numerical Algorithms for PDEs and Neural Networks.
    arXiv:2107.14742 [math.NA], July 2021.

    Theses

  1. M. Augustin:
    A Method of Fundamental Solutions in Poroelasticity to Model the Stress Field in Geothermal Reservoirs.
    PhD-Thesis in Mathematics,
    University of Kaiserslautern, Kaiserslautern, Germany, September 2014.
    Published in Lecture Notes in Geosystems Mathematics and Computing
    Birkhäuser, Basel, 2015.

  2. M. Augustin:
    Numerische Untersuchungen eines unstetigen Galerkin-Verfahrens zur Lösung der Konvektions-Diffusions Gleichung.
    Diploma Thesis in Mathematics,
    Saarland University, Saarbrücken, Germany, January 2010.

  3. M. Augustin:
    Zweidimensionale Konvektionsstrukturen im Horton-Rogers-Lapwood-System unter Berücksichtigung des Soret-Effekts.
    Diploma Thesis in Physics,
    Saarland University, Saarbrücken, Germany, March 2009.

Talks
  1. M. Augustin, S. Andris, J. Weickert:
    Linking RBF Interpolation and PDE-based Inpainting.
    Curves and Surfaces, Arcachon, France, June-July 2018.

  2. M. Augustin, S. Andris, J. Weickert:
    From Geomathematics to Image Compression.
    International Conference "Inverse Problems: Modeling and Simulation" (IPMS), Malta, May 2018.

  3. M. Augustin:
    A new approach to computing poroelastic stresses.
    European Numerical Mathematics and Advanced Application (ENUMATH), Ankara, Turkey, September 2015.

  4. M. Augustin:
    Methods of fundamental solutions in poroelasticity.
    Joint Mathematics Meeting, AMS Special Session on Geosystems Mathematics, San Antonio, Texas, January 2015.

  5. M. Augustin:
    Modeling the stress field in geothermal reservoirs.
    15th IAMG Conference on Frontiers of Mathematical Geosciences, Madrid, Spain, September 2013.

  6. M. Augustin:
    Modeling the stress field in geothermal reservoirs.
    Workshop Geomathematics 2013, St. Martin, Germany, April 2013.

  7. M. Augustin:
    Stress field simulations in geothermal reservoirs.
    Joint Mathematics Meeting, AMS Special Session on Frontiers in Geomathematics, San Diego, California, January 2013.

  8. M. Augustin:
    Modellierung des Spannungsfeldes in geothermischen Reservoiren.
    DGK Geothermiekongress, Karlsruhe, Germany, November 2012.

  9. M. Augustin:
    On convection patterns of binary fluid mixtures in porous media.
    10th International Meeting on Thermodiffusion, Brussels, Belgium, June 2012.

  10. M. Augustin:
    Modeling the stress field in deep geothermal reservoirs.
    Joint Mathematics Meeting, AMS Special Session on Frontiers in Geomathematics, Boston, Massachusetts, January 2012.

  11. M. Augustin:
    Modellierung des Spannungsfeldes geothermischer Reservoire.
    DGK Geothermiekongress, Karlsruhe, Germany, November 2010.


Teaching

    Theses Advisor

  1. Katharina Bonaventura: Non-overlapping Domain Decomposition for Homogeneous Diffusion Inpainting. B.Sc. Thesis in Computer Science, 2021.
  2. Viktor Daropoulos: Inpainting with Particle Hydrodynamics. M.Sc. Thesis in Computer Science, 2019.

Reviewing Activities

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