Technische Universität Darmstadt
Fachbereich Mathematik
AG Numerik und wissenschaftliches Rechnen
Technische Universität Darmstadt
Fachbereich Mathematik
 
Alf Gerisch
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List of Publications

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Books

  1. A. Gerisch, R. Penta, J. Lang (eds.)
    Multiscale Models in Mechano and Tumor Biology: Modeling, Homogenization, and Applications. Lecture Notes in Computational Science and Engineering, volume 122, Springer, Cham, 2018.
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Peer-Reviewed Papers

  1. Chiara Villa, Alf Gerisch, Mark A.J. Chaplain
    A novel nonlocal partial differential equation model of endothelial progenitor cell cluster formation during the early stages of vasculogenesis. Journal of Theoretical Biology, Volume 534, (2022), article 110963.
  2. Chiara Villa, Mark A.J. Chaplain, Alf Gerisch, Tommaso Lorenzi
    Mechanical Models of Pattern and Form in Biological Tissues: The Role of Stress-Strain Constitutive Equations. Bull Math Biol, Volume 83, (2021), article 80, 38 pages.
  3. Yunfeng Mao, Alf Gerisch, Jens Lang, Michael C. Böhm, Florian Müller-Plathe
    Uncertainty Quantification Guided Parameter Selection in a Fully Coupled Molecular Dynamics-Finite Element Model of the Mechanical Behavior of Polymers. J. Chem. Theory Comput., Volume 17, (2021), 3760-3771.
  4. Ram Jiwari and Alf Gerisch
    A local radial basis function differential quadrature semi-discretisation technique for the simulation of time-dependent reaction-diffusion problems. Engineering Computations, Volume 38, (2021), 2666-2691.
  5. A. Buttenschön, T. Hillen, A. Gerisch, K. Painter
    A space-jump derivation for non-local models of cell-cell adhesion and non-local chemotaxis. Journal of Mathematical Biology, Volume 76 (2018), 429-456.
    Access paper via SpringerNature SharedIt
  6. P. Domschke, D. Trucu, A. Gerisch, M.A.J. Chaplain
    Structured models of cell migration incorporating molecular binding processes. Journal of Mathematical Biology, Volume 75 (2017), 1517-1561.
    Access paper via SpringerNature SharedIt
  7. D. Schröder, A. Gerisch, J. Lang
    Space-Time Adaptive Linearly Implicit Peer Methods for Parabolic Problems. Journal of Computational and Applied Mathematics, Volume 316 (2017), 330-344.
  8. R. Penta, A. Gerisch
    The asymptotic homogenization elasticity tensor properties for composites with material discontinuities. Continuum Mech. Thermodyn., Volume 29 (2017), 187-206.
    Access paper via SpringerNature SharedIt
  9. R. Penta, K. Raum, Q. Grimal, S. Schrof, A. Gerisch
    Can a continuous mineral foam explain the stiffening of aged bone tissue? A micromechanical approach to mineral fusion in musculoskeletal tissues. Bioinspir. Biomim., Volume 11 (2016), 035004.
  10. R. Penta, A. Gerisch
    Investigation of the potential of asymptotic homogenization for elastic composites via a three-dimensional computational study. Computing and Visualization in Science, Volume 17 (2016), 185-201.
  11. K.J. Painter, J.M. Bloomfield, J.A. Sherratt, A. Gerisch
    A nonlocal model for contact attraction and repulsion in heterogeneous populations. Bulletin of Mathematical Biology, Volume 77 (2015), 1132-1165.
  12. A. Gerisch, A. Naumann, J. Wensch
    Defect corrected averaging for highly oscillatory problems. Applied Mathematics and Computation, Volume 261 (2015), 90-103.
  13. S. Liu, A. Gerisch, M. Rahimi, J. Lang, M.C. Böhm, F. Müller-Plathe
    Robustness of a New Molecular Dynamics-Finite Element Coupling Approach for Soft Matter Systems Analyzed by Uncertainty Quantification. Journal of Chemical Physics, Volume 142 (2015), 104105 (11 pages).
  14. M. Granke, Q. Grimal, W.J. Parnell, K. Raum, A. Gerisch, F. Peyrin, A. Saïed, P. Laugier
    To what extent can cortical bone millimeter-scale elasticity be predicted by a two-phase composite model with variable porosity? Acta Biomaterialia, Volume 12 (2015), 207-215.
  15. P. Domschke, D. Trucu, A. Gerisch, M.A.J. Chaplain
    Mathematical modelling of cancer invasion: Implications of cell adhesion variability for tumour infiltrative growth patterns. J. Theor. Biol., Volume 361 (2014), 41-60.
  16. S. Tiburtius, S. Schrof, F. Molnar, P. Varga, F. Peyrin, Q. Grimal, K. Raum, A. Gerisch
    On the elastic properties of mineralized turkey leg tendon tissue: multiscale model and experiment. Biomech Model Mechanobiol, Volume 13 (2014), 1003-1023.
  17. D. Rohrbach, S. Lakshmanan, F. Peyrin, M. Langer, A. Gerisch, Q. Grimal, P. Laugier, K. Raum
    Spatial distribution of tissue level properties in a human femoral cortical bone. Journal of Biomechanics, Volume 45 (2012), 2264-2270.
  18. K. Raum, Q. Grimal, P. Laugier, A. Gerisch
    Multiscale structure-functional modeling of lamellar bone. Proceedings of Meetings on Acoustics (POMA), Volume 9 (2011), 020005-020005-15.
  19. Q. Grimal, K. Raum, A. Gerisch, P. Laugier
    A determination of the minimum sizes of representative volume elements for the prediction of cortical bone elastic properties. Biomech Model Mechanobiol, Volume 10 (2011), 925-937.
  20. V. Peiffer, A. Gerisch, D. Vandepitte, H. Van Oosterwyck, L. Geris
    A hybrid bioregulatory model of angiogenesis during bone fracture healing. Biomech Model Mechanobiol, Volume 10 (2011), 383-395.
  21. V. Andasari, A. Gerisch, G. Lolas, A.P. South and M.A.J. Chaplain
    Mathematical modeling of cancer cell invasion of tissue: biological insight from mathematical analysis and computational simulation. J. Math. Biol., Volume 63 (2011), 141-171.
  22. L. Geris, A. Gerisch, R.C. Schugart
    Mathematical Modeling in Wound Healing, Bone Regeneration and Tissue Engineering. Acta Biotheor., Volume 58 (2010), 355-367.
  23. J.M.A. Ashbourne, L. Geris, A. Gerisch, C.J.S. Young
    Numerical simulation of two-dimensional and three-dimensional axisymmetric advection-diffusion systems with complex geometries using finite-volume methods. Proc. R. Soc. A, Volume 466 (2010), 1621-1643.
  24. A. Gerisch
    On the approximation and efficient evaluation of integral terms in PDE models of cell adhesion. IMA J. Numer. Anal., Volume 30 (2010), 173-194. DOI: 10.1093/imanum/drp027.
  25. A. Gerisch, J. Lang, H. Podhaisky, R. Weiner
    High-order linearly implicit two-step peer - finite element methods for time-dependent PDEs. Appl. Numer. Math. Volume 59 (2009), 624-638.

    A preliminary version of this paper has been published as Report 06-13 of the series of Reports on Numerical Mathematics, Martin-Luther-Universität Halle-Wittenberg.

  26. A. Gerisch, M.A.J. Chaplain
    Mathematical modelling of cancer cell invasion of tissue: Local and non-local models and the effect of adhesion. J. Theor. Biol. Volume 250 (2008), 684-704.
  27. L. Geris, A. Gerisch, J. Vander Sloten, R. Weiner, H. Van Oosterwyck
    Angiogenesis in Bone Fracture Healing: a Bioregulatory Model. J. Theor. Biol., Volume 251 (2008), 137-158.
  28. J. Wensch, A. Gerisch, S. Posch
    Optimised coupling of hierarchies in image registration. Image and Vision Computing, Volume 26 (2008), 1000-1011.
  29. Q. Grimal, K. Raum, A. Gerisch, P. Laugier
    Derivation of the mesoscopic elasticity tensor of cortical bone from quantitative impedance images at the micron scale. Computer Methods in Biomechanics and Biomedical Engineering, Volume 11 (2008), 147-157.
  30. A. Gerisch, M. Kotschote, R. Zacher
    Well-posedness of a quasilinear hyperbolic-parabolic system arising in mathematical biology. NoDEA Nonlinear differ. equ. appl., Volume 14 (2007), 593-624.

    A preliminary version of this paper has been published as Report 04-24 of the series of Reports on Analysis and Numerical Mathematics, Martin-Luther-Universität Halle-Wittenberg.

  31. K. R. Driessel, A. Gerisch
    Zero-preserving iso-spectral flows based on parallel sums. LAA, Volume 421 (2007), 69-84.
  32. L. Geris, A. Gerisch, Ch. Maes, G. Carmeliet, R. Weiner, J. Vander Sloten, H. Van Oosterwyck
    Mathematical modeling of fracture healing in mice: Comparison between experimental data and numerical simulation results. Med. Biol. Eng. Comput., Volume 44 (2006), 280-289.
  33. A. Gerisch, M. A. J. Chaplain
    Robust numerical methods for taxis-diffusion-reaction systems: Applications to biomedical problems. Math. Comput. Modelling, Volume 43 (2006), 49-75.
  34. M.P. Calvo, A. Gerisch
    Linearly implicit Runge-Kutta methods and approximate matrix factorization. Appl. Numer. Math., Volume 53 (2005), 183-200.

    Correction: On page 187, line 6, it should read ${\hat a}_{32} = - 0.35$, i.e. the minus sign is missing in the published paper.

  35. A. Gerisch, R. Weiner
    The positivity of low order explicit Runge-Kutta schemes applied in splitting methods. Computers and Mathematics with Applications, Volume 45 (2003), 53-67.

    A preliminary version of this paper has been published as Report 99-35 of the series of Reports on Numerical Mathematics, Martin-Luther-Universität Halle-Wittenberg.

  36. A. Gerisch, J.G. Verwer
    Operator splitting and approximate factorization for taxis-diffusion-reaction models. Appl. Numer. Math., Volume 42 (2002), 159-176.

    A preliminary version of this paper has been published as CWI Report MAS-R0026 (CWI, Amsterdam, September 2000) in the series of reports on Modelling, Analysis and Simulation at CWI, Amsterdam.

  37. A. Gerisch, D.F. Griffiths, R. Weiner, M.A.J. Chaplain
    A Positive Splitting Method for Mixed Hyperbolic-Parabolic Systems. Numer. Methods Partial Differential Equations, Volume 17 (2001), 152-168.

    A preliminary version of this paper has been published under the title Splitting Methods for Mixed Hyperbolic-Parabolic Systems (revised version of July 27, 1999) as Numerical Analysis Report NA/186, University of Dundee, December 1998.

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Peer-Reviewed Book Chapters

  1. A. Voss-Böhme, A. Gerisch
    Multi-Scale Analysis of Contact-Dependent Interaction in Tissue Aggregation and Invasion. pages 156-168 in: Olaf Wolkenhauer (ed.) Systems Medicine: Integrative, Qualitative and Computational Approaches Academic Press, Oxford, 2021 (published online August 2020).
  2. R. Penta, A. Gerisch
    An introduction to asymptotic homogenization. pages 1-26 (Chapter 1) in: A. Gerisch, R. Penta, J. Lang (eds.) Multiscale Models in Mechano and Tumor Biology: Modeling, Homogenization, and Applications. Lecture Notes in Computational Science and Engineering, volume 122, Springer, Cham, 2018.
  3. A. Madzvamuse, A. Gerisch, R. Barreira
    Cross-diffusion in reaction-diffusion models: analysis, numerics and applications. pages 385-392 in: Quintela P. et al. (eds.) Progress in Industrial Mathematics at ECMI 2016. Mathematics in Industry, volume 26, Springer, Cham, 2017.
  4. D. Trucu, P. Domschke, A. Gerisch, M.A.J. Chaplain
    Multiscale Computational Modelling and Analysis of Cancer Invasion. pages 275-321 in: L. Preziosi, M.A.J. Chaplain, A. Pugliese (eds.) Mathematical Models and Methods for Living Systems: Levico Terme, Italy 2014. Springer International Publishing, 2016.
  5. L. Geris, A. Gerisch
    Mathematical Modelling of Cell Adhesion in Tissue Engineering using Continuum Models. pages 431-450 in: A. Gefen (ed.) Cellular and Biomolecular Mechanics and Mechanobiology. , Volume 4 of Studies in Mechanobiology, Tissue Engineering and Biomaterials, Springer Verlag Berlin Heidelberg, 2011.
  6. A. Gerisch, K.J. Painter
    Mathematical Modeling of Cell Adhesion and Its Applications to Developmental Biology and Cancer Invasion. Chapter 12 in: A. Chauvière, L. Preziosi, C. Verdier (eds.) Cell Mechanics: From Single Scale-Based Models to Multiscale Modeling. Chapman & Hall/CRC, 2010.
  7. A. Gerisch, L. Geris
    A finite volume spatial discretisation for taxis-diffusion-reaction systems with axi-symmetry: application to fracture healing. pages 299-311 in Mathematical Modeling of Biological Systems, A. Deutsch, L. Brusch, H. Byrne, G. de Vries, H. Herzel (Eds.), Birkhäuser Boston, 2007.
  8. A. Gerisch, L. Geris, H. Van Oosterwyck, J. Vander Sloten, R. Weiner
    Reliable and efficient numerical simulation of a model of tissue differentiation in a bone chamber. pages 60-76 in: G. Bischof (Ed.), Micro- and Nanostructures of Biological Systems, ISBN 3-8322-3868-9, Shaker Verlag, Aachen, 2005.

    A preliminary version of this paper has been published as Report 04-26 of the series of Reports on Numerical Mathematics, Martin-Luther-Universität Halle-Wittenberg.

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Peer-Reviewed Published Conference Contributions

  1. K. Raum, Q. Grimal, A. Gerisch
    Insight into the Structure-Function Relationship of the Bone Lamellar Unit through Finite Element Modelling Based on High-Frequency SAM Data
    in: World Congress on Medical Physics and Biomedical Engineering, September 7 - 12, 2009, Munich, Germany. Editors: R. Magjarevic, O. Dössel, W.C. Schlegel, IFMBE Proceedings, Volume 25/4, 2246-2249, 2010.
  2. A. T. Lawniczak, A. Gerisch, B. Di Stefano
    OSI Network-layer Abstraction: Analysis of Simulation Dynamics and Performance Indicators
    in: SCIENCE OF COMPLEX NETWORKS: From Biology to the Internet and WWW: CNET 2004. Editors: J. F. F. Mendes et al., AIP Conference Proceedings, Volume 776, 166-200, 2005.
  3. A. T. Lawniczak, K. P. Maxie, A. Gerisch
    From Individual to Collective Behaviour in CA Like Models of Data Communication Networks
    in: Cellular Automata: 6th International Conference on Cellular Automata for Research and Industry, ACRI 2004, Amsterdam, The Netherlands, October 25-28, 2004. Proceedings, Editors: Peter M. A. Sloot, Bastien Chopard, Alfons G. Hoekstra, Lecture Notes in Computer Science, Volume 3305, 325-334, Springer-Verlag Heidelberg, 2004.
  4. A. Gerisch, A. T. Lawniczak, R. A. Budiman, H. Fukś, H. E. Ruda
    Surface Roughening in Homoepitaxial Growth: A Lattice Gas Cellular Automaton Model
    in: Cellular Automata: 6th International Conference on Cellular Automata for Research and Industry, ACRI 2004, Amsterdam, The Netherlands, October 25-28, 2004. Proceedings, Editors: Peter M. A. Sloot, Bastien Chopard, Alfons G. Hoekstra, Lecture Notes in Computer Science, Volume 3305, 286-295, Springer-Verlag Heidelberg, 2004.
  5. A. Gerisch, A. T. Lawniczak, R. A. Budiman, H. E. Ruda, H. Fukś
    Lattice gas cellular automaton modeling of surface roughening in homoepitaxial growth in nanowires
    in: Proceedings of CCECE 2003-CCGEI 2003, Montréal, Quebec, Canada, Volume 2, 1413-1416, 2003. (ISSN: 0840-7789)
  6. A. Gerisch, H. Podhaisky
    Splitting Methods for the Simulation of Tumor Angiogenesis Models
    in: M. Deville, R. Owens (Eds.), Proceedings of the 16th IMACS World Congress, Lausanne, Switzerland, published on CD-ROM, Rutgers University, New Brunswick, NJ, 2000. (ISBN 3-9522075-1-9)
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Thesis

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Other Publications

  1. A. Gerisch, R. Weiner
    Let's stick together: Numerische Simulation von Zelladhäsionsprozessen
    Unimagazin scientia halensis, Issue 3 (2008), 24-25.
  2. A.T. Lawniczak, P. Zhao, A. Gerisch, and B. Di Stefano
    Modelling flow and congestion in packet switching network
    IEEE Canadian Review, Volume 39 (2002), 23-27.


Last Modification: 30.11.2022 14:18
Author: Alf Gerisch
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