Differential-Algebraic Systems Group

Research Areas

  • Applied and numerical mathematics, in particular coupled systems of differential-algebraic and partial differential equations
  • Multidisciplinary projects in the area of vehicle dynamics, material sciences and fluid mechanics
  • Modeling and numerics of shape memory materials
  • Isogeometric finite elements
  • Haemodynamics and dynamics of skeletal muscles

Publications

  • S. Plunder, B. Simeon:
    The mean-field limit for particle systems with uniform full-rank constraints.
    To appear in Kinet. Relat. Models.
     
  • B. Bauer, M. Roller, J. Linn, B. Simeon:
    An Isogeometric One-Dimensional Kirchhoff-Love Type Model for Developable Elastic Ribbons
    To appear in J. Comp. Appl. Math.
     
  • B. Simeon:
    Die Macht der Computermodelle. Quellen der Erkenntnis oder digitale Orakel?
    To appear in Springer-Verlag.
     
  • J. Kleinert, B. Simeon:
    Differential-algebraic equations and beyond: from smooth to nonsmooth constrained dynamical systems.
    In Novel Mathematics Inspired by Industrial Challenges, M. Günther, W. Schilders, Eds., Springer, pp. 73–132, 2022.
    [doi]  [www]
     
  • D. Manvelyan, B. Simeon, U. Wever:
    A physics-based model reduction approach for node-to-segment contact problems in linear elasticity.
    Int. J. Numer. Methods Eng. (Early View), pp. 1–27, 2022.
    [doi]  [www]
     
  • M. Chasapi, L. Mester, B. Simeon, S. Klinkel:
    Isogeometric analysis of 3D solids in boundary representation for problems in nonlinear solid mechanics and structural dynamics.
    Int. J. Numer. Methods Eng., vol.123, pp. 1228–1252, 2022.
    [doi]  [www]
     
  • J. Arf, B. Simeon:
    A space-time isogeometric method for the partial differential-algebraic system of Biot's poroelasticity model.
    Electron. Trans. Numer. Anal., vol. 55, pp. 310–340, 2022.
    [doi]  [www]
     
  • H. van Brummelen, C. Vuik, M. Möller, C. Verhoosel, B. Simeon, B. Jüttler, B. (Eds.):
    Isogeometric Analysis and Applications 2018.
    Springer Lecture Notes Computational Science and Engineering, 2021.
    [doi]  [www]
     
  • D. Manvelyan, B. Simeon, U. Wever:
    An effcient model order reduction scheme for dynamic contact in linear elasticity.
    Comput. Mech., vol 68, pp. 1283–1295, 2021.
    [doi]  [www]
     
  • M. H. Gfrerer, B. Simeon:
    Fiber-based modeling and simulation of skeletal muscles.
    Multibody Syst. Dyn., vol. 52, pp. 1–30, 2021.
    [doi]  [www]
     
  • A. Shamanskiy, B. Simeon:
    Mesh moving techniques in fluid-structure interaction: robustness, accumulated distortion and computational efficiency.
    Comput. Mech., vol 67, pp. 583–600, 2021.
    [doi]  [www]
     
  • B. Bauer, M. Roller, J. Linn, B. Simeon:
    One-Dimensional Modelling of Developable Elastic Strips by Geometric Constraints and their Link to Surface Isometry.
    In ECCOMAS Thematic Conference on Multibody Dynamics (pp. 359–368). Budapest University of Technology and Economics, 2021.
    [doi]  [www]
     
  • B. Bauer, C, Arioli, B. Simeon:
    Generating star-shaped blocks for scaled boundary multipatch IGA.
    Springer Lecture Notes: Conference on Isogeometric Analysis and Applications 2018, pp. 1–25, 2021.
    [doi]  [www]
     
  • S. Plunder, B. Simeon:
    Coupled systems of linear differential-algebraic and kinetic equations with application to the mathematical modelling of muscle tissue.
    In Progress in Differential-Algebraic Equations II, Reis, T., Grundel, S., Schöps, S. (eds), pp. 357–395, 2020.
    [doi]  [www]
     
  • A. Shamanskiy, M. H. Gfrerer, J. Hinz, B. Simeon:
    Isogeometric parametrization inspired by large elastic deformation.
    Comput Methods Appl. Mech. Eng., vol. 363, p. 112920, 2020.
    [doi]  [www]
     
  • A. Leichner, H. Andrä, B. Simeon:
    A contact algorithm for voxel-based meshes using an implicit boundary representation.
    Comput. Methods Appl. Mech. Eng., vol. 352, pp. 276–299, 2019.
    [doi]  [www]
     
  • C. Arioli, A. Shamanskiy, S. Klinkel, B. Simeon:
    Scaled Boundary Parametrizations in Isogeometric Analysis.
    Comput. Methods Appl. Mech. Eng., vol. 349, pp. 576–594, 2019.
    [doi]  [www]
     
  • J. Jahnke, S. Steidel, M. Burger, B. Simeon:
    Efficient Particle Simulation Using a Two-Phase DEM-Lookup Approach.
    In European Congress on Computational Methods in Applied Sciences and Engineering, pp. 425–432, Springer, 2019.
    [doi]  [www]
     
  • M. H. Gfrerer, B. Simeon:
    Fiber-Based Modeling of Muscles in the Musculoskeletal System.
    In Progress in Industrial Mathematics at ECMI 2018, pp. 189–197, Springer, Cham 2019.
    [doi]  [www]
     
  • A. Shamanskiy, B. Simeon:
    Isogeometric simulation of thermal expansion for twin screw compressors.
    IOP Conf. Ser.: Mater. Sci. Eng., vol. 425, p. 012031, 2018.
    [doi]  [www]
     
  • M. Harutyunyan, B Simeon:
    On a saddle point problem arising from magneto-elastic coupling.
    Appl. Math. Lett., vol. 83, pp. 156–163, 2018.
    [doi]  [www] 
     
  • M. H. Gfrerer, B. Simeon:
    Fiber-based modeling of muscles in the musculoskeletal system.
    PAMM, vol. 18, p. e201800016, 2018.
    [doi]  [www]
     
  • F. Schneider, M. Burger, M. Arnold, B. Simeon:
    A new approach for force-displacement co-simulation using kinematic coupling constraints.
    ZAMM, vol. 97, pp. 1147–1166, 2017.
    [doi]  [www] 
     
  • A. Goyal, B. Simeon:
    On Penalty-free Formulations for Multipatch Isogeometric Kirchhoff-Love Shells.
    Math. Comput. Simul., vol. 136, pp. 78–103, 2017.
    [doi]  [www] 
     
  • B. Simeon:
    On the History of Differential-Algebraic Equations. A Retrospective with Personal Sidetrips.
    In Surveys in Differential-Algebraic Equations IV. A. Ilchmann, T. Reis (eds.) pp. 1–39, 2017.
    [doi]  [www]
     
  • F. Dietrich, D. Merkert, B. Simeon:
    Derivation of higher-order terms in FFT-based numerical homogenization.
    In European Conference on Numerical Mathematics and Advanced Applications, pp. 289–297, 2017.
    [doi]  [www]
     
  • C. Giannelli, B. Jüttler, S. K. Kleiss, A. Mantzaflaris, B. Simeon, J. Špeh:
    THB-splines: an effective mathematical technology for adaptive refinement in geometric design and isogeometric analysis.
    Comput. Methods Appl. Mech. Eng., vol. 299, pp. 337–365, 2016.
    [doi]  [www] 
     
  • O. Weeger, U. Wever, B. Simeon:
    On the use of modal derivatives for nonlinear model order reduction.
    Comput. Methods Appl. Mech. Eng., vol. 108, pp. 1579–1602, 2016.
    [doi]  [www] 
     
  • Kleinert, J., Simeon, B., Dressler, K.:
    Nonsmooth Contact Dynamics for the Large-Scale Simulation of Granular Material.
    J. Comput. Appl. Math., vol. 316, pp. 345–357, 2016.
    [doi]  [www] 
     
  • Chen, L., Simeon, B., Klinkel, S.:
    A NURBS based Galerkin approach for the analysis of solids in boundary representation.
    Comput. Methods Appl. Mech. Eng., vol. 305, pp. 777–805, 2016.
    [doi]  [www] 
     
  • Jüttler, B., Simeon, B. (Eds.):
    Isogeometric Analysis and Applications 2014.
    Springer Lecture Notes Computational Science and Engineering, 2015.
    [doi]  [www] 
     
  • B. Simeon:
    Mechanical Systems.
    Encyclopedia of Applied and Computational Mathematics, pp. 865–874, 2016.
    [doi]  [www] 
     
  • D. Fußeder, B. Simeon:
    Algorithmic Aspects of Isogeometric Shape Optimization.
    Isogeometric Analysis and Applications 2014. Algorithmic Aspects of Isogeometric Shape Optimization Jüttler, Bert and Simeon, Bernd (eds.)
    Lecture Notes in Computational Science and Engineering, vol. 107, pp. 183–207, 2015.
    [doi]  [www] 
     
  • D. Fußeder, B. Simeon, A. Vuong:
    Fundamental Aspects of Shape Optimization in the Context of Isogeometric Analysis.
    Comput. Methods Appl. Mech. Eng., vol. 286, pp. 313–331, 2015.
    [doi]  [www] 
     
  • D. Merkert, H, Andrä, M, Kabel, M, Schneider, B, Simeon:
    An Efficient Algorithm to Include Sub-Voxel Data in FFT-Based Homogenization for Heat Conductivity.
    Recent Trends in Computational Engineering-CE2014. pp. 267–279, 2015.
    [doi]  [www] 
     
  • A. Roth, A. Klar, B. Simeon, E. Zharovsky:
    A Semi-Lagrangian Method for 3-D Fokker Planck Equations for Stochastic Dynamical Systems on the Sphere.
    J. Sci. Comput., vol. 61, pp. 513–532, 2014.
    [doi]  [www]
     
  • D. Merkert, H. Andrä, M. Kabel, M. Schneider, B. Simeon:
    Voxel-based fast solution of the Lippmann-Schwinger equation with smooth material interfaces.
    Proc. Appl. Math. Mech., vol. 14, pp. 579–580, 2014.
    [doi] [www] 
     
  • J. Kleinert, B. Simeon, M. Obermayr:
    An Inexact Interior Point Method for the Large-Scale Simulation of Granular Material.
    Comput. Methods Appl. Mech. Eng., vol. 278, pp. 567–598, 2014.
    [doi]  [www]
     
  • J. Vuong, B. Simeon:
    On Finite Element Method-Flux Corrected Transport Stabilization for Advection-Diffusion Problems in a Partial Differential-Algebraic Framework.
    Comput. Methods Appl. Mech. Eng., vol. 262, pp. 115–126, 2014.
    [doi]  [www]
     
  • L. Blanchard, R. Duvigneau, A. Vuong, B. Simeon:
    Shape Gradient for Isogeometric Structural Design.
    J. Optim. Theory Appl., vol. 161, pp. 361–367, 2014.
    [doi]  [www] 
     
  • M. Harutyunyan, B. Simeon:
    Mathematical Modeling and Numerical Simulation of a Magnetostrictive Euler-Bernoulli Beam.
    Proc. Appl. Math. Mech., vol. 14, pp. 517–518, 2014.
    [doi]  [www] 
     
  • O. Weeger, U. Wever, B. Simeon:
    Nonlinear frequency response analysis of structural vibrations.
    Comput. Mech., vol. 54, pp.1477–1495, 2014.
    [doi]  [www] 
     
  • U. Becker, B. Simeon, M. Burger:
    On Rosenbrock methods for the time integration of nearly incompressible materials and their usage for nonlinear model reduction.
    J. Comput. Appl. Math., vol. 262, pp. 333–345, 2014.
    [doi]  [www]
     
  • S. Gonzalez-Pinto, D. Hernandez-Abreu, B. Simeon:
    Strongly A-Stable First Stage Explicit Collocation Methods with Stepsize Control for Stiff and Differential-Algebraic Systems.
    J. Comput. Appl. Math., vol. 259, pp. 138–152, 2014.
    [doi][www]
     
  • A. Goyal, M. Dörfel, B. Simeon, A. Vuong:
    Isogeometric shell discretizations for flexible multibody dynamics.
    Multibody Syst. Dyn., vol. 30, pp. 139–151, 2013.
    [doi]  [www]
     
  • B. Simeon:
    Computational Flexible Multibody Dynamics: A Differential-Algebraic Approach.
    Springer: Berlin Heidelberg, 2013.
    978-3-642-35157-0
    [doi]  [www]
     
  • W. Dornisch, S. Klinkel, B. Simeon:
    Isogeometric Reissner-Mindlin shell analysis with exactly calculated director vectors.
    Comput. Methods Appl. Mech. Eng., vol. 253, pp. 491–504, 2013.
    [doi]  [www]
     
  • A. Vuong, B. Simeon:
    On Isogeometric Analysis and Its Usage for Stress Calculation.
    H.G. Bock, X. P. Hoang, R. Rannacher and J. P. Schlöder (eds.) Modeling, Simulation and Optimization of Complex Processes, Proceedings of the Fourth International Conference on High Performance Scientific Computing, March 2-6, 2009, Hanoi, Vietnam. Springer: 305–314, 2012.
    [doi]  [www]
     
  • Ch. Heinrich, B. Simeon, St. Boschert:
    A Finite Volume Method on NURBS Geometries and its Application in Isogeometric Fluid-Structure Interaction.
    Math. Comput. Simul., vol. 82, pp. 1645–1666, 2012.
    [doi]  [www]
     
  • E. Zharovsky, A. Moosaie, A. Le Duc, M. Manhart, B. Simeon:
    On the numerical solution of a convection-diffusion equation for particle orientation dynamics on geodesic grids.
    Appl. Numer. Math., vol. 62, pp. 1554–1566, 2012.
    [doi]  [www]
     
  • A. Vuong, C. Giannelli, B. Jüttler, B. Simeon:
    A Hierarchical Approach to Local Refinement in Isogeometric Analysis.
    Comput. Methods Appl. Mech. Eng., vol. 200, pp. 3554–3567, 2011.
    [doi]  [www]
     
  • M. R. Dörfel, B. Simeon:
    Fluid-Structure Interaction: Acceleration of Strong Coupling by Preconditioning of the Fixed-Point Iteration.
    Numerical Mathematics and Advanced Applications. Springer: 741–749, 2011.
    [doi]  [www]
     
  • A. Vuong, Ch. Heinrich, B. Simeon:
    ISOGAT: A 2D Tutorial Matlab Code for Isogeometric Analysis.
    Comput. Aided Geom. Des., vol. 27, pp. 644–655, 2010.
    Link to corresponding software see:  [pdf]
    [doi]  [www]

  • Steffen Plunder, Bernd Simeon (2022).
    The mean-field limit for particle systems with uniform full-rank constraints.
    submitted. (arXiv Preprint # 2203.07249).
    [www]

  • Bernd Simeon.
    Die Macht der Computermodelle – Quellen der Erkenntnis oder digitale Orakel?
    Springer, 2023, ISBN-10: ‎366266298, ISBN-13: ‎978-3662662984.
    [www]
  • Bernd Simeon.
    Computational Flexible Multibody Dynamics – A Differential-Algebraic Approach.
    Springer, 2013, ISBN-13: ‎978-3-642-35157-0.
    [www]

Current Research Projects

 

Coupled analysis of active biological processes for meniscus tissue regeneration:
 

Project members:    Prof. Dr. Bernd Simeon, M. Sc. Henry Jäger and  Dr. Elise Grosjean

Project start:  02/2022

Funding:  Deutsche Forschungsgemeinschaft (DFG, German Research Foundation)

Project partners: 

Project contents and goals:

This project is part of SPP 2311 program (Robuste Kopplung kontinuumsbiomechanischer in silico Modelle für aktive biologische Systeme als Vorstufe klinischer Applikationen - Co-Design von Modellierung, Numerik und Nutzbarkeit).

During the last decades, mathematical modeling and simulation have become valuable tools for investigating complex biomedical systems. They significantly contribute to understand different aspects of a biological process, often allowing to extend the study results to related, mutually conditioned processes. This project is concerned with modeling, simulation and experimental validation for a prominent biomedical problem: the meniscus regeneration and involved cell and tissue-level phenomena.
Clinical studies indicate that partial and total meniscectomies lead to prevalence of premature osteoarthritis in knee joints. Therefore, substantial efforts are being made towards finding adequate regenerative tissue for meniscus replacement. Although there are some solutions described in the literature, to date the optimal substitute has not been developed. Most regenerative approaches are clinically motivated and focus rather on the practical application than on the micro- and macroscopic cellular mechanisms and the interactions with the scaffold material. The latter viewpoint is promising in the sense that it aims to understand the basic control mechanisms in cell-scaffold interactions under different environmental parameters, thus providing a selective prognosis of the most significant combinations of these parameters.

Thus, in collaboration with biologists, mathematicians, and engineers, our aim is to realize a sensitivity analysis on the meniscus regeneration simulations through differential-based methods. Moreover, the time scales of the different processes differ vastly and call for appropriate co-simulation strategies as well as model order reduction techniques. While meaningful clinical data is very difficult to obtain from in vivo meniscus tissue, this off-the-wall approach provides comprehensive underpinnings for the mathematical modeling and numerical simulation.
 


Scaled boundary isogeometrische Analyse mit leistungsstarken Merkmalen für getrimmte Objekte,

Kontinuität höherer Ordnung und die dynamische Strukturanalyse:

 

Projektmitarbeiter:    Prof. Dr. Bernd Simeon und M. Sc. Jeremias Nathanael Arf

Projektstart:  2020

Projektpartner:   Prof. Dr.-Ing. Sven Klinkel und M. Sc. Mathias Reichle (RWTH Aachen)

Förderung:         Deutsche Forschungsgemeinschaft (DFG)
 
 

Project Content and Objectives:

The integration of CAD procedures and FEM has been established through isogeometric analysis. In this approach, the computational domains are often defined by their boundaries. This is precisely where Scaled-Boundary Isogeometric Analysis (SB-IGA) comes into play, which deals with the parametrization of domains based on NURBS boundary surfaces. In the project, carried out in cooperation with RWTH Aachen, the focus lies on coupling various computational domains and ensuring global smoothness of the underlying basis functions. Furthermore, the advantages of the SB-IGA approach in the context of "trimming," i.e., the addition and removal of regions in CAD, are examined. Theoretical considerations and methods will then be applied in the field of structural dynamics.

 

The following graphic shows an "SB-IGA mesh of Scordelis-Lo shell" (left) as well as the corresponding "z-displacement" (right):