AG Differential-Algebraische Systeme

Forschungsgebiete

  • Angewandte und numerische Mathematik, insbesondere gekoppelte Systeme differential-algebraischer und partieller Differentialgleichungen
  • Multidisziplinäre Projekte in den Feldern Fahrzeugdynamik, Materialwissenschaften und Strömungsmechanik
  • Modellierung und Numerik von Formgedächtnismaterialien
  • Isogeometrische Finite Elemente
  • Haemodynamik und Dynamik der Skelett-Muskulatur

Publikationen

  • 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]

Aktuelle Forschungsprojekte

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)
 
 

Projektinhalt und Ziele:

Die Verbindung von CAD Verfahren und FEM wurde durch die isogeometrische Analysis etabliert. Dabei werden die Berechnungsgebiete oft durch deren Ränder definiert. Genau hier setzt Scaled-Boundary Isogeometric Analysis (SB-IGA) an, die sich mit der Parametrisierung von Gebieten  auf der Grundlage von NURBS Randflächen beschäftigt. Im Projekt, welches in Kooperation mit der RWTH Aachen bearbeitet wird, steht die Kopplung verschiedener Berechnungsgebiete sowie die globale Glattheit der zugrundeliegenden Ansatzfunktionen im Vordergrund. Des Weiteren wird untersucht, welche Vorteile der SB-IGA  Ansatz im Kontext von "Trimming", d.h. dem Zu- und Wegschneiden von Gebieten in CAD, aufweist. Die theoretischen Überlegungen und Methoden sollen dann im Bereich der Strukturdynamik angewendet werden.

 

Die nachfolgende Graphik zeigt ein "SB-IGA mesh of Scordelis-Lo shell" (li.) sowie die zugehörige "z-displacement" (re.):

Auswahl vergangener Forschungsprojekte

 

DYMARA - Ein dynamisches Manikin mit faserbasierter Modellierung der Skelettmuskulatur:
 

Projektmitarbeiter:    Prof. Dr. Bernd Simeon und Dr. Ing. Michael Gfrerer                           

Projektdauer:     Dez. 2016 - Dez. 2019   

Förderung:   BMBF - Verbundprojekt

In DYMARA kooperieren die Arbeitsgruppen von

  • Prof. Dr. Bernd Simeon (TU Kaiserslautern, Felix-Klein-Zentrum)
  • Prof. Dr.-Ing. habil. Sigrid Leyendecker (Friedrich-Alexander-Universität Erlangen-Nürnberg, Lehrstuhl für Angewandte Dynamik)
  • Dr. Michael Burger (Fraunhofer Institut für Techno- und Wirtschaftsmathematik)

mit den Praxispartnern

  • fleXstructures GmbH, Kaiserslautern
  • MaRhyThe-Systems GmbH & Co. KG, Gröbenzel
     

Projektinhalt und Ziele:

Das Verbundprojekt DYMARA hat die Entwicklung eines innovativen digitalen Menschmodells (Manikins) mit  detaillierter Modellierung der Skelettmuskulatur und schnellen numerischen Algorithmen zum Ziel. Mit diesem Manikin soll es möglich werden, den Menschen simulationsgestützt auf optimale Weise in sein Arbeitsumfeld zu integrieren und Ermüdungen, Erkrankungen sowie Unfälle am Arbeitsplatz zu vermeiden. Neben diesen ergonomischen Gesichtspunkten soll das Menschmodell auch zur Therapieplanung im muskulären Bereich und zur Gestaltung von Prothesen und Orthesen eingesetzt werden können. Um die Dynamik des muskuloskeletalen Systems hinreichend genau zu erfassen, wird ein Modellierungsansatz verfolgt, der auf der Methode der mechanischen Mehrkörpersysteme (MKS) basiert. Solche Modelle sind durch die Robotik inspiriert und werden bereits heute in vielen biomechanischen Anwendungsfeldern eingesetzt. Die Modellierung der Muskulatur stellt jedoch nach wie vor eine große Herausforderung dar, insbesondere wenn Aspekte wie Rechenzeit auf der einen und Berücksichtigung der anatomischen und physiologischen Gegebenheiten auf der anderen Seite zu beachten sind. Hier setzen wir mit unserem Projekt an: Ein neu zu entwickelndes eindimensionales Kontinuumsmodell, das einzelne Muskelfaserbündel realitätsnah beschreibt, soll die bisher üblichen diskreten Kraftelemente im MKS-Modell ersetzen und mit schnellen, problemangepassten numerischen Algorithmen zur Berechnung von Bewegungssequenzen und zur Steuerung des Manikins kombiniert werden.
 


MOTOR - Multi-ObjecTive design Optimization of fluid eneRgy machines:
 

Projektmitarbeiter:  Prof. Dr. Bernd Simeon und Dipl. Math. Alexander Shamanskiy

Projektdauer:  Sept. 2015 - Sept. 2018

Projektseite:              project-motor.eu


Projektpartner:

  • Delft University of Technology (Netherlands)
  • Caterpillar (Sweden)
  • ESS Engineering Software Steyr GmbH (Austria)
  • Johannes Kepler University of Linz (Austria)
  • Maritime Research Institute Nederland (Netherlands)
  • Mavel (Czech Republic)
  • MTU Aero Engines AG, Munich (Germany)
  • University of West Bohemia (Czech Republic)
  • TU Dortmund University (Germany)
  • TU Kaiserslautern (Germany)
  • Von Karman Institute of Fluid Dynamics (Belgium)


Projektinhalt und Ziele:

The MOTOR project focuses on ICT-enabled design optimization technologies for fluid energy machines
(FEMs) that transfer mechanical energy to and from the fluid, in particular for aircraft engines, ship pro-
pellers, water turbines, and screw machines. The performance of these machines essentially depends
on the shape of their geometry, which is described by functional free-form surfaces. Even small modifica-
tions have significant impact on the performance; hence the design process requires a very accurate
representation of the geometry.
Our vision is to link all computational tools involved in the chain of design, simulation and optimization to
the same representation of the geometry, thereby reducing the number of approximate conversion steps
between different representations. The improved accuracy and reliability of numerical simulations ena-
bles the design of more efficient FEMs by effective design optimization methods. MOTOR also exploits
the synergies between the design optimization technologies for the different types of FEMs that have so
far been developed independently.
MOTOR adopts a modular approach for developing novel methodologies and computational tools and
integrating them into real process chains, contributing

  • a volumetric mesh generator with exact interface matching for multi-domain geometries enabling a high-order multi-physics simulations with enhanced accuracy,
  • an isogeometric analysis simulation toolbox for CFD, CSM, and FSI problems and advanced interactive visualization toolkit for high-order solutions, and
  • automatic shape optimization based on a multi-level approach in the parameterization enabling different levels of shape variety to combine design space exploration with local searches.

The effectiveness of our approach in terms of reduced time to production and increased efficiency of theoptimally designed product will be validated by developing four proof-of-concept demonstrators with themodernized process chains.