Institutionen der Universität Bayreuth
Lehrstuhl Angewandte Mathematik - Univ.-Prof. Dr. Anton Schiela

Model Predictive Control : Engineering Methods for Economists.
Hrsg.: Daniilidis, Aris ; Grüne, Lars ; Haunschmied, Josef ; Tragler, Gernot
Cham, Switzerland : Springer , 2025 . - 198 S. - (Dynamic Modeling and Econometrics in Economics and Finance ; 31 )

Weigl, Laura ; Schiela, Anton:
Newton's method for nonlinear mappings into vector bundles.
Bayreuth , 2024 . - 31 S.
DOI: https://doi.org/10.48550/arXiv.2404.04073

Köhne, Frederik ; Philipp, Friedrich M. ; Schaller, Manuel ; Schiela, Anton ; Worthmann, Karl:
L∞-error bounds for approximations of the Koopman operator by kernel extended dynamic mode decomposition.
Ilmenau ; Bayreuth , 2024 . - 21 S.
DOI: https://doi.org/10.48550/arXiv.2403.18809

Sproll, Tobias:
Numerical Identification of Motor Units in Muscle Tissue from High Resolution EMG Data.
Bayreuth , 2024 . - VIII, 103 S.
( Dissertation, 2024 , Universität Bayreuth, Fakultät für Mathematik, Physik und Informatik)
DOI: https://doi.org/10.15495/EPub_UBT_00007473

Köhne, Frederik ; Kreis, Leonie ; Schiela, Anton ; Herzog, Roland:
Adaptive Step Sizes for Preconditioned Stochastic Gradient Descent.
Bayreuth ; Heidelberg , 2023 . - 31 S.
DOI: https://doi.org/10.48550/arXiv.2311.16956

Herzog, Roland ; Köhne, Frederik ; Kreis, Leonie ; Schiela, Anton:
Frobenius-Type Norms and Inner Products of Matrices and Linear Maps with Applications to Neural Network Training.
Bayreuth ; Heidelberg , 2023 . - 14 S.
DOI: https://doi.org/10.48550/arXiv.2311.15419

Herberg, Evelyn ; Herzog, Roland ; Köhne, Frederik ; Kreis, Leonie ; Schiela, Anton:
Sensitivity-Based Layer Insertion for Residual and Feedforward Neural Networks.
Bayreuth ; Heidelberg , 2023 . - 15 S.
DOI: https://doi.org/10.48550/arXiv.2311.15995

Pötzl, Bastian ; Schiela, Anton ; Jaap, Patrick:
Inexact Proximal Newton methods in Hilbert spaces.
In: Computational Optimization and Applications. (16 August 2023) . - S. 1-37.
DOI: https://doi.org/10.1007/s10589-023-00515-x

Sproll, Tobias ; Schiela, Anton:
Numerical Solution of an Identifcation Problem in Electromyography.
Bayreuth , 2023 . - 21 S.

Herberg, Evelyn ; Herzog, Roland ; Köhne, Frederik:
Time Regularization in Optimal Time Variable Learning.
Heidelberg , 2023 . - 9 S.
DOI: https://doi.org/10.48550/arXiv.2306.16111

Pötzl, Bastian:
Inexact Proximal Newton Methods for Finite Strain Plasticity.
Bayreuth , 2023 . - X, 215 S.
( Dissertation, 2023 , Universität Bayreuth, Fakultät für Mathematik, Physik und Informatik)
DOI: https://doi.org/10.15495/EPub_UBT_00007159

Grüne, Lars ; Schaller, Manuel ; Schiela, Anton:
Efficient Model Predictive Control for parabolic PDEs with goal oriented error estimation.
In: SIAM Journal on Scientific Computing. Bd. 44 (2022) Heft 1 . - A471-A500.
DOI: https://doi.org/10.1137/20M1356324

Faulwasser, Timm ; Grüne, Lars ; Humaloja, Jukka-Pekka ; Schaller, Manuel:
The interval turnpike property for adjoints.
In: Pure and Applied Functional Analysis. Bd. 7 (2022) Heft 4 . - S. 1187-1207.

Pötzl, Bastian ; Schiela, Anton ; Jaap, Patrick:
Second order semi-smooth proximal Newton methods in Hilbert spaces.
In: Computational Optimization and Applications. Bd. 82 (2022) . - S. 465-498.
DOI: https://doi.org/10.1007/s10589-022-00369-9

Schaller, Manuel:
Sensitivity Analysis and Goal Oriented Error Estimation for Model Predictive Control.
Bayreuth , 2021 . - IX, 185 S.
( Dissertation, 2021 , Universität Bayreuth, Fakultät für Mathematik, Physik und Informatik)
DOI: https://doi.org/10.15495/EPub_UBT_00005538

Grüne, Lars ; Schaller, Manuel ; Schiela, Anton:
Abstract nonlinear sensitivity and turnpike analysis and an application to semilinear parabolic PDEs.
In: ESAIM : Control, Optimisation and Calculus of Variations. Bd. 27 (2021) . - 56.
DOI: https://doi.org/10.1051/cocv/2021030

Sproll, Tobias ; Schiela, Anton:
An adjoint approach to identification in Electromyography : Modeling and first order optimality conditions.
In: Inverse Problems. Bd. 37 (2021) Heft 12 . - 125012.
DOI: https://doi.org/10.1088/1361-6420/ac362c

Ortiz, Julián:
Constrained Optimization on Manifolds.
Bayreuth , 2020 . - IX, 193 S.
( Dissertation, 2020 , Universität Bayreuth, Fakultät für Mathematik, Physik und Informatik)
DOI: https://doi.org/10.15495/EPub_UBT_00005186

Siegl, Alexander:
Iterative Löser zur Schrittberechnung in einer Composite-Step Methode.
Bayreuth , 2020 . - ii, 64 S.
(Masterarbeit, 2020 , Universität Bayreuth, Fakultät für Mathematik, Physik und Informatik, Mathematisches Institut)

Grüne, Lars ; Schaller, Manuel ; Schiela, Anton:
Exponential sensitivity analysis for Model Predictive Control of PDEs.
Department of Mathematics, University of Bayreuth
Bayreuth , 2020 . - 4 S.

Grüne, Lars:
Why does strict dissipativity help in model predictive control?
Department of Mathematics, University of Bayreuth
Bayreuth , 2020 . - 4 S.

Grüne, Lars ; Schaller, Manuel ; Schiela, Anton:
Exponential sensitivity and turnpike analysis for linear quadratic optimal control of general evolution equations.
In: Journal of Differential Equations. Bd. 268 (2020) Heft 12 . - S. 7311-7341.
DOI: https://doi.org/10.1016/j.jde.2019.11.064

Grüne, Lars ; Junge, Oliver:
From Bellman to Dijkstra : Set oriented construction of globally optimal controllers.
In: Junge, Oliver ; Schütze, Oliver ; Froyland, Gary ; Ober-Blöbaum, Sina ; Padberg-Gehle, Kathrin (Hrsg.): Advances in dynamics, optimization and computation : a volume dedicated to Michael Dellnitz on the occasion of his 60th birthday. - Cham : Springer, 2020 . - S. 265-294 . - (Studies in Systems, Decision and Control ; 304 )
DOI: https://doi.org/10.1007/978-3-030-51264-4_11

Banholzer, Stefan ; Fabrini, Giulia ; Grüne, Lars ; Volkwein, Stefan:
Multiobjective model predictive control of a parabolic advection-diffusion-reaction equation.
In: Mathematics. Bd. 8 (2020) Heft 5 . - 777.
DOI: https://doi.org/10.3390/math8050777

Schiela, Anton ; Stöcklein, Matthias:
Algorithms for Optimal Control of Elastic Contact Problems with Finite Strain.
Bayreuth , 2019 . - 21 S.

Ortiz, Julián ; Schiela, Anton:
A composite step method for equality constrained optimization on manifolds.
Bayreuth , 2019 . - 27 S.

Schiela, Anton ; Ortiz, Julián:
Second order directional shape derivatives.
Bayreuth , 2019 . - 25 S.

Müller, Georg:
Optimal control of time-discretized contact problems.
Bayreuth , 2019 . - x, 213 S.
( Dissertation, 2019 , Universität Bayreuth, Fakultät für Mathematik, Physik und Informatik)
DOI: https://doi.org/10.15495/EPub_UBT_00004379

Grüne, Lars ; Schaller, Manuel ; Schiela, Anton:
Sensitivity Analysis of Optimal Control for a Class of Parabolic PDEs Motivated by Model Predictive Control.
In: SIAM Journal on Control and Optimization. Bd. 57 (2019) Heft 4 . - S. 2753-2774.
DOI: https://doi.org/10.1137/18M1223083

Schaller, Manuel ; Schiela, Anton ; Stöcklein, Matthias:
A Composite Step Method with Inexact Step Computations for PDE Constrained Optimization.
Bayreuth , 2018 . - 29 S.

Schiela, Anton ; Stöcklein, Matthias:
Optimal Control of Static Contact in Finite Strain Elasticity.
Bayreuth , 2018 . - 28 S.

Grüne, Lars ; Schaller, Manuel ; Schiela, Anton:
Sensitivity analysis of optimal control motivated by model predictive control.
In: Proceedings of the 23rd International Symposium on Mathematical Theory of Networks and Systems. - Hong Kong , 2018 . - S. 93-96

Deutschen, Thomas ; Gasser, Sophie ; Schaller, Manuel ; Siehr, Jochen:
Modeling the self-discharge by voltage decay of a NMC/graphite lithium-ion cell.
In: Journal of Energy Storage. Bd. 19 (2018) . - S. 113-119.
DOI: https://doi.org/10.1016/j.est.2018.07.003

Sproll, Tobias ; Schiela, Anton ; Lowery, Madeleine:
Numerical Identification of Motor Units using an Optimal Control Approach.
In: IFAC-PapersOnLine. Bd. 51 (2018) Heft 2 . - S. 174-179.
DOI: https://doi.org/10.1016/j.ifacol.2018.03.030

Christof, Constantin ; Müller, Georg:
A Note on the Equivalence and the Boundary Behavior of a Class of Sobolev Capacities.
Bayreuth , 2017 . - 27 S.

Clason, Christian ; Schiela, Anton:
Optimal control of elliptic equations with positive measures.
In: ESAIM : Control, Optimisation and Calculus of Variations. Bd. 23 (2017) Heft 1 . - S. 217-240.
DOI: https://doi.org/10.1051/cocv/2015046

Stöcklein, Matthias:
Optimal Control of Static Contact Problems in Linear Elasticity.
Bayreuth, Germany , 2016 . - 96 S.
(Masterarbeit, 2016 , Universität Bayreuth, Department of Mathematics, Faculty of Mathematics, Physics and Computer Science)

Müller, Georg ; Schiela, Anton:
On the Control of Time Discretized Dynamical Contact Problems.
Bayreuth , 2016 . - 35 S.

Lubkoll, Lars ; Schiela, Anton ; Weiser, Martin:
An affine covariant composite step method for optimization with PDEs as equality constraints.
Konrad-Zuse-Zentrum für Informationstechnik Berlin
Berlin , 2015 . - 40 S. - (ZIB-Report ; 15-09 )

Schiela, Anton:
A flexible framework for cubic regularization algorithms for non-convex optimization in function space.
Hamburg-Harburg , 2014 . - 26 S. - (Bericht / Technische Universität Hamburg-Harburg, Institut für Mathematik ; 183 )

Hintermüller, Michael ; Schiela, Anton ; Wollner, Winnifried:
The length of the primal-dual path in Moreau-Yosida-based path-following methods for state constrained optimal control.
In: SIAM Journal on Optimization. Bd. 24 (2014) Heft 1 . - S. 108-126.
DOI: https://doi.org/10.1137/120866762

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Schiela, Anton ; Ulbrich, Stefan:
Operator preconditioning for a class of inequality constrained optimal control problems.
In: SIAM Journal on Optimization. Bd. 24 (2014) Heft 1 . - S. 435-466.
DOI: https://doi.org/10.1137/120877532

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Lubkoll, Lars ; Schiela, Anton ; Weiser, Martin:
An optimal control problem in polyconvex hyperelasticity.
In: SIAM Journal on Control and Optimization. Bd. 52 (2014) Heft 3 . - S. 1403-1422.
DOI: https://doi.org/10.1137/120876629

Rez.:

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Sander, Oliver ; Schiela, Anton:
Variational analysis of the coupling between a geometrically exact Cosserat rod and an elastic continuum.
In: Zeitschrift für angewandte Mathematik und Physik. Bd. 65 (2014) Heft 6 . - S. 1261-1288.
DOI: https://doi.org/10.1007/s00033-013-0389-y

Rez.:

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Schiela, Anton:
A concise proof for existence and uniqueness of solutions of linear parabolic PDEs in the context of optimal control.
In: Systems & Control Letters. Bd. 62 (2013) Heft 10 . - S. 895-901.
DOI: https://doi.org/10.1016/j.sysconle.2013.06.013

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Schiela, Anton ; Wachsmuth, Daniel:
Convergence analysis of smoothing methods for optimal control of stationary variational inequalities with control constraints.
In: ESAIM : Mathematical Modelling and Numerical Analysis. Bd. 47 (2013) Heft 3 . - S. 771-787.
DOI: https://doi.org/10.1051/m2an/2012049

Rez.:

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Schiela, Anton:
An interior point method in function space for the efficient solution of state constrained optimal control problems.
In: Mathematical Programming Series A. Bd. 138 (2013) Heft 1-2 . - S. 83-114.
DOI: https://doi.org/10.1007/s10107-012-0595-y

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Deuflhard, Peter ; Schiela, Anton:
Katz und Maus.
In: Besser als Mathe : Moderne angewandte Mathematik aus dem MATHEON zum Mitmachen. 2., aktualisierte Auflage. - Wiesbaden : Springer Fachmedien, 2013 . - S. 29-40
DOI: https://doi.org/10.1007/978-3-658-01004-1_5

Klapproth, Corinna ; Schiela, Anton ; Deuflhard, Peter:
Adaptive numerical integration of dynamical contact problems.
2012
Veranstaltung: Thematic Conference of the European Community on Computational Methods in Applied Sciences (ECCOMAS), 2nd International Conference on Computational Contact Mechanics (ICCCM 2011) , 15.-17. Juni 2011 , Hannover, Germany.
(Veranstaltungsbeitrag: Kongress/Konferenz/Symposium/Tagung , Vortrag )

Klapproth, Corinna ; Schiela, Anton ; Deuflhard, Peter:
Fast algorithms for the simulation of human knee joint motion.
In: Proceedings of the IASTED International Conference on Biomedical Engineering (BioMed 2012), February 15-17, 2012, Innsbruck, Austria. - Anaheim, CA : ACTA Press, 2012 . - S. 696-699
DOI: https://doi.org/10.2316/P.2012.764-176

Deuflhard, Peter ; Schiela, Anton ; Weiser, Martin:
Mathematical cancer therapy planning in deep regional hyperthermia.
In: Acta Numerica. Bd. 21 (2012) . - S. 307-378.
DOI: https://doi.org/10.1017/S0962492912000049

Rez.:

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Götschel, Sebastian ; Weiser, Martin ; Schiela, Anton:
Solving Optimal Control Problems with the Kaskade 7 Finite Element Toolbox.
In: Dedner, Andreas ; Flemisch, Bernd ; Klöfkorn, Robert (Hrsg.): Advances in DUNE : Proceedings of the DUNE User Meeting, Held in October 6th–8th 2010 in Stuttgart, Germany. - Berlin : Springer, 2012 . - S. 101-112
DOI: https://doi.org/10.1007/978-3-642-28589-9_8

Klapproth, Corinna ; Schiela, Anton ; Deuflhard, Peter:
Adaptive timestep control for the contact-stabilized Newmark method.
In: Numerische Mathematik. Bd. 119 (2011) Heft 1 . - S. 49-81.
DOI: https://doi.org/10.1007/s00211-011-0374-3

Rez.:

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Schiela, Anton ; Wollner, Winnifried:
Barrier Methods for Optimal Control Problems with Convex Nonlinear Gradient State Constraints.
In: SIAM Journal on Optimization. Bd. 21 (2011) Heft 1 . - S. 269-286.
DOI: https://doi.org/10.1137/080742154

Rez.:

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Hinze, Michael ; Schiela, Anton:
Discretization of interior point methods for state constrained elliptic optimal control problems : optimal error estimates and parameter adjustment.
In: Computational Optimization and Applications. Bd. 48 (2011) Heft 3 . - S. 581-600.
DOI: https://doi.org/10.1007/s10589-009-9278-x

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Schiela, Anton ; Günther, Andreas:
An interior point algorithm with inexact step computation in function space for state constrained optimal control.
In: Numerische Mathematik. Bd. 119 (2011) Heft 2 . - S. 373-407.
DOI: https://doi.org/10.1007/s00211-011-0381-4

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Meyer, Christian ; Panizzi, Lucia ; Schiela, Anton:
Uniqueness criteria for the adjoint equation in state-constrained elliptic optimal control.
In: Numerical Functional Analysis and Optimization. Bd. 32 (2011) Heft 9 . - S. 983-1007.
DOI: https://doi.org/10.1080/01630563.2011.587074

Rez.:

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Schiela, Anton ; Weiser, Martin:
Barrier Methods for a Control Problem from Hyperthermia Treatment Planning.
In: Recent Advances in Optimization and its Applications in Engineering. - Berlin : Springer, 2010 . - S. 419-428
DOI: https://doi.org/10.1007/978-3-642-12598-0_36

Klapproth, Corinna ; Schiela, Anton ; Deuflhard, Peter:
Consistency results on Newmark methods for dynamical contact problems.
In: Numerische Mathematik. Bd. 116 (2010) Heft 1 . - S. 65-94.
DOI: https://doi.org/10.1007/s00211-010-0300-0

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Deuflhard, Peter ; Kornhuber, Ralf ; Sander, Oliver ; Schiela, Anton ; Weiser, Martin:
Mathematics cures virtual patients.
In: MATHEON - Mathematics for Key Technologies. - Zürich : European Math. Soc., 2010 . - S. 7-25 . - (EMS Series in Industrial and Applied Mathematics ; 1 )
DOI: https://doi.org/10.4171/137

Schiela, Anton:
Barrier methods for optimal control problems with state constraints.
In: SIAM Journal on Optimization. Bd. 20 (2009) Heft 2 . - S. 1002-1031.
DOI: https://doi.org/10.1137/070692789

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Schiela, Anton:
An extended mathematical framework for barrier methods in function space.
In: Bercovier, Michel ; Gander, Martin J. ; Kornhuber, Ralf ; Widlund, Olof (Hrsg.): Domain decomposition methods in science and engineering XVIII. - Berlin : Springer, 2009 . - S. 201-208 . - (Lecture Notes in Computational Science and Engineering ; 70 )
DOI: https://doi.org/10.1007/978-3-642-02677-5_21

Rez.:

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Haller-Dintelmann, Robert ; Meyer, Christian ; Rehberg, Joachim ; Schiela, Anton:
Hölder continuity and optimal control for nonsmooth elliptic problems.
In: Applied Mathematics and Optimization. Bd. 60 (2009) Heft 3 . - S. 397-428.
DOI: https://doi.org/10.1007/s00245-009-9077-x

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Schiela, Anton:
Interior point methods in function space : Newton path-following and adaptivity.
In: Oberwolfach Reports. Bd. 6 (2009) Heft 04 . - S. 254-256.
DOI: https://doi.org/10.4171/OWR/2009/04

Prüfert, Uwe ; Schiela, Anton:
The minimization of a maximum-norm functional subject to an elliptic PDE and state constraints.
In: ZAMM : Journal of Applied Mathematics and Mechanics = Zeitschrift für angewandte Mathematik und Mechanik. Bd. 89 (2009) Heft 7 . - S. 536-551.
DOI: https://doi.org/10.1002/zamm.200800097

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Klapproth, Corinna ; Deuflhard, Peter ; Schiela, Anton:
A perturbation result for dynamical contact problems.
In: Numerical Mathematics : Theory, Methods and Applications. Bd. 2 (2009) Heft 3 . - S. 237-257.
DOI: https://doi.org/10.4208/nmtma.2009.m9003

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Schiela, Anton:
State constrained optimal control problems with states of low regularity.
In: SIAM Journal on Control and Optimization. Bd. 48 (2009) Heft 4 . - S. 2407-2432.
DOI: https://doi.org/10.1137/080727610

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Weiser, Martin ; Gänzler, Tobias ; Schiela, Anton:
A control reduced primal interior point method for a class of control constrained optimal control problems.
In: Computational Optimization and Applications. Bd. 41 (2008) Heft 1 . - S. 127-145.
DOI: https://doi.org/10.1007/s10589-007-9088-y

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Schiela, Anton:
A simplified approach to semismooth Newton methods in function space.
In: SIAM Journal on Optimization. Bd. 19 (2008) Heft 3 . - S. 1417-1432.
DOI: https://doi.org/10.1137/060674375

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Schiela, Anton ; Weiser, Martin:
Superlinear convergence of the control reduced interior point method for PDE constrained optimization.
In: Computational Optimization and Applications. Bd. 39 (2008) Heft 3 . - S. 369-393.
DOI: https://doi.org/10.1007/s10589-007-9057-5

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Schiela, Anton:
Optimality Conditions for Convex State Constrained Optimal Control Problems with Discontinuous States.
Konrad-Zuse-Zentrum für Informationstechnik Berlin
Berlin , 2007 . - (ZIB-Report ; 07-35 )

Schiela, Anton:
A continuity result for Nemyckii Operators and some applications in PDE constrained optimal control.
Konrad-Zuse-Zentrum für Informationstechnik Berlin
Berlin , 2006 . - (ZIB-Report ; 06-41 )

Schiela, Anton:
Convergence of the Control Reduced Interior Point Method for PDE Constrained Optimal Control with State Constraints.
Konrad-Zuse-Zentrum für Informationstechnik Berlin
Berlin , 2006 . - (ZIB-Report ; 06-16 )

Weiser, Martin ; Schiela, Anton ; Deuflhard, Peter:
Asymptotic mesh independence of Newton's method revisited.
In: SIAM Journal on Numerical Analysis. Bd. 42 (2005) Heft 5 . - S. 1830-1845.
DOI: https://doi.org/10.1137/S0036142903434047

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Weiser, Martin ; Schiela, Anton:
Function space interior point methods for PDE constrained optimization.
In: Proceedings in Applied Mathematics and Mechanics. Bd. 4 (2004) Heft 1 . - S. 43-46.
DOI: https://doi.org/10.1002/pamm.200410011

Schiela, Anton ; Bornemann, Folkmar:
Sparsing in real time simulation.
In: ZAMM : Journal of Applied Mathematics and Mechanics = Zeitschrift für angewandte Mathematik und Mechanik. Bd. 83 (2003) Heft 10 . - S. 637-647.
DOI: https://doi.org/10.1002/zamm.200310070

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Schiela, Anton ; Olsson, Hans:
Mixed-mode integration for real-time simulation.
In: Papers of the Modelica Workshop 2000. - Linköping, Sweden : Modelica Association, 2000 . - S. 69-75