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2. Index concepts for linear differential-algebraic equations in finite and infinite dimensions

Author

Erbay, Mehmet, Jacob, Birgit, Morris, Kirsten, Reis, Timo, and Tischendorf, Caren

Subjects
Mathematics - Dynamical Systems
Abstract

Different index concepts for linear differential-algebraic equations are defined in the general Banach space setting, and compared. For regular finite-dimensional linear differential-algebraic equations, all these indices exist and are equivalent. For infinite-dimensional systems, the situation is more complex. It is proven that although some indices imply others, in general they are not equivalent. The situation is illustrated with a number of examples.

Published
2024

3. Splitting Methods for Linear Coupled Field-Circuit DAEs

Author

Diab, Malak, Tischendorf, Caren, Bock, Hans Georg, Series Editor, de Hoog, Frank, Series Editor, Friedman, Avner, Series Editor, Gupta, Arvind, Series Editor, Nachbin, André, Series Editor, Ozawa, Tohru, Series Editor, Pulleyblank, William R., Series Editor, Rusten, Torgeir, Series Editor, Santosa, Fadil, Series Editor, Seo, Jin Keun, Series Editor, Tornberg, Anna-Karin, Series Editor, van Beurden, Martijn, editor, Budko, Neil V., editor, Ciuprina, Gabriela, editor, Schilders, Wil, editor, Bansal, Harshit, editor, and Barbulescu, Ruxandra, editor

Published
2024
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4. Waveform relaxation for low frequency coupled field/circuit differential-algebraic models of index 2

Author

Garcia, Idoia Cortes, Pade, Jonas, Schöps, Sebastian, and Tischendorf, Caren

Subjects
Mathematics - Numerical Analysis, Computer Science - Computational Engineering, Finance, and Science, 35Q61, 65Z05, 65L05, 68W10
Abstract

Motivated by the task to design quench protection systems for superconducting magnets in particle accelerators we address a coupled field/circuit simulation based on a magneto-quasistatic field modeling. We investigate how a waveform relaxation of Gau{\ss}-Seidel type performs for a coupled simulation when circuit solving packages are used that describe the circuit by the modified nodal analysis. We present sufficient convergence criteria for the coupled simulation of FEM discretised field models and circuit models formed by a differential-algebraic equation (DAE) system of index 2. In particular, we demonstrate by a simple benchmark system the drastic influence of the circuit topology on the convergence behavior of the coupled simulation.

Published
2020

5. Generalized Circuit Elements

Author

Garcia, Idoia Cortes, Schöps, Sebastian, Strohm, Christian, and Tischendorf, Caren

Subjects
Mathematics - Numerical Analysis, 34A09, 35Q61, 78A25, 94C05, 65L80, 78M10, 78M12, 94C15
Abstract

The structural analysis, i.e., the investigation of the differential-algebraic nature, of circuits containing simple elements, i.e., resistances, inductances and capacitances is well established. However, nowadays circuits contain all sorts of elements, e.g. behavioral models or partial differential equations stemming from refined device modelling. This paper proposes the definition of generalized circuit elements which may for example contain additional internal degrees of freedom, such that those elements still behave structurally like resistances, inductances and capacitances. Several complex examples demonstrate the relevance of those definitions.

Published
2019

12. Einführung

Author

Bärwolff, Günter, Tischendorf, Caren, Bärwolff, Günter, and Tischendorf, Caren

Published
2022
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18. Splitting Methods for Linear Circuit DAEs of Index 1 in port-Hamiltonian Form

Author

Diab, Malak, Tischendorf, Caren, Bock, Hans Georg, Series Editor, de Hoog, Frank, Series Editor, Friedman, Avner, Series Editor, Gupta, Arvind, Series Editor, Nachbin, André, Series Editor, Ozawa, Tohru, Series Editor, Pulleyblank, William R., Series Editor, Rusten, Torgeir, Series Editor, Santosa, Fadil, Series Editor, Seo, Jin Keun, Series Editor, Tornberg, Anna-Karin, Series Editor, van Beurden, Martijn, editor, Budko, Neil, editor, and Schilders, Wil, editor

Published
2021
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19. Waveform Relaxation for Low Frequency Coupled Field/Circuit Differential-Algebraic Models of Index 2

Author

Garcia, Idoia Cortes, Pade, Jonas, Schöps, Sebastian, Tischendorf, Caren, Bock, Hans Georg, Series Editor, de Hoog, Frank, Series Editor, Friedman, Avner, Series Editor, Gupta, Arvind, Series Editor, Nachbin, André, Series Editor, Ozawa, Tohru, Series Editor, Pulleyblank, William R., Series Editor, Rusten, Torgeir, Series Editor, Santosa, Fadil, Series Editor, Seo, Jin Keun, Series Editor, Tornberg, Anna-Karin, Series Editor, van Beurden, Martijn, editor, Budko, Neil, editor, and Schilders, Wil, editor

Published
2021
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20. MathEnergy – Mathematical Key Technologies for Evolving Energy Grids

Author

Clees, Tanja, Baldin, Anton, Benner, Peter, Grundel, Sara, Himpe, Christian, Klaassen, Bernhard, Küsters, Ferdinand, Marheineke, Nicole, Nikitina, Lialia, Nikitin, Igor, Pade, Jonas, Stahl, Nadine, Strohm, Christian, Tischendorf, Caren, Wirsen, Andreas, Bock, Hans Georg, Series Editor, de Hoog, Frank, Series Editor, Friedman, Avner, Series Editor, Gupta, Arvind, Series Editor, Nachbin, André, Series Editor, Ozawa, Tohru, Series Editor, Pulleyblank, William R., Series Editor, Rusten, Torgeir, Series Editor, Santosa, Fadil, Series Editor, Seo, Jin Keun, Series Editor, Tornberg, Anna-Karin, Series Editor, Göttlich, Simone, editor, Herty, Michael, editor, and Milde, Anja, editor

Published
2021
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23. Generalized Elements for a Structural Analysis of Circuits

Author

Cortes Garcia, Idoia, Schöps, Sebastian, Strohm, Christian, Tischendorf, Caren, Ilchmann, Achim, Editor-in-Chief, Reis, Timo, Editor-in-Chief, Biegler, Larry, Editorial Board Member, Campbell, Stephen, Editorial Board Member, Führer, Claus, Editorial Board Member, Gerdts, Matthias, Editorial Board Member, Grundel, Sara, Editorial Board Member, Kunkel, Peter, Editorial Board Member, Linh, Vu Hoang, Editorial Board Member, März, Roswitha, Editorial Board Member, Riaza, Ricardo, Editorial Board Member, Sager, Sebastian, Editorial Board Member, Schöps, Sebastian, Editorial Board Member, Simeon, Bernd, Editorial Board Member, Trenn, Stephan, Editorial Board Member, and Zerz, Eva, Editorial Board Member

Published
2020
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25. Holistic / Monolithic Time Integration

Author

Schoenmaker, Wim, Brachtendorf, Hans-Georg, Bittner, Kai, Tischendorf, Caren, Strohm, Christian, Bock, Hans Georg, Series Editor, de Hoog, Frank, Series Editor, Friedman, Avner, Series Editor, Gupta, Arvind, Series Editor, Nachbin, André, Series Editor, Ozawa, Tohru, Series Editor, Pulleyblank, William R., Series Editor, Rusten, Torgeir, Series Editor, Santosa, Fadil, Series Editor, Seo, Jin Keun, Series Editor, Tornberg, Anna-Karin, Series Editor, ter Maten, E. Jan W., editor, Brachtendorf, Hans-Georg, editor, Pulch, Roland, editor, Schoenmaker, Wim, editor, and De Gersem, Herbert, editor

Published
2019
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26. EM-Equations, Coupling to Heat and to Circuits

Author

Schoenmaker, Wim, Brachtendorf, Hans-Georg, Bittner, Kai, Tischendorf, Caren, Strohm, Christian, Bock, Hans Georg, Series Editor, de Hoog, Frank, Series Editor, Friedman, Avner, Series Editor, Gupta, Arvind, Series Editor, Nachbin, André, Series Editor, Ozawa, Tohru, Series Editor, Pulleyblank, William R., Series Editor, Rusten, Torgeir, Series Editor, Santosa, Fadil, Series Editor, Seo, Jin Keun, Series Editor, Tornberg, Anna-Karin, Series Editor, ter Maten, E. Jan W., editor, Brachtendorf, Hans-Georg, editor, Pulch, Roland, editor, Schoenmaker, Wim, editor, and De Gersem, Herbert, editor

Published
2019
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27. Discretizations

Author

Schoenmaker, Wim, Brachtendorf, Hans-Georg, Bittner, Kai, Tischendorf, Caren, Strohm, Christian, Bock, Hans Georg, Series Editor, de Hoog, Frank, Series Editor, Friedman, Avner, Series Editor, Gupta, Arvind, Series Editor, Nachbin, André, Series Editor, Ozawa, Tohru, Series Editor, Pulleyblank, William R., Series Editor, Rusten, Torgeir, Series Editor, Santosa, Fadil, Series Editor, Seo, Jin Keun, Series Editor, Tornberg, Anna-Karin, Series Editor, ter Maten, E. Jan W., editor, Brachtendorf, Hans-Georg, editor, Pulch, Roland, editor, Schoenmaker, Wim, editor, and De Gersem, Herbert, editor

Published
2019
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28. Nanoelectronic Coupled Problems Solutions – Highlights from the nanoCOPS Project

Author

Tischendorf, Caren, ter Maten, E. Jan W., Schoenmaker, Wim, Bock, Hans Georg, Series Editor, de Hoog, Frank, Series Editor, Friedman, Avner, Series Editor, Gupta, Arvind, Series Editor, Nachbin, André, Series Editor, Ozawa, Tohru, Series Editor, Pulleyblank, William R., Series Editor, Rusten, Torgeir, Series Editor, Santosa, Fadil, Series Editor, Seo, Jin Keun, Series Editor, Tornberg, Anna-Karin, Series Editor, ter Maten, E. Jan W., editor, Brachtendorf, Hans-Georg, editor, Pulch, Roland, editor, Schoenmaker, Wim, editor, and De Gersem, Herbert, editor

Published
2019
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29. Gas Network Benchmark Models

Author

Benner, Peter, Grundel, Sara, Himpe, Christian, Huck, Christoph, Streubel, Tom, Tischendorf, Caren, Ilchmann, Achim, Editor-in-Chief, Reis, Timo, Editor-in-Chief, Biegler, Larry, Editorial Board Member, Campbell, Stephen, Editorial Board Member, Führer, Claus, Editorial Board Member, Gerdts, Matthias, Editorial Board Member, Grundel, Sara, Editorial Board Member, Kunkel, Peter, Editorial Board Member, Linh, Vu Hoang, Editorial Board Member, März, Roswitha, Editorial Board Member, Riaza, Ricardo, Editorial Board Member, Sager, Sebastian, Editorial Board Member, Schöps, Sebastian, Editorial Board Member, Simeon, Bernd, Editorial Board Member, Trenn, Stephan, Editorial Board Member, Zerz, Eva, Editorial Board Member, and Mehrmann, Volker, editor

Published
2019
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30. Coupled Circuit Device Simulation

Author

Bittner, Kai, Brachtendorf, Hans Georg, Schoenmaker, Wim, Strohm, Christian, Tischendorf, Caren, Bock, Hans Georg, Series Editor, de Hoog, Frank, Series Editor, Friedman, Avner, Series Editor, Gupta, Arvind, Series Editor, Nachbin, André, Series Editor, Ozawa, Tohru, Series Editor, Pulleyblank, William R., Series Editor, Rusten, Torgeir, Series Editor, Santosa, Fadil, Series Editor, Seo, Jin Keun, Series Editor, Tornberg, Anna-Karin, Series Editor, Langer, Ulrich, editor, Amrhein, Wolfgang, editor, and Zulehner, Walter, editor

Published
2018
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31. Stability Analysis of Electromagnetic Transient Simulations

Author

Schoenmaker, Wim, Strohm, Christian, Bittner, Kai, Brachtendorf, Hans Georg, Tischendorf, Caren, Bock, Hans Georg, Series Editor, de Hoog, Frank, Series Editor, Friedman, Avner, Series Editor, Gupta, Arvind, Series Editor, Nachbin, André, Series Editor, Ozawa, Tohru, Series Editor, Pulleyblank, William R., Series Editor, Rusten, Torgeir, Series Editor, Santosa, Fadil, Series Editor, Seo, Jin Keun, Series Editor, Tornberg, Anna-Karin, Series Editor, Langer, Ulrich, editor, Amrhein, Wolfgang, editor, and Zulehner, Walter, editor

Published
2018
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34. MathEnergy – Mathematical Key Technologies for Evolving Energy Grids

Author

Clees, Tanja, primary, Baldin, Anton, additional, Benner, Peter, additional, Grundel, Sara, additional, Himpe, Christian, additional, Klaassen, Bernhard, additional, Küsters, Ferdinand, additional, Marheineke, Nicole, additional, Nikitina, Lialia, additional, Nikitin, Igor, additional, Pade, Jonas, additional, Stahl, Nadine, additional, Strohm, Christian, additional, Tischendorf, Caren, additional, and Wirsen, Andreas, additional

Published
2021
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42. Quasi-regular DAEs

Author

Lamour, René, März, Roswitha, Tischendorf, Caren, Lamour, René, März, Roswitha, and Tischendorf, Caren

Published
2013
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46. Nonregular DAEs

Author

Lamour, René, März, Roswitha, Tischendorf, Caren, Lamour, René, März, Roswitha, and Tischendorf, Caren

Published
2013
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50. Stability issues

Author

Lamour, René, März, Roswitha, Tischendorf, Caren, Lamour, René, März, Roswitha, and Tischendorf, Caren

Published
2013
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