Prof. Dr. Caren Tischendorf
Profil
Forschungsthemen25
DFG-Sachbeihilfe: Efficient Quasi Monte Carlo Methods and Their Application in Quantum Field Theory
Quelle ↗Förderer: DFG Sachbeihilfe Zeitraum: 01/2014 - 12/2016 Projektleitung: Prof. Dr. Caren Tischendorf, Prof. Dr. Andreas Griewank
ECMATH - Stability analysis of power networks and power network models
Quelle ↗Förderer: Einstein Stiftung Berlin Zeitraum: 10/2014 - 05/2017 Projektleitung: Prof. Dr. Caren Tischendorf
Entwicklung von Verfahren zur Optimierung von Gastransportnetzen
Quelle ↗Förderer: Wirtschaftsunternehmen / gewerbliche Wirtschaft Zeitraum: 06/2014 - 07/2014 Projektleitung: Prof. Dr. Caren Tischendorf
Entwicklung von Verfahren zur Optimierung von Gastransportnetzen
Quelle ↗Förderer: Wirtschaftsunternehmen / gewerbliche Wirtschaft Zeitraum: 10/2014 - 10/2014 Projektleitung: Prof. Dr. Caren Tischendorf
Entwicklung von Verfahren zur Optimierung von Gastransportnetzen
Quelle ↗Förderer: Wirtschaftsunternehmen / gewerbliche Wirtschaft Zeitraum: 08/2014 - 09/2014 Projektleitung: Prof. Dr. Caren Tischendorf
Entwicklung von Verfahren zur Optimierung von Gastransportnetzen
Quelle ↗Zeitraum: 08/2014 - 09/2014 Projektleitung: Prof. Dr. Caren Tischendorf
Entwicklung von Verfahren zur Optimierung von Gastransportnetzen
Quelle ↗Zeitraum: 06/2014 - 07/2014 Projektleitung: Prof. Dr. Caren Tischendorf
Entwicklung von Verfahren zur Optimierung von Gastransportnetzen
Quelle ↗Förderer: Wirtschaftsunternehmen / gewerbliche Wirtschaft Zeitraum: 10/2013 - 01/2014 Projektleitung: Prof. Dr. Caren Tischendorf
Entwicklung von Verfahren zur Optimierung von Gastransportnetzen
Quelle ↗Zeitraum: 10/2014 - 10/2014 Projektleitung: Prof. Dr. Caren Tischendorf
EU: Simulation in Multiscale Physical and Biological Systems (STIMULATE)
Quelle ↗Förderer: Horizon 2020: Innovative Training Network ITN Zeitraum: 06/2018 - 11/2022 Projektleitung: Prof. Dr. Caren Tischendorf
EXC 2046/1 AG Tischendorf
Quelle ↗Förderer: DFG Exzellenzstrategie Cluster Zeitraum: 01/2019 - 07/2022 Projektleitung: Prof. Dr. Caren Tischendorf
EXC 2046/1 Math+ Hauptkonto
Quelle ↗Förderer: DFG Exzellenzinitiative Cluster Zeitraum: 01/2019 - 12/2021 Projektleitung: Prof. Dr. Caren Tischendorf
EXC 2046: Berlin Mathematics Research Center (MATH+)
Quelle ↗Förderer: DFG Exzellenzstrategie Cluster Zeitraum: 01/2019 - 12/2024 Projektleitung: Prof. Dr. Caren Tischendorf, Prof. Dr. Michael Hintermüller, Prof. Dr. Max Klimm, Prof. Dr. Dörte Kreher, Prof. Chris Wendl, Prof. Dr. Bettina Rösken-Winter, Prof. Dr. rer. nat. Dr. h.c. Edda Klipp
FZ: Stable Transient Modeling and Simulation of Flow Networks (TP B27)
Quelle ↗Förderer: DFG sonstige Programme Zeitraum: 05/2012 - 05/2014 Projektleitung: Prof. Dr. Caren Tischendorf
Kompression von Scharen von Simulationsergebnissen
Quelle ↗Zeitraum: 01/2013 - 12/2014 Projektleitung: Prof. Dr. Caren Tischendorf
Lösung gekoppelter Probleme in der Nanoelektronik (nanoCOPS)
Quelle ↗Zeitraum: 11/2013 - 10/2016 Projektleitung: Prof. Dr. Caren Tischendorf
Modellierung, Stabilität und Synchronisation von Verkehrsnetzwerken
Quelle ↗Förderer: Einstein Stiftung Berlin Zeitraum: 06/2017 - 12/2018 Projektleitung: Prof. Dr. Caren Tischendorf
Numerische Analysis Abstrakter Differential-Algebraischer Gleichungen
Quelle ↗Förderer: DFG Sachbeihilfe Zeitraum: 03/2013 - 12/2013 Projektleitung: Prof. Dr. Caren Tischendorf
Numerische Simulation von Hochfrequenz-Schaltungen der Kommunikationstechnik
Quelle ↗Förderer: Bundesministerium für Forschung, Technologie und Raumfahrt Zeitraum: 06/2004 - 05/2007 Projektleitung: Prof. Dr. Caren Tischendorf
Online-Simulation und -optimierung zur energieeffizienten Pumpensteuerung in Trinkwasserverteilungssystemen, TP3
Quelle ↗Förderer: Bundesministerium für Forschung, Technologie und Raumfahrt Zeitraum: 07/2012 - 06/2014 Projektleitung: Prof. Dr. Caren Tischendorf
SFB-TRR 154/1: Hierarchische PDAE-Surrogate-Modellierung und stabile PDAE-Netzwerk-Diskretisierung zur Simulation großer instationärer Gasnetzwerke (TP C02)
Quelle ↗Förderer: DFG Sonderforschungsbereich Zeitraum: 10/2014 - 06/2022 Projektleitung: Prof. Dr. Caren Tischendorf
SFB/TRR 154/3: Simulation und Steuerung gekoppelter Netzwerk-Differential-algebraischer Gleichungen (TP C02)
Quelle ↗Förderer: DFG Sonderforschungsbereich Zeitraum: 07/2022 - 06/2026 Projektleitung: Prof. Dr. Caren Tischendorf
Verbundprojekt 05M2013 - KoSMos: Modellreduktionsbasierte Simulation von gekoppleten PDAE-Systemen. Teilprojekt 3
Quelle ↗Förderer: Bundesministerium für Forschung, Technologie und Raumfahrt Zeitraum: 07/2013 - 06/2016 Projektleitung: Prof. Dr. Caren Tischendorf
Verbundprojekt SOFA: Gekoppelte Simulation und Optimierung für robustes virtuelles Fahrzeugdesign; Teilprojekt Schaltung und Elektromagnetismus
Quelle ↗Förderer: Bundesministerium für Forschung, Technologie und Raumfahrt Zeitraum: 11/2013 - 12/2013 Projektleitung: Prof. Dr. Caren Tischendorf
Verbundvorhaben: MathEnergy - Mathematische Schlüsseltechniken für Energienetze im Wandel, TP Szenarienanalyse gekoppelter Gas- und Stromnetze
Quelle ↗Förderer: Bundesministerium für Wirtschaft und Energie Zeitraum: 10/2016 - 01/2021 Projektleitung: Prof. Dr. Caren Tischendorf
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Publikationen25
Top 25 nach Zitationen — Quelle: OpenAlex (BAAI/bge-m3 embedded für Matching).
266 Zitationen · DOI
International Journal of Circuit Theory and Applications · 234 Zitationen · DOI
The development of integrated circuits requires powerful numerical simulation programs. Naturally, there is no method that treats all the different kinds of circuits successfully. The numerical simulation tools provide reliable results only if the circuit model meets the assumptions that guarantee a successful application of the integration software. Owing to the large dimension of many circuits (about 107 circuit elements) it is often difficult to find the circuit configurations that lead to numerical difficulties. In this paper, we analyse electric circuits with respect to their structural properties in order to give circuit designers some help for fixing modelling problems if the numerical simulation fails. We consider one of the most frequently used modelling techniques, the modified nodal analysis (MNA), and discuss the index of the differential algebraic equations (DAEs) obtained by this kind of modelling. Copyright © 2000 John Wiley & Sons, Ltd.
ZAMM ‐ Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik · 73 Zitationen · DOI
Abstract In electric circuit simulation we are confronted with highly nonlinear DAEs with low smoothness properties. They may have index 2 but they do not belong to the class of Hessenberg form systems that are well understood. The classic and the charge‐oriented modified analysis are shown to lead to the same DAE‐index if the circuit models satisfy some natural assumptions. We present a topological criteria for calculating the index. This makes it possible to determine the index also for high‐dimensional circuit equation systems.
72 Zitationen
Applied Numerical Mathematics · 54 Zitationen · DOI
Differential-algebraic equations forum · 50 Zitationen · DOI
Mathematical Models and Methods in Applied Sciences · 50 Zitationen · DOI
In refined network analysis, a compact network model is combined with distributed models for semiconductor devices in a multiphysics approach. For linear RLC networks containing diodes as distributed devices, we construct a mathematical model that combines the differential-algebraic network equations of the circuit with elliptic boundary value problems modeling the diodes. For this mixed initial-boundary value problem of partial differential-algebraic equations a first existence result is given.
Applied Numerical Mathematics · 39 Zitationen · DOI
International Journal of Circuit Theory and Applications · 36 Zitationen · DOI
Abstract In this paper we present several semistate or differential‐algebraic models arising in nodal analysis of nonlinear circuits including memristors. The goal is to characterize the tractability index of these models under strict passivity assumptions, a key issue for the numerical simulation of circuit dynamics. We show that the main model, which combines memristors' fluxes and charges, is index two. From a technical point of view, this result is based on the use of a projector along the image of the leading matrix, in contrast to previous index analyses. For charge‐controlled memristors, the elimination of fluxes yields an index one system in topologically nondegenerate circuits, and an index two model otherwise. Analogous results are also proved to hold for flux‐controlled memristors. Our framework accommodates coupling effects among resistors, memristors, capacitors and inductors. Copyright © 2010 John Wiley & Sons, Ltd.
Dynamical Systems · 36 Zitationen · DOI
The dynamical behaviour of nonlinear electrical circuits is usually modelled in the time domain by differential–algebraic equations (DAEs). The differential–algebraic formalism drives qualitative analyses based on linearization to a matrix pencil setting. In this context, the present paper performs a spectral analysis of matrix pencils and DAEs arising in nonlinear circuit theory. Specifically, the non-singularity, hyperbolicity and asymptotic stability of equilibria are addressed in terms of circuit topology. The differential–algebraic framework puts the results beyond those already known for state-space models, unfeasible in many actual problems. The topological conditions arising in this qualitative study are proved independent of those supporting the index, and therefore they apply to both index-1 and index-2 configurations. The approach illustrates how graph theory, matrix analysis and DAE theory interact in the dynamical study of nonlinear circuits.
Applied Numerical Mathematics · 34 Zitationen · DOI
SIAM Journal on Scientific Computing · 34 Zitationen · DOI
In electric circuit simulation the charge-oriented modified nodal analysis may lead to highly nonlinear DAEs with low smoothness properties. They may have index 2 but they do not belong to the class of Hessenberg form systems that are well understood. In the present paper, on the background of a detailed analysis of the resulting structure, it is shown that charge-oriented modified nodal analysis yields the same index as does the classical modified nodal analysis. Moreover, for index 2 DAEs in the charge-oriented case, a further careful analysis with respect to solvability, linearization, and numerical integration is given.
Differential-algebraic equations forum · 31 Zitationen · DOI
On the stability of solutions of autonomous index-I tractable and quasilinear index-2 tractable DAEs
1994Circuits Systems and Signal Processing · 28 Zitationen · DOI
Mathematical and Computer Modelling of Dynamical Systems · 26 Zitationen · DOI
A coupled system modelling an electric circuit containing semiconductors is presented. The modified nodal analysis leads to a differential algebraic equation (DAE) describing the electric network. The nonlinear behaviour of the semiconductors is modelled by the drift diffusion equations. Coupling relations are defined and a generalization of the tractability index to systems of infinite dimensions is presented and applied to the resulting partial differential algebraic equation (PDAE). The PDAE turns out to have the same index as the electrical network equations.
25 Zitationen · DOI
Journal of Water Resources Planning and Management · 23 Zitationen · DOI
The Newton-based global gradient algorithm (GGA) (also known as the Todini and Pilati method) is a widely used method for computing the steady-state solution of the hydraulic variables within a water distribution system (WDS). The Newton-based computation involves solving a linear system of equations arising from the Jacobian of the WDS equations. This step is the most computationally expensive process within the GGA, particularly for large networks involving up to O(105) variables. An increasingly popular solver for large linear systems of the M-matrix class is the algebraic multigrid (AMG) method, a hierarchical-based method that uses a sequence of smaller dimensional systems to approximate the original system. This paper studies the application of AMG to the steady-state solution of WDSs through its incorporation as the linear solver within the GGA. The form of the Jacobian within the GGA is proved to be an M-matrix (under specific criteria on the pipe resistance functions), and thus able to be solved using AMG. A new interpretation of the Jacobian from the GGA is derived, enabling physically based interpretations of the AMG’s automatically created hierarchy. Finally, extensive numerical studies are undertaken where it is seen that AMG outperforms the sparse Cholesky method with node reordering (the solver used in EPANET2), incomplete LU factorization (ILU), and PARDISO, which are standard iterative and direct sparse linear solvers.
Journal of Evolution Equations · 21 Zitationen · DOI
Journal of Computational and Applied Mathematics · 19 Zitationen · DOI
Differential-algebraic equations forum · 19 Zitationen · DOI
Mathematical and Computer Modelling of Dynamical Systems · 16 Zitationen · DOI
We introduce a model order reduction (MOR) procedure for differential-algebraic equations, which is based on the intrinsic differential equation contained in the starting system and on the remaining algebraic constraints. The decoupling procedure in differential and algebraic part is based on the projector and matrix chain which leads to the definition of tractability index. The differential part can be reduced by using any MOR method, we use Krylov-based projection methods to illustrate our approach. The reduction on the differential part induces a reduction on the algebraic part. In this paper, we present the method for index-1 differential-algebraic equations. We implement numerically this procedure and show numerical evidence of its validity. Keywords: differential algebraic equations, tractability index, model order reduction, modified decomposition of DAEs
Mathematical Methods in the Applied Sciences · 16 Zitationen · DOI
The time-domain characterization of qualitative properties of electrical circuits requires the combined use of mathematical concepts and tools coming from digraph theory, applied linear algebra and the theory of differential-algebraic equations. This applies, in particular, to the analysis of the circuit hyperbolicity, a key qualitative feature regarding oscillations. A linear circuit is hyperbolic if all of its eigenvalues are away from the imaginary axis. Characterizing the hyperbolicity of a strictly passive circuit family is a two-fold problem, which involves the description of (so-called topologically non-hyperbolic) configurations yielding purely imaginary eigenvalues (PIEs) for all circuit parameters and, when this is not the case, the description of the parameter values leading to PIEs. A full characterization of the problem is shown here to be feasible for certain circuit topologies. The analysis is performed in terms of differential-algebraic branch-oriented circuit models, which drive the spectral study to a matrix pencil setting, and makes systematic use of a matrix-based formulation of digraph properties. Several examples illustrate the results. Copyright © 2010 John Wiley & Sons, Ltd.
Mathematics of Computation · 15 Zitationen · DOI
Modern modeling approaches for circuit simulation such as the modified nodal analysis (MNA) lead to differential-algebraic equations (DAEs). The index of a DAE is a measure of the degree of numerical difficulty. In general, the higher the index is, the more difficult it is to solve the DAE. In this paper, we consider a broader class of analysis methods called the hybrid analysis. For nonlinear time-varying circuits with general dependent sources, we give a structural characterization of the tractability index of DAEs arising from the hybrid analysis. This enables us to determine the tractability index efficiently, which helps to avoid solving higher index DAEs in circuit simulation.
edoc Publication server (Humboldt University of Berlin) · 13 Zitationen · DOI
Abstract differential algebraic systems (ADASs), i.e., differential algebraic systems with operators acting in real Hilbert spaces are introduced for a systematical treatment of coupled systems of PDEs, DAEs and integral equations. Using the finite-dimensional decoupling theory for DAEs as motivation, this paper will examine what one appropriate analogue is for infinite-dimensional systems. This leads to an index definition for ADASs. Thereby, instead of the inherent regular ODE one obtains an explicit (abstract) differential equation. In particular, when discussing PDAEs, the inherent regular differential equation is actually a parabolic PDE. The decoupling procedure provides, additionally, appropriate initial and boundary conditions for unique solvability of the coupled systems. The concept to handle ADASs is explained in different case studies.
Computers & Mathematics with Applications · 13 Zitationen · DOI
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SFB/TRR 154/3: Simulation und Steuerung gekoppelter Netzwerk-Differential-algebraischer Gleichungen (TP C02)
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Lösung gekoppelter Probleme in der Nanoelektronik (nanoCOPS)
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Lösung gekoppelter Probleme in der Nanoelektronik (nanoCOPS)
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SFB/TRR 154/3: Simulation und Steuerung gekoppelter Netzwerk-Differential-algebraischer Gleichungen (TP C02)
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EXC 2046: Berlin Mathematics Research Center (MATH+)
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Stammdaten
Identität, Organisation und Kontakt aus HU-FIS.
- Name
- Prof. Dr. Caren Tischendorf
- Titel
- Prof. Dr.
- Fakultät
- Mathematisch-Naturwissenschaftliche Fakultät
- Institut
- Institut für Mathematik
- Arbeitsgruppe
- Angewandte Mathematik
- Telefon
- +49 30 2093-45325
- HU-FIS-Profil
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- 26.4.2026, 01:13:10