PDAE models of integrated circuits and index analysis

Mathematical and Computer Modelling of Dynamical Systems

Volumn 13, Issue 1, 2007, Pages 1-17

  Bodestedt, Martin ^a   Tischendorf, Caren ^a  

^a TECHNISCHE UNIVERSITÄT BERLIN   (Germany)

Author keywords

Coupled system; Index analysis; Partial differential algebraic equation; Semiconductor

Indexed keywords

COUPLED SYSTEMS; DIFFERENTIAL ALGEBRAIC EQUATIONS; DRIFTDIFFUSION EQUATIONS; INDEX ANALYSIS; INFINITE DIMENSIONS; MODIFIED NODAL ANALYSIS; NONLINEAR BEHAVIOURS; PARTIAL DIFFERENTIAL-ALGEBRAIC EQUATIONS;

DIFFERENTIAL EQUATIONS; ELECTRIC LINES; SEMICONDUCTOR MATERIALS;

ELECTRIC NETWORK ANALYSIS;

EID: 33847143634     PISSN: 13873954     EISSN: 17445051     Source Type: Journal    
DOI: 10.1080/13873950600557329     Document Type: Article

References (19)

1. Harier, E. and Wanner, G., 1989, Solving Ordinary Differential Equations, II. (Berlin: Springer-Verlag).
2. März, R., 2003, Nonlinear Differential-Algebraic Equations with Properly Formulated Leading Term. Technical Report, Humboldt University of Berlin.
3. Lamour, R., März, R. and Tischendorf, C., 2001, PDAEs and Further Mixed Systems as Abstract Differential Algebraic Systems. Technical Report, Humboldt University of Berlin.
4. Feldman, U. and Günther, M., 1993, The DAE-Index in Electric Circuit Simulation. Technical Report, Technical University Munich.
5. Estèvez Schwarz, D. and Tischendorf, C., 2000, Structural Analysis of Electric Circuits and Consequences for MNA. Int. J. Circ. Theor. Appl., 28, 131-162.
6. Führer, C. and Leimkuhler, B.J., 1991, Numerical Solution of Differential-Algebraic Equations for Constrained Mechanical Motion. Numer. Math., 59, 55-69.
7. Bartel, A., First-Order Thermal PDAE Models in Electric Circuit Design. Paper presented at the 4th MATHMOD, Vienna, Austria, 5-7 February, 2003.
8. Sze, S.M., 1981, Physics of Semiconductor Devices (New York: John Wiley).
9. Markowich, P.A., 1986, The Stationary Semiconductor Device Equations (Vienna: Springer).
10. Zeidler, E., 1990, Nonlinear Functional Analysis and its Applications, II/A (New York: Springer).
11. Tischendorf, C., 1999, Topological Index Calculation of Differential-Algebraic Equations in Circuit Simulation. Surveys Math. Indust., 8, 187-199.
12. Troianiello, G.M., 1987, Elliptic Differential Equations and Obstacle Problems (New York: Plenum Press).
13. März, R., 2003, Differential Algebraic Systems with Properly Stated Leading Term and MNA Equations. In: K. Antreich, R. Bulirsch, A. Gilg and P. Rentrop (Eds), Mathematical Modeling, Simulation and Optimization of Integrated Electrical Circuits, Vol. 146, (Basel: Birkhäuser), pp. 135-141.
14. Higueras, I., März, R. and Tischendorf, C., 2000, Stability Preserving Integration of Index-1 DAEs. Appl. Numer. Math., 45, 175-200.
15. Higueras, I., März, R. and Tischendorf, C., 2003, Stability Preserving Integration of Index-2 DAEs. Appl. Numer. Math., 45, 201-229.
16. Ali, G., Bartel, A., Günther, M. and Tischendorf, C., 2003, Elliptic Partial Differential-Algebraic Multiphysics Models in Electrical Network Design. Mathematical Models & Methods in Applied Sciences, 13(9), 1261-1278.
17. Tischendorf, C., 2004.Coupled Systems of Differential Algebraic and Partial Differential Equations in Circuit and Device Simulation. Modeling and Numerical Analysis. Habilitation Thesis, Humboldt University of Berlin.
18. Selva Soto, M. and Tischendorf, C., 2004, Numerical Analysis of DAEs from Coupled Circuit and Semiconductor Simulation, Technical Report, Humboldt University of Berlin.
19. Schulz, S., 2002, Ein PDAE-Netzwerkmodell als Abstraktes Differential-Algebraisches System. Diploma Thesis, Humboldt University of Berlin.