Speeding up waveform relaxation algorithms

• Autorzy: Ossowski M. , Kuczyński A.

Warianty tytułu

PL

Przyśpieszenie algorytmów relaksacyjnych

• Konferencja: Międzynarodowe Warsztaty "Computational Problems of Electrical Engineering"
• Języki publikacji: EN

Abstrakty

EN

The paper deals with a problem of improving efficiency of the waveform relaxation (WR) algorithms for linear and nonlinear dynamic circuits. An algorithm for solving differential equations using multisplitting concept and overlapping procedures, was formulated in a way that provides the convergence of iteration process. In order to split the circuit into independent parts, the chosen branches are cut off and appropriate sources, voltage or current, are inserted instead of eliminated links. Voltages and currents of these sources form an additional set of algebraic variables, carrying information between separated parts. The conditions that are to ensure the convergence of iteration process were considered. The special circuit splitting and overlapping, guarantee fulfilment of the convergence conditions.

PL

Artykuł rozważa problem przyspieszania działania algorytmów relaksacyjnych typu WR (waveform relaxation) w analizie dynamicznych obwodów liniowych i nieliniowych. Zdefiniowano metodę podziału sieci na wiele podobwodów umożliwiającą rozwiązanie układu równań różniczkowych przy zapewnieniu zbieżności procesu iteracyjnego. Przedyskutowano warunki zbieżności procesu relaksacji i zaproponowano metodę podziału sieci z nakładaniem się pewnych podobwodow na siebie.

Słowa kluczowe

EN

relaxation algorithm; circuit analysis

PL

algorytm relaksacyjny; analiza dekompozycyjna; obwód

• Wydawca: Wydawnictwo SIGMA-NOT
• Czasopismo: Przegląd Elektrotechniczny
• Rocznik: 2005
• Tom: R. 81, nr 2
• Strony: 66--70
• Opis fizyczny: Bibliogr. 16 poz., rys.

Twórcy

autor

Ossowski M.

• Institute of the Electrotechnics, Measuremants and Material Science, Technical University of Lodz, ul.Stefanowskiego 18/22, 00-000 Lodz, Poland

autor

Kuczyński A.

• Institute of the Electrotechnics, Measuremants and Material Science, Technical University of Lodz, ul.Stefanowskiego 18/22, 00-000 Lodz, Poland

• Technical University of Lodz

Bibliografia

• [1] Janssen J., Vandewalle S.: Multigrid Waveform Relaxation on Spatial Finite Element Meshes: The continuous-time case, SIAM J. NUMER. ANAL., vol. 33, no.2 , pp. 456-474, April 1996.
• [2] Jiang Y., Luk W., Wing O.: Convergence-Theoretics of Classical and Krylow Waveform Relaxation Methods for Differential-Algebraic Equations, IEICE , JEICE Trans. Fundamentals, vol. E-80-A, no.10, pp.1969-1971, October 1997.
• [3] Jiang Y., Wing O.: On the spectra of waveform relaxation operators for circuit equations, IEICE Trans. Fundamentals, vol. E-81-A, no.4, April 1998.
• [4] Jiang Y., Wing O.: A note on convergence conditions of waveform relaxation algorithms for nonlinear-algebraic equations, Applied Numerical Mathematics, vol.36 no. 2-3, Feb. 2001, pp. 281-297.
• [5] Kuczynski A., Ossowski M.: The two-level waveform relaxation algorithm, Proceedings of IX International Symposium on Theoretical Electrical Engineering, ISTET'2001, Linz, Austria, stron 4, 2001.
• [6] Kuczynski A., Ossowski M.: Convergence of the two-level waveform relaxation algorithm, Proceedings of XXV International Symposium on Theoretical Electrical Engineering, IC-SPETO-2002, Gliwice-Ustron, pp.337-340.
• [7] Lelarasmee E., Ruehli A.E., Sangiovanni-Vincentelli A.L.: The Waveform relaxation methods for time-domain analysis of large-scale integrated circuits, IEEE Trans. On Computer-Aided Design, vol. CAD 1, no.6 , pp. 131-145, July 1982.
• [8] Ossowski M., Kuczynski A.: Zachowanie algorytmów relaksacyjnych w analizie układów nieliniowych o wielu punktach równowagi, Proceedings of XXV International Symposium on Theoretical Electrical Engineering, IC-SPETO-2002, Gliwice-Ustron, pp.212-222.
• [9] Ossowski M., Kuczynski A.: Waveform relaxation methods for solving dynamic circuits having multiple equilibrium points, Proceedings of XXVI International Symposium on Theoretical Electrical Engineering, IC-SPETO-2003, Gliwice-Niedzica,
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• [14] Gardner M.J., Ruheli A., Optimaized waveform relaxation methods for RC type circuits, IEEE Trans. On Circuits and Systems, vol. 51, No. 4, April 2004.
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