Multi-Splitting Waveform Relaxation Methods for Solving the Initial Value Problem of Linear Integral-Differential-Algebraic Equations

Xiao Lin Lin; Yuan Sang; Hong  Wei; Li Ming Liu; Yu Mei Wang; Rong Hui Lu

doi:10.4028/www.scientific.net/AMR.403-408.1763

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HomeAdvanced Materials ResearchAdvanced Materials Research Vols. 403-408Multi-Splitting Waveform Relaxation Methods for...

Multi-Splitting Waveform Relaxation Methods for Solving the Initial Value Problem of Linear Integral-Differential-Algebraic Equations

Abstract:

We present the multi-splitting waveform relaxation (MSWR) methods for solving the initial value problem of linear integral-differential-algebraic equations. Based on the spectral radius of the derived operator by decoupled process, a convergent condition is proposed for the MSWR method. Finally we discussed the convergent condition of discrete-time case of MSWR.

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Periodical:

Advanced Materials Research (Volumes 403-408)

Pages:

1763-1766

DOI:

https://doi.org/10.4028/www.scientific.net/AMR.403-408.1763

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Online since:

November 2011

Authors:

Xiao Lin Lin, Yuan Sang, Hong Wei, Li Ming Liu, Yu Mei Wang, Rong Hui Lu

Keywords:

Circuit Simulation, Initial Value Problem, Linear Integral-Differential-Algebraic Equations, Multi-Splitting Waveform Relaxation, Spectra of Linear Operators

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References

[1] E. Lelarasmee, A. Ruehli and A.L. Sangiovanni-Vincentelli, The waveform relaxation method for time-domain analysis of large scale integrated circuit, IEEE Trans. Computer- Aided Design, Vol. 1(1982), pp.131-145.

DOI: 10.1109/tcad.1982.1270004

Google Scholar

[2] J. K. White and A. Sangiovanni-Vincentelli, Relaxation Techniques for the Simulation of VLSI Circuits, Kulwer Academic Publishers, Boston, (1986).

Google Scholar

[3] G.D. Gristede, A.E. Ruehli and C.A. Zukowski, Convergence properties of waveform relaxation circuit simulation methods, IEEE Transactions on Circuits and Systems-Part I, Vol. 45: 7(1998), p.726–738.

DOI: 10.1109/81.703839

Google Scholar

[4] Y.L. Jiang, R.M.M. Chen and O. Wing, Improving convergence performance of relaxation-based transient analysis by matrix splitting in circuit simulation, IEEE Transactions on Circuits and Systems - Part I, Vol. 48: 6(2001), p.769–780.

DOI: 10.1109/81.928160

Google Scholar

[5] Y.L. Jiang and O. Wing, A note on the spectra and pseudospectra of waveform relaxation operators for linear differential-algebraic equations, SIAM Journal on Numerical Analysis, Vol. 38: 1(2000), p.186–201.

DOI: 10.1137/s0036142997327063

Google Scholar

[6] T. Kato, Perturbation Theory for Linear Operators, Springer-Verlag, Berlin, (1984).

Google Scholar

[7] L. N. Trefethen, Pseudospectra of linear operators, SIAM Review, Vol. 39(1997), pp.383-406.

DOI: 10.1137/s0036144595295284

Google Scholar

[8] X. L. Lin and L. Wang, Computing periodic solutions of linear differential equations by multi-splittings waveform relaxation[J], Proceedings on the 2010 International Conference on Computer Application and System Modeling, Vol. 6(2010).

DOI: 10.1109/iccasm.2010.5620759

Google Scholar

[9] X. L. Lin, J. Heng and Y. P. Wang, Multi-split ting waveform relaxation algorithm for linear integral-differential-algebraic equations, Journal of Shaanxi University of Science and Technology, Vol. 26: 2(2008), pp.118-124.

Google Scholar