Windowing Waveform Relaxation of Initial Value Problems

We present a windowing technique of waveform relaxation for dynamic systems. An effective estimation on window length is derived by an iterative error expression provided here. Relaxation processes can be speeded up if one takes the windowing technique in advance. Numerical experiments are given to further illustrate the theoretical analysis.

[1]  Yao-Lin Jiang,et al.  Improving convergence performance of relaxation-based transient analysis by matrix splitting in circuit simulation , 2001 .

[2]  Hong Zhang A NOTE ON WINDOWING FOR THE WAVEFORM RELAXATION , 1994 .

[3]  Charles A. Zukowski,et al.  Convergence properties of waveform relaxation circuit simulation methods , 1998 .

[4]  Jacob K. White,et al.  Accelerated waveform methods for parallel transient simulation of semiconductor devices , 1996, IEEE Trans. Comput. Aided Des. Integr. Circuits Syst..

[5]  Kevin Burrage,et al.  A Jacobi Waveform Relaxation Method for ODEs , 1998, SIAM J. Sci. Comput..

[6]  Wai-Shing Luk,et al.  Convergence-Theoretics of Classical and Krylov Waveform Relaxation Methods for Differential-Algebraic Equations (Special Section on VLSI Design and CAD Algorithms) , 1997 .

[7]  Yao-Lin Jiang,et al.  Periodic waveform relaxation solutions of nonlinear dynamic equations , 2003, Appl. Math. Comput..

[8]  Richard M. M. Chen,et al.  A Parallel Decoupling Technique to Accelerate Convergence of Relaxation Solutions of Integral-Differential-Algebraic Equations , 2001, J. Interconnect. Networks.

[9]  Andrew M. Stuart,et al.  Waveform relaxation as a dynamical system , 1997, Math. Comput..

[10]  Yao-Lin Jiang,et al.  A note on convergence conditions of waveform relatxation algorithms for nonlinear differential—algebraic equations , 2001 .

[11]  Stefan Vandewalle,et al.  Efficient Parallel Algorithms for Solving Initial-Boundary Value and Time-Periodic Parabolic Partial Differential Equations , 1992, SIAM J. Sci. Comput..

[12]  O. Nevanlinna,et al.  Convergence of dynamic iteration methods for initial value problems , 1987 .

[13]  Benedict Leimkuhler,et al.  Rapid convergence of waveform relaxation , 1993 .

[14]  Benedict J. Leimkuhler Estimating Waveform Relaxation Convergence , 1993, SIAM J. Sci. Comput..

[15]  Alberto L. Sangiovanni-Vincentelli,et al.  The Waveform Relaxation Method for Time-Domain Analysis of Large Scale Integrated Circuits , 1982, IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems.

[16]  Yao-Lin Jiang,et al.  Monotone Waveform Relaxation for Systems of Nonlinear Differential-Algebraic Equations , 2000, SIAM J. Numer. Anal..