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2005年03月25日

【期刊论文】Wayeform Relaxation of Nonlinear Second-order Differential Equations*

蒋耀林， Yao-Lin Jiang，， Richard M.M. Chen， and Omar Wing

This paper was published in IEEE Trans. Circuits and System-Part I (vol. 48, no.11, pp. 1344-1347, 2001).，-0001，（）：

-1年11月30日

In this paper wc give a simple theorem Oil the waveform relaxation (WR) solution for a systenl of nonlinear SOeOnd-order diffcrential equations It is shown that if the nornl of certain matrices derived froln the Jacobians of the systenl equations is less than one, then the WR solution converges It is also the first tillle that a convergence condition is obtained for this general kind of nonlinear systems in the WR literarture Numerieal experinlents arc providcd to confirm the theoretical analysis.

Sccond-ordcr differential equations,， waveform relaxation parellcl processing,， circuit sinnllation

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2005年03月25日

【期刊论文】Computing Periodic Solutions of Linear Differential-Algebraic Equations by Waveform Relaxation*

蒋耀林， YAO-LIN JIANG§， AND RICHARD M M CHEN†

This paper was published in Mthematics of Computation (vol. 74, no.250, pp. 781-804, 2005).，-0001，（）：

-1年11月30日

摘要

We propose an algorithm, which is based on the wavefnrm relaxation (WR) approach, to coinpnte the periodic sohltions of a linear system described by difierential algebraic equations For this kind of two-point boundary problems, we derive an analytic expression of the spectral set for the periodic WR operator. We show that the periodic WR algorithm is convergent if the snpreinllIn value of the spectral radii for a series of matrices derived froln the system is less than one. Numerlcal examples, where discrete wavefnrms are computed with a backward-difie, rence fnrmnla. filrther ilhlstrate the correctness of the theoretical work in this paper.

Differential-algebraic equations,， periodic solutions.， wavefirom relaxation,， spectra of linear operators,， linear multistep methods,， finite-difference,， nnnlerical analysis,， scientific computing,， circuit sinmlatlon.，

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2005年03月25日

【期刊论文】Improving ConVergence Performance of Relaxation-based Transient Analysis by Matrix Splitting in Circuit Simulation*

蒋耀林， Yao-Lin Jiang，， Richard M.M. Chen， and Omar Wing

This paper was published in IEEE Trans. Circuits and System-Part I (vol. 48, no.6, pp. 789-780, 2001).，-0001，（）：

-1年11月30日

摘要

We study the convergence performance of relaxation-based algorithms for circuit sinmlation in the time doraain The circuits are modelled by linem integral-difierential-algebraic equations. We show that in theory convergence depends only on the spectral properties of certain matrices when splitting is applied to the circuit matrices to set up the waveforill relaxation solution of a circuit. A new decoupling technique is derived, which speeds up the convergence of relaxation-based algorithlns. In function spaces a Krylov's subspace method. namely the waveforirl generalized minimal residual algorithm，is also presented in the paper. Nuinerical examples are given to illustrate how judicious splitting mal how Krylov's method Call help improve convergence in sorlle situations.

Linear integral-difierential-algebraic equations,， waveforill relaxation,， Krylov'， s subspace method,， matrix splitting,， transient analysis parallel processing,， circuit simulation

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2005年03月25日

【期刊论文】On Time-Domain Simulation of Lossless Transmission Lines with Nonlinear Terminations*

蒋耀林， Yao-Lin Jiang

This paper was published in SIAM Journal on Numerical Analysis (vol. 42, no.3, pp. 1018-1031, 2004).，-0001，（）：

-1年11月30日

摘要

A tiine-domain approach is presented to solve nonlinear circuits with loss less translnission lines. Mathenlatically,the circuits are described by a special kind of nonlinear differential-algebraic equatious fDAEs)with multiple staut delays. In order to directly compute these delay systems in time-domaiu, decoupling by waveform relaxatiou (WR) is applied to the systems. For the relaxation-based umthod we provide a uew convergeuce proof. Nunlerical experimeuts are giveu to illustrate the novel approach.

Nonlinear circuits， transnlission lines,， differential-algebraic equations with multiple delays,， waveorm relaxation,， circuit simulation.，

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2005年03月25日

【期刊论文】A General Approach to Waveform Relaxat ion Solutions of Nonlinear Differential-Algebraic Equations: The Continuous-Time and Discrete-Time Cases*

蒋耀林， YAO-LIN JIANG

This paper was published in IEEE Trans. Circuits and System-Part I (vol. 51, no.9, pp. 1770-1780, 2004).，-0001，（）：

-1年11月30日

摘要

For a general class of nonlinear differential-Mgebraic equations of index one, we develop and unify a convergence theory on waveform relaxation (WR). Convergenee conditions are achieved fnr the eases of continuous-time and discrete time WR approximations. Most of known convergence results in this field can be easily derived from tile new theory established here.

Differential-algebraic equations， waveform relaxation， continuous-time and discrete-time WR iterations， convergence conditions， numerical algorithms， circuit simulation.，

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