Schwarz Waveform Relaxation for a Neutral Functional Partial Differential Equation Model of Lossless Coupled Transmission Lines
Schwarz Waveform Relaxation for a Neutral Functional Partial Differential Equation Model of Lossless Coupled Transmission Lines
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DOI：
10.1137/110860975
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发表时间：
2013-04
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影响因子：
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通讯作者：
Shulin Wu;Tingzhu Huang
中科院分区：
文献类型：
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作者：
Shulin Wu;Tingzhu Huang
本文研究了求解无损耗耦合传输线偏中立型泛函微分方程的Schwarz波形松弛算法的收敛行为。我们首先在Dirichlet和Robin类型的传输条件下对算法进行了连续级别的分析。结果表明，只要选择合适的参数，利用Robin传输条件可以显著提高算法的收敛速度。然后在空间上对模型问题进行离散化，并在半离散水平上研究SWR算法。由于半离散SWR算法更接近完全离散化算法，如果能通过考虑空间离散化的影响来进一步提高算法的收敛效果将是可取的。对于这一点，我们证明了对于Dirichlet传输条件，在连续和半离散水平上分析的SWR算法的收敛速度是相等的。然而，对于罗宾的传播..。
In this paper, we investigate the convergence behavior of the Schwarz waveform relaxation (SWR) algorithm for partial neutral functional differential equations which arise from lossless coupled transmission lines. We first analyze the algorithm at continuous level with transmission conditions of Dirichlet and Robin type. We show that the convergence rate of the algorithm can be significantly improved by using the Robin transmission condition, provided the involved parameter is chosen properly. Then we discretize the model problem in space and investigate the SWR algorithm at the semidiscrete level. It would be desirable if the convergence could be further improved by considering the influence of the space discretization, since the semidiscrete SWR algorithm is closer to the fully discretized algorithm. For this point, we show that for the Dirichlet transmission condition the convergence rate of the SWR algorithm analyzed at the continuous and semidiscrete levels is equal. However, for the Robin transmissi...