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首页> 外文期刊>Applied Computational Electromagnetics Society journal >A Novel Dirichlet-Neumann Random-Walk Algorithm for the Solution of Time-Harmonic Helmholtz Equation at Multiple Wavelength Length Scales: 1D and 2D Verification
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A Novel Dirichlet-Neumann Random-Walk Algorithm for the Solution of Time-Harmonic Helmholtz Equation at Multiple Wavelength Length Scales: 1D and 2D Verification

机译：一种新的Dirichlet-Neumann随机行走算法，用于求解多波长尺度下的时间谐波Helmholtz方程：一维和二维验证

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摘要

The electrical properties of IC interconnects at multi-GHz frequencies must be described with Maxwell's equations. We have created an entirely new floating random-walk (RW) algorithm to solve the time-harmonic Maxwell-Helmholtz equations. Traditional RW algorithms for Maxwell-Helmholtz equations are constrained to length scales that are less than a quarter-wavelength. This is because of the problem of resonance in finite-domain Green's function for Helmholtz equation at multiple quarter-wavelength length scales. In this paper, we report the major discovery of extending our floating RW algorithm beyond a quarter-wavelength. The problem of Green's function resonance has been eliminated by the use of an infinite-domain Green's function. In this work, we formulate this algorithm and describe its successful application to homogeneous and heterogeneous 1D problems and homogeneous 2D problems. We believe, that with additional work, this RW algorithm will prove useful in the development of CAD tools for electromagnetic analysis of IC interconnect systems. It can be noted that the algorithm exhibits full parallelism, requiring minimal interprocessor communication. Thus, significant performance enhancement can be expected in any future parallel software or hardware implementation.
机译：必须使用Maxwell方程描述在数GHz频率下IC互连的电特性。我们创建了一种全新的浮动随机游走（RW）算法来求解时谐Maxwell-Helmholtz方程。用于Maxwell-Helmholtz方程的传统RW算法被限制为小于四分之一波长的长度尺度。这是因为在多个四分之一波长长度标度下，Helmholtz方程的有限域格林函数共振的问题。在本文中，我们报告了将浮动RW算法扩展到四分之一波长以外的主要发现。通过使用无限域格林函数，消除了格林函数共振的问题。在这项工作中，我们制定了该算法，并描述了该算法在同构和异构1D问题和同构2D问题上的成功应用。我们相信，随着额外的工作，这种RW算法将在开发用于IC互连系统的电磁分析的CAD工具方面被证明是有用的。可以注意到，该算法表现出完全的并行性，需要最少的处理器间通信。因此，在任何未来的并行软件或硬件实现中都可以期待显着的性能增强。

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