Floating Random Walk-Based Capacitance Extraction for General Non-Manhattan Conductor Structures

Xu, Zhezhao; Zhang, Chao; Yu, Wenjian

doi:10.1109/tcad.2016.2561968

Cited by 17 publications

(4 citation statements)

References 22 publications

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“…3; 2nd sphere center: (10,13,12); 2nd sphere shell radius: 8; "External" sphere radius: 31.155; δ: 10 −8 . Usually, the bias order is the same as the order of δ, so, in this and following examples, error of methods is equal to statistical error.…”

Section: Mutual Capacitance Of Two Spheres In Free Spacementioning

confidence: 99%

“…1st sphere radius: 3; 1st sphere center: (10,13,12); 1st sphere shell radius: 5; 2nd sphere radius: 31; 2nd sphere center:…”

Section: Mutual Capacitance Of Two Spheres In Free Spacementioning

confidence: 99%

“…To simplify the procedure for modeling a Random Walk, the problem was discretized. The development of the method of Random Walk on Cubes in various directions (multiple dielectrics, non-Manhattan polygonal shapes, optimizations) can be found, for example, in [12][13][14]. Besides the statistical error of Monte Carlo approximations, Walk on Cubes have additional bias because of the approximation of Green's function for cubes using the Fourier series.…”

Section: Introductionmentioning

confidence: 99%

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Monte Carlo Algorithms for the Extracting of Electrical Capacitance

Кузнецов¹,

Сипин²

2021

Mathematics

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We present new Monte Carlo algorithms for extracting mutual capacitances for a system of conductors embedded in inhomogeneous isotropic dielectrics. We represent capacitances as functionals of the solution of the external Dirichlet problem for the Laplace equation. Unbiased and low-biased estimators for the capacitances are constructed on the trajectories of the Random Walk on Spheres or the Random Walk on Hemispheres. The calculation results show that the accuracy of these new algorithms does not exceed the statistical error of estimators, which is easily determined in the course of calculations. The algorithms are based on mean value formulas for harmonic functions in different domains and do not involve a transition to a difference problem. Hence, they do not need a lot of storage space.

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Section: Mutual Capacitance Of Two Spheres In Free Spacementioning

confidence: 99%

“…1st sphere radius: 3; 1st sphere center: (10,13,12); 1st sphere shell radius: 5; 2nd sphere radius: 31; 2nd sphere center:…”

Section: Mutual Capacitance Of Two Spheres In Free Spacementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Monte Carlo Algorithms for the Extracting of Electrical Capacitance

Кузнецов¹,

Сипин²

2021

Mathematics

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“…学术界也研发了基于悬浮随机行走的电容提取软件 RWCap [3,5] . 为将其扩展到大规模复杂结构 [6][7][8][9][10] , 提高其并行处理能力 [11][12][13] , 相关学者也进行了大量的研究.…”

Section: 传统的电容提取方法包括有限差分、有限元以unclassified

Accelerated Generation of Multi-Dielectric Green’s Function Table

Yang¹,

Yu²

2021

J Comput-Aided Design Comput Graphics

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A new method for fast generation of multi-dielectric Green's function table is proposed. The new method utilizes the symmetric property of multi-dielectric Green's function table. By inserting virtual homogeneous Neumann boundary inside the transition cube, the original cube with FDM grid imposed is cut down to one fourth of itself, which leads to smaller FDM matrices and faster generation of Green's function tables. The symmetry of multi-dielectric Green's function table is proved in theory and furthermore a new method for its fast computation is proposed who is implemented in C++ and whose efficiency and accuracy are validated through numerical experiments on a server with 32 cores. The experimental results show that the proposed method brings more than 8X speed-up compared to original FDM. Meanwhile, the Green function tables obtained are just as same as the original FDM. With the proposed method, pre-characterization time cost can be significantly reduced in FRW based capacitance extraction for multi-dielectric VLSI structures.

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