Hierarchical Block Boundary-Element Method (HBBEM): A Fast Field Solver for 3-D Capacitance Extraction

Lu, Taotao; Wang, Zeyi; Yu, Wenjian

doi:10.1109/tmtt.2003.821228

Cited by 35 publications

(7 citation statements)

References 24 publications

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“…Obtained in such a way matrix C can be used to combine boundary method with FEM [24,25,26]. Some authors [15,27,28] call it boundary capacitance matrix (BCM) to emphasize its resemblance to the matrices describing coupling capacitances of the systems of conductors. C elements express charge induced on boundary elements in terms of their potentials.…”

Section: Direct Trefftz Methodsmentioning

confidence: 99%

The scalability of the matrices in direct Trefftz method in 2D Laplace problem

Borkowski

2016

Engineering Analysis with Boundary Elements

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This paper presents an interesting property of the matrices that may be obtained with the use of direct Trefftz method. It is proved analytically for 2D Laplace problem that values of the elements of matrices describing the capacitance of two scaled domains are inversely proportional to the scalability factor. As an example of the application the capacitance extraction problem is chosen. Concise description of the algorithm in which the scalability property can be utilized is given. Furthermore some numerical results of the algorithm are presented.

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Section: Direct Trefftz Methodsmentioning

confidence: 99%

The scalability of the matrices in direct Trefftz method in 2D Laplace problem

Borkowski

2016

Engineering Analysis with Boundary Elements

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“…For ease of presentation, we assume that the medium is homogeneous with permittivity . For examples on how to apply the BEM in media with complex dielectric configurations, the reader is referred to [4], [5], [9]. Starting from the integral equation formulation 7where is the computational domain, is the union of the boundary of the motif and the surfaces of the conductors, is the unit vector normal to , , is the free space Green's function, is the volumetric charge density, and is the electric potential.…”

Section: A Computing Local Interactions Within Motifsmentioning

confidence: 99%

“…The main difference between our algorithm and the standard BEM hierarchical methods ( [4], [5]) is that our algorithm resolves the global interactions without assembling/solving any expensive linear systems. Instead, our algorithm resolves the global interactions using random walks to simulate the Markov Chains.…”

Section: F Comparison Versus Other Hierarchical Algorithmsmentioning

confidence: 99%

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A Markov Chain Based Hierarchical Algorithm for Fabric-Aware Capacitance Extraction

El-Moselhy

Elfadel

Daniel

2010

IEEE Trans. Adv. Packag.

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In this paper, we propose a hierarchical algorithm to compute the 3-D capacitances of a large number of topologically different layout configurations that are all assembled from the same basic layout motifs. Our algorithm uses the boundary element method in order to compute a Markov transition matrix (MTM) for each motif. The individual motifs are connected together by building a large Markov chain. Such Markov chain can be simulated extremely efficiently using Monte Carlo simulations (e.g., random walks). The main practical advantage of the proposed algorithm is its ability to extract the capacitance of a large number of layout configurations in a complexity that is basically independent of the number of configurations. For instance, in a large 3-D layout example, the capacitance calculation of 1000 different configurations assembled from the same motifs is accomplished in the time required to solve independently two configurations, i.e., a 500 speedup.

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“…The ACA method (Lu et al, 2004;Benedetti et al, 2008) is in the context of methods in which the improvement comes from the acceleration of the solver, with the use of hierarchical matrices, introduced by Hackbusch (1999) . The system matrix is approximate by a low-rank expansion.…”

Section: Introductionmentioning

confidence: 99%

An Iterative Parallel Solver in GPU Applied to Frequency Domain Linear Water Wave Problems by the Boundary Element Method

Molina

Martínez-Castro

Ortiz

2018

Front. Built Environ.

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In this paper a parallel iterative solver based on the Generalized Minimum Residual Method (GMRES) with complex-valued coefficients is explored, with applications to the Boundary Element Method (BEM). The solver is designed to be executed in a GPU (Graphic Processing Unit) device, exploiting its massively parallel capabilities. The BEM is a competitive method in terms of reduction in the number of degrees of freedom. Nonetheless, the BEM shows disadvantages when the dimension of the system grows, due to the particular structure of the system matrix. With difference to other acceleration techniques, the main objective of the proposed solver is the direct acceleration of existing standard BEM codes, by transfering to the GPU the solver task. The CUDA programming language is used, exploiting the particular architecture of the GPU device for complex-valued systems. To explore the performances of the solver, two linear water wave problems have been tested: the frequency-dependent added mass and damping matrices of a 3D floating body, and the Helmholtz equation in a 2D domain. A NVidia GeForce GTX 1080 graphic card has been used. The parallelized GMRES solver shows reductions in computing times when compared with its CPU implementation.

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Hierarchical Block Boundary-Element Method (HBBEM): A Fast Field Solver for 3-D Capacitance Extraction

Cited by 35 publications

References 24 publications

The scalability of the matrices in direct Trefftz method in 2D Laplace problem

The scalability of the matrices in direct Trefftz method in 2D Laplace problem

A Markov Chain Based Hierarchical Algorithm for Fabric-Aware Capacitance Extraction

An Iterative Parallel Solver in GPU Applied to Frequency Domain Linear Water Wave Problems by the Boundary Element Method

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