Improved separators by multigrid methods

1996 International Conference on Simulation of Semiconductor Processes and Devices. SISPAD '96 (IEEE Cat. No.96TH8095) Pub Date : 1996-09-02 DOI:10.1109/SISPAD.1996.865326

K. Gartner, W. Fichtner

{"title":"Improved separators by multigrid methods","authors":"K. Gartner, W. Fichtner","doi":"10.1109/SISPAD.1996.865326","DOIUrl":null,"url":null,"abstract":"The graph partitioning problem has many different applications. One of them is the partitioning problem in parallel computations. With respect to process and device simulation we see two direct connections: (a) for some parallel solution methods we are interested in device simulation; good approximations of best separators are essential; (b) the equations to be solved here have properties pretty close to those of diffusion-convection equations-so the problem is a test case for the algebraic MG algorithm aimed at the device equations. The combinatorial problem is known to be NP hard-so different types of heuristic solutions are in use: stimulated annealing at the one end and the approximate solution of an analytic analog -the Neumann eigenvalue problem-at the other. By means of multigrid algorithms wider classes of problems, not only Neumann eigenvalue problems, can and will be efficiently solved. Therefore we are interested in more general analytic analogs, demonstrate the possibility to solve the related discrete problems and the potential of improvement.","PeriodicalId":341161,"journal":{"name":"1996 International Conference on Simulation of Semiconductor Processes and Devices. SISPAD '96 (IEEE Cat. No.96TH8095)","volume":"1 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"1996-09-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"1996 International Conference on Simulation of Semiconductor Processes and Devices. SISPAD '96 (IEEE Cat. No.96TH8095)","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1109/SISPAD.1996.865326","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}

引用次数: 0

Abstract

The graph partitioning problem has many different applications. One of them is the partitioning problem in parallel computations. With respect to process and device simulation we see two direct connections: (a) for some parallel solution methods we are interested in device simulation; good approximations of best separators are essential; (b) the equations to be solved here have properties pretty close to those of diffusion-convection equations-so the problem is a test case for the algebraic MG algorithm aimed at the device equations. The combinatorial problem is known to be NP hard-so different types of heuristic solutions are in use: stimulated annealing at the one end and the approximate solution of an analytic analog -the Neumann eigenvalue problem-at the other. By means of multigrid algorithms wider classes of problems, not only Neumann eigenvalue problems, can and will be efficiently solved. Therefore we are interested in more general analytic analogs, demonstrate the possibility to solve the related discrete problems and the potential of improvement.

查看原文本刊更多论文

采用多网格方法改进了分离器

图划分问题有许多不同的应用。其中之一是并行计算中的分区问题。关于过程和设备仿真，我们看到了两个直接联系:(a)对于一些我们对设备仿真感兴趣的并行解决方法;最佳分离器的良好近似是必不可少的;(b)这里待解的方程具有与扩散对流方程非常接近的性质，因此该问题是针对器件方程的代数MG算法的测试用例。众所周知，组合问题是NP困难的，因此使用了不同类型的启发式解决方案:一端是受激退火，另一端是解析模拟-诺伊曼特征值问题的近似解。通过多网格算法，不仅可以求解诺伊曼特征值问题，还可以求解更广泛的问题。因此，我们对更一般的解析类比感兴趣，展示解决相关离散问题的可能性和改进的潜力。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

求助全文

约1分钟内获得全文求助全文

来源期刊

1996 International Conference on Simulation of Semiconductor Processes and Devices. SISPAD '96 (IEEE Cat. No.96TH8095)

自引率

0.00%

发文量