中大機構典藏-NCU Institutional Repository-提供博碩士論文、考古題、期刊論文、研究計畫等下載:Item 987654321/72332
English  |  正體中文  |  简体中文  |  全文筆數/總筆數 : 66984/66984 (100%)
造訪人次 : 23031781      線上人數 : 209
RC Version 7.0 © Powered By DSPACE, MIT. Enhanced by NTU Library IR team.
搜尋範圍 查詢小技巧:
  • 您可在西文檢索詞彙前後加上"雙引號",以獲取較精準的檢索結果
  • 若欲以作者姓名搜尋,建議至進階搜尋限定作者欄位,可獲得較完整資料
  • 進階搜尋


    請使用永久網址來引用或連結此文件: http://ir.lib.ncu.edu.tw/handle/987654321/72332


    題名: Parallel Multiscale Finite Element with Adaptive Bubble Enrichment Method
    作者: 李孟哲;Li,Meng-Zhe
    貢獻者: 數學系
    關鍵詞: 多尺度有限元素法;自適應氣泡函式;多孔介質;非均質問題;橢圓問題;Multiscale finite element method;Adaptive bubble function;Porous media;Heterogeneous problem;Elliptic problem
    日期: 2016-07-25
    上傳時間: 2016-10-13 14:48:08 (UTC+8)
    出版者: 國立中央大學
    摘要: 模擬在多孔介質中的流體運動,通常使用達西定律(Darcy′s law)計算流體的流場,它是一個在非均值滲透透性下的橢圓問題,而多尺度的方法是一類適合解這樣非均質問題的方法。多尺度有限元素法(multiscale finite element method)可以將細網格(fine-grid)的大問題分解成多個在粗網格(coarse-grid)與子網格(sub-grid)上較小的問題,且在非均質(heterogeneous)的問題上較不會遺漏細微的資訊,但是近似解的精確度容易受到多尺度基底(multiscale basis)的影響,所以我們從多重網格法(multigrid method)引進smoothing的概念進而發展自適應多尺度有限元素法(iApMsFEM),透過迭代過程自動調整多尺度基底來得到近似解,再根據多尺度有限元素法的特性將它平行化來達到加速的效果。但是,自適應多尺度有限元素法因為多尺度基底的改變必須重複的作一些計算量較大的運算,為了改善自適應多尺度有限元素法的這個缺點,我們發展multiscale finite element with adaptive bubble enrichment method (MsFEM_bub),不再透過迭代過程改善多尺度基底來修正數值解,而是透過迭代過程改善氣泡函數(bubble function)來修正數值解,因為多尺度基底不再隨著迭代而改變,所以可以大幅減少那些重複的計算。
      在實驗階段,透過均質(homogeneous)與非均質的橢圓問題來尋找 MsFEM_bub 的最佳參數設定以及探討其延展性(scability),也透過這些的問題來比較 MsFEM_bub 與多尺度自適應有限元素法和多重網格法的差異。這份論文的實驗結果皆是在國立中央大學數學系的叢集電腦與國家高速網路與計算中心的ALPS上實驗而得到的。;To simulate some physical behavior of fluid in a porous media, we usually compute the flow field by Darcy′s law which is an elliptic problem with heterogeneous permeability. And the multiscale methods are suitable to solve the heterogeneous problem. Multiscale finite element method (MsFEM) can separate the huge fine-grid problem into several small sub-grid problems and coarse-grid problem, and it less lost important fine-grid information for the heterogeneous problem when it does information exchange between fine-grid and coarse-grid. But the accuracy of MsFEM is easily affected by the multiscale basis. Therefore, we develop the iteratively adaptive multiscale finite element method (iApMsFEM) which introduces the conception of smoothing from the multi-grid method (MG). iApMsFEM can update the multiscale basis by iteration and then it can improve the approximation. We also can use some properties of MsFEM to parallel and accelerate iApMsFEM. But iApMsFEM must do some repeated computations because that the multiscale basis is updated as the method iterates. To improve this disadvantage, we develop multi-scale finite element with adaptive bubble enrichment method (MsFEM_bub) which no longer update the multiscale basis but update the bubble function in the iteration process to modify the approximation. Because of the fixed multiscale basis, we can avoid those repeated computations.

    In the numerical experiment, we use the homogeneous and heterogeneous elliptic problems to find the best parameter of MsFEM_bub and test its scalability. And we also use these problems to compare the difference between MsFEM_bub, iApMsFEM and MG. In this thesis, all of the numerical results are produced by the cluster Leopard in National Central University Department of Mathematics and ALPS in National Center for High-performance Computing (NCHC, NARLabs).
    顯示於類別:[數學研究所] 博碩士論文

    文件中的檔案:

    檔案 描述 大小格式瀏覽次數
    index.html0KbHTML398檢視/開啟


    在NCUIR中所有的資料項目都受到原著作權保護.

    社群 sharing

    ::: Copyright National Central University. | 國立中央大學圖書館版權所有 | 收藏本站 | 設為首頁 | 最佳瀏覽畫面: 1024*768 | 建站日期:8-24-2009 :::
    DSpace Software Copyright © 2002-2004  MIT &  Hewlett-Packard  /   Enhanced by   NTU Library IR team Copyright ©   - 回饋  - 隱私權政策聲明