- 學位論文
無元素法之分散式計算
A Study on Distributed Computation of the Element Free Galerkin Method
摘要
無元素法模擬問題時只需要節點資料，不需要描述節點關係的元素，其中節點的形狀函數利用變動式最小平方近似法建立。由於無元素法各節點的形狀函數可能不同，必需在程式中建立，所以計算量較一般有限元素法多，因此如何有效提昇無元素法的計算效率是一個重要的課題。 本研究主要嘗試利用個人電腦叢集進行無元素法的平行計算。無元素法的平行計算可以從下面幾方面著手：(1)節點、高斯積分點、取樣點搜尋的平行處理。(2) 節點形狀函數的平行處理。(3)聯立方程式的平行處理。本研究主要說明無元素法節點搜尋的平行處理，及利用共軛梯度法配合變寬帶觀念求解聯立方程式的平行處理，以節省計算時間，最後利用幾個數值算例說明該方法的成果。
並列摘要
The main feature of Element free Galerkin method (EFGM) is that the construction of shape functions is based on the moving least-square (MLS) interpolation technique, which requires only nodal data and not any connectivity requirement among these nodes. The nodal shape function of the EFGM is constructed through some searching algorithms and the MLS technique and it may varies at each node. Previous experience shows that for the same problem to be solved, the computation time required by the EFGM is more than it required by the finite element method. Hence, how to improve the computational efficiency becomes an important issue in the further development of the EFGM. The study is mainly based on using Pc Clusters. There are several possible solutions to improve the computational efficiency of EFGM. Firstly, Parallel computation of searching for finding corresponding nodal points when constructing shape function. Secondly, Parallel computation of constructing shape function. Thirdly, Parallel computation of solving the system governing equations. The skyline solution technique and parallel computation of conjugate gradient method is adopted to solve the system equations with large sparse coefficient matrix typically obtained in the EFGM. Then, Numerical simulations of 2D elastostatic and elastodynamic problems demonstrate that the adoption of that three solutions technique into the EFGM can largely reduce the computation time than the one using conventional solving technique.