Parallel Multiscale Finite Element with Adaptive Bubble Enrichment Method

• Main Authors: Meng-Zhe Li, 李孟哲
• Other Authors: Feng-Nan Hwang
• Format: Others
• Language: zh-TW
• Published: 2016
• Online Access: http://ndltd.ncl.edu.tw/handle/f5b2xm

碩士 === 國立中央大學 === 數學系 === 104 === 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).