A two-level overlapping Schwarz method with energy-minimizing multiscale coarse basis functions
Publication in refereed journal

香港中文大學研究人員
替代計量分析
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其它資訊
摘要A two-level overlapping Schwarz method is developed for second order elliptic problems with highly oscillatory and high contrast coefficients, for which it is known that the standard coarse problem fails to give a robust preconditioner. In this paper, we develop energy minimizing multiscale finite element functions to form a more robust coarse problem. First, a local spectral problem is solved in each non-overlapping coarse subdomain, and dominant eigenfunctions are selected as auxiliary functions, which are crucial for the high contrast case. The required multiscale basis functions are then obtained by minimizing an energy subject to some orthogonality conditions with respect to the auxiliary functions. Due to an exponential decay property, the minimization problem is solved locally on oversampling subdomains, that are unions of a few coarse subdomains. The coarse basis functions are therefore local and can be computed efficiently. The resulting preconditioner is shown to be robust with respect to the contrast in the coefficients as well as the overlapping width in the subdomain partition. Numerical results are included to confirm the theory and show the performance.
著者Junxian Wang, Eric Chung, Hyea Hyun Kim
期刊名稱Journal of Computational and Applied Mathematics
出版年份2020
月份5
卷號370
出版社Elsevier
文章號碼112600
國際標準期刊號0377-0427
電子國際標準期刊號1879-1778
語言美式英語

上次更新時間 2020-25-09 於 12:40