A BDDC algorithm with adaptive primal constraints for staggered discontinuous Galerkin approximation of elliptic problems with highly oscillating coefficients

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• 作者：Hyea Hyun Kim^a ; ^{hhkim@khu.ac.kr" class="auth_mail" title="E-mail the corresponding author} ; ^{hyeahyun@gmail.com" class="auth_mail" title="E-mail the corresponding author} ; Eric T. Chung^b ; ^{tschung@math.cuhk.edu.hk" class="auth_mail" title="E-mail the corresponding author} ; Chenxiao Xu^c ; ^{chenxiao.xu@stonybrook.edu" class="auth_mail" title="E-mail the corresponding author}
• 关键词：BDDC algorithm ; Staggered discontinuous Galerkin method ; Primal unknowns ; Generalized eigenvalue problem
• 刊名：Journal of Computational and Applied Mathematics
• 出版年：2017
• 出版时间：February 2017
• 年：2017
• 卷：311
• 期：Complete
• 页码：599-617
• 全文大小：1429 K

文摘

A BDDC (Balancing Domain Decomposition by Constraints) algorithm for a staggered discontinuous Galerkin approximation is considered. After applying domain decomposition method, a global linear system on the subdomain interface unknowns is obtained and solved by the conjugate gradient method combined with a preconditioner. To construct a preconditioner that is robust to the coefficient variations, a generalized eigenvalue problem on each subdomain interface is solved and primal unknowns are selected from the eigenvectors using a predetermined tolerance. By the construction of the staggered discontinuous Galerkin methods, the degrees of freedom on subdomain interfaces are shared by only two subdomains, and hence the construction of primal unknowns are simplified. The resulting BDDC algorithm is shown to have the condition number bounded by the predetermined tolerance. A modified algorithm for parameter dependent problems is also introduced, where the primal unknowns are only computed in an offline stage. Numerical results are included to show the performance of the proposed method and to verify the theoretical estimate.