2020/12/03 by Siu Wun Cheung, Cheung, Siu Wun, Eric T. Chung +7
Computer Science · Engineering · #Advanced Mathematical Modeling in Engineering #Advanced Numerical Methods in Computational Mathematics #Composite Material Mechanics #FOS: Mathematics #Numerical Analysis (math.NA)
paper · pdf · doi:10.48550/arxiv.2012.01817
openalex publication_date 2020/12/03 · openalex created_date 2022/10/01 · openalex updated_date 2026/07/28
In this paper, we develop an iterative scheme to construct multiscale basis\nfunctions within the framework of the Constraint Energy Minimizing Generalized\nMultiscale Finite Element Method (CEM-GMsFEM) for the mixed formulation. The\niterative procedure starts with the construction of an energy minimizing\nsnapshot space that can be used for approximating the solution of the model\nproblem. A spectral decomposition is then performed on the snapshot space to\nform global multiscale space. Under this setting, each global multiscale basis\nfunction can be split into a non-decaying and a decaying parts. The\nnon-decaying part of a global basis is localized and it is fixed during the\niteration. Then, one can approximate the decaying part via a modified\nRichardson scheme with an appropriately defined preconditioner. Using this set\nof iterative-based multiscale basis functions, first-order convergence with\nrespect to the coarse mesh size can be shown if sufficiently many times of\niterations with regularization parameter being in an appropriate range are\nperformed. Numerical results are presented to illustrate the effectiveness and\nefficiency of the proposed computational multiscale method.\n