An improved Multiscale FEM for the free vibrations of heterogeneous solids. (15th March 2022)

• Record Type: Journal Article
• Authors: Oleksy, Marta; Cecot, Witold; Rachowicz, Waldemar; Nessel, Michał
• Is Part Of: Computers & mathematics with applications. Volume 110(2022)
• Page Start: 110
• Page End: 122
• Publication Date: 2022-03-15
• Subjects: MsFEM -- Dynamic condensation -- Upscaling -- Complex architecture; Electronic data processing -- Periodicals; Mathematics -- Data processing -- Periodicals; 510.28541
• DOI: 10.1016/j.camwa.2022.02.002
• Languages: English
• ISSNs: 0898-1221

Abstract

Abstract: We present an improvement of the Multiscale Finite Element Method (MsFEM). MsFEM incorporates fine-scale features of a domain through special oscillatory coarse-scale trial functions and its essential step is an online computation of these special functions defined using local auxiliary problems. Our enhancement makes use of the dynamic condensation that transmits the construction of the oscillatory basis functions exclusively to the coarse mesh skeleton (element interfaces) where we defined special 1D eigenproblems. Consequently, both the approximation error and computational cost are reduced. Moreover, arbitrary coarse mesh element geometries, like polytopal ones, may be used without any additional modifications. We illustrate the accuracy and convergence of the improved method with higher order approximation through selected plane strain examples.