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This content will become publicly available on May 3, 2024

Title: Exponentially Convergent Multiscale Finite Element Method
We provide a concise review of the exponentially convergent multiscale finite element method (ExpMsFEM) for efficient model reduction of PDEs in heterogeneous media without scale separation and in high-frequency wave propagation. The ExpMsFEM is built on the non-overlapped domain decomposition in the classical MsFEM while enriching the approximation space systematically to achieve a nearly exponential convergence rate regarding the number of basis functions. Unlike most generalizations of the MsFEM in the literature, the ExpMsFEM does not rely on any partition of unity functions. In general, it is necessary to use function representations dependent on the right-hand side to break the algebraic Kolmogorov n-width barrier to achieve exponential convergence. Indeed, there are online and offline parts in the function representation provided by the ExpMsFEM. The online part depends on the right-hand side locally and can be computed in parallel efficiently. The offline part contains basis functions that are used in the Galerkin method to assemble the stiffness matrix; they are all independent of the right-hand side, so the stiffness matrix can be used repeatedly in multi-query scenarios.  more » « less
Award ID(s):
2205590
NSF-PAR ID:
10437516
Author(s) / Creator(s):
; ;
Date Published:
Journal Name:
Communications on Applied Mathematics and Computation
ISSN:
2096-6385
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
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