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Authors: Leonardo A. Poveda, Juan Galvis, and Eric Chung
Volume 502, Issue C
Published: 25 June 2024 Publication History
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Abstract
This paper investigates an efficient exponential integrator generalized multiscale finite element method for solving a class of time-evolving partial differential equations in bounded domains. The proposed method first performs the spatial discretization of the model problem using constraint energy minimizing generalized multiscale finite element method (CEM-GMsFEM). This approach consists of two stages. First, the auxiliary space is constructed by solving local spectral problems, where the basis functions corresponding to small eigenvalues are captured. The multiscale basis functions are obtained in the second stage using the auxiliary space by solving local energy minimization problems over the oversampling domains. The basis functions have exponential decay outside the corresponding local oversampling regions. We shall consider the first and second-order explicit exponential Runge-Kutta approach for temporal discretization and to build a fully discrete numerical solution. The exponential integration strategy for the time variable allows us to take full advantage of the CEM-GMsFEM as it enables larger time steps due to its stability properties. We derive the error estimates in the energy norm under the regularity assumption. Finally, we will provide some numerical experiments to sustain the efficiency of the proposed method.
Highlights
•
Multiscale reduction methods are efficient and accurate to solve problems with high-contrast media.
•
The presence of high-contrast coefficients reduces the stability region of time discretization.
•
Implicit methods must solve nonlinear equations, which can be a bottleneck computation.
•
Exponential integrators are alternative techniques and use robust time-stepping.
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Published In
Journal of Computational Physics Volume 502, Issue C
Apr 2024
488 pages
ISSN:0021-9991
Issue’s Table of Contents
Elsevier Inc.
Publisher
Academic Press Professional, Inc.
United States
Publication History
Published: 25 June 2024
Author Tags
- Parabolic problems
- Multiscale finite element method
- Time integration
- Exponential integrator
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