Multiscale modeling of wave propagation with exponential integration and GMsFEM

IF 3.4 2区数学 Q1 MATHEMATICS, APPLIED

Communications in Nonlinear Science and Numerical Simulation Pub Date : 2025-04-15 DOI:10.1016/j.cnsns.2025.108825

Wei Xie , Juan Galvis , Yin Yang , Yunqing Huang

引用次数: 0

Abstract

Numerical simulation of wave propagation in heterogeneous media is widely used in engineering and various applications. However, direct numerical simulation of wave propagation in such media is often impractical due to the need for extremely small time steps and fine spatial grids. In this paper, we propose a new multiscale model reduction method for solving the wave equation in heterogeneous media by combining the generalized multiscale finite element method (GMsFEM) with exponential integrators (EI). For spatial discretization, we construct local multiscale basis functions within the GMsFEM framework to capture microscopic behavior. EI enhances time integration stability, overcoming limitations of traditional finite difference schemes for time discretizations in high-contrast media. Three numerical examples are presented to demonstrate the efficiency of our method.

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基于指数积分和GMsFEM的波传播多尺度模拟

波在非均质介质中传播的数值模拟在工程和各种应用中有着广泛的应用。然而，由于需要极小的时间步长和精细的空间网格，直接数值模拟波在这种介质中的传播往往是不切实际的。本文将广义多尺度有限元法（GMsFEM）与指数积分法（EI）相结合，提出了求解非均匀介质中波动方程的一种新的多尺度模型简化方法。对于空间离散化，我们在GMsFEM框架内构建局部多尺度基函数来捕捉微观行为。EI增强了时间积分的稳定性，克服了传统有限差分格式在高对比度介质中进行时间离散的局限性。最后给出了三个数值算例，验证了该方法的有效性。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Communications in Nonlinear Science and Numerical Simulation MATHEMATICS, APPLIED-MATHEMATICS, INTERDISCIPLINARY APPLICATIONS

CiteScore

6.80

自引率

7.70%

发文量

378

审稿时长

78 days

期刊介绍： The journal publishes original research findings on experimental observation, mathematical modeling, theoretical analysis and numerical simulation, for more accurate description, better prediction or novel application, of nonlinear phenomena in science and engineering. It offers a venue for researchers to make rapid exchange of ideas and techniques in nonlinear science and complexity. The submission of manuscripts with cross-disciplinary approaches in nonlinear science and complexity is particularly encouraged. Topics of interest: Nonlinear differential or delay equations, Lie group analysis and asymptotic methods, Discontinuous systems, Fractals, Fractional calculus and dynamics, Nonlinear effects in quantum mechanics, Nonlinear stochastic processes, Experimental nonlinear science, Time-series and signal analysis, Computational methods and simulations in nonlinear science and engineering, Control of dynamical systems, Synchronization, Lyapunov analysis, High-dimensional chaos and turbulence, Chaos in Hamiltonian systems, Integrable systems and solitons, Collective behavior in many-body systems, Biological physics and networks, Nonlinear mechanical systems, Complex systems and complexity. No length limitation for contributions is set, but only concisely written manuscripts are published. Brief papers are published on the basis of Rapid Communications. Discussions of previously published papers are welcome.