一维波动问题长时间积分的HMM分析
Analysis of HMM for One Dimensional Wave Propagation Problems Over Long Time
AI总结：
针对具有快速波动材料系数的一维波动问题，提出并分析了基于异质多尺度方法的长时间积分数值方法，有效捕捉长时间后的色散效应并显著降低计算复杂度。
摘要：
多尺度问题通过直接模拟计算成本高昂，因为必须在一个由问题最大尺度决定的域上表示最小尺度。我们遵循异质多尺度方法的框架，开发并分析了新的多尺度波动数值方法。这些数值方法将宏观和微观尺度的模拟耦合起来，用于处理具有快速波动材料系数的问题。新方法的计算复杂度显著低于传统技术。我们重点研究了应用于周期和非周期介质中一维波动问题长时间积分的HMM逼近，并表明长时间后出现的色散效应被完全捕捉。
英文摘要：
Multiscale problems are computationally costly to solve by direct simulation because the smallest scales must be represented over a domain determined by the largest scales of the problem. We have developed and analyzed new numerical methods for multiscale wave propagation following the framework of the heterogeneous multiscale method. The numerical methods couple simulations on macro- and microscales for problems with rapidly fluctuating material coefficients. The computational complexity of the new method is significantly lower than that of traditional techniques. We focus on HMM approximation applied to long time integration of one-dimensional wave propagation problems in both periodic and non-periodic medium and show that the dispersive effect that appear after long time is fully captured.
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