快速质量集总多尺度波传播模拟
Fast mass lumped multiscale wave propagation modelling
摘要：
在本文中，我们调查使用的质量集总完全显式时间步进计划的离散化的波动方程与底层材料参数，在任意精细尺度变化。我们结合了蛙跳计划的时间离散与多尺度技术称为局部正交分解的空间离散。为了加快该方法，并使其完全明确，一个特殊的质量集中的方法，依赖于一个适当的插值算子。该算子也用于局部正交分解的构造，并且是该方法的一个关键特征。我们证明了该方法收敛于二阶的能量范数，与领先的常数，不依赖于材料参数变化的尺度。我们还说明了一组数值实验中的质量集总方法的性能。
英文摘要：
In this paper, we investigate the use of a mass lumped fully explicit time stepping scheme for the discretisation of the wave equation with underlying material parameters that vary at arbitrarily fine scales. We combine the leapfrog scheme for the temporal discretisation with the multiscale technique known as Localized Orthogonal Decomposition for the spatial discretisation. To speed up the method and to make it fully explicit, a special mass lumping approach is introduced that relies on an appropriate interpolation operator. This operator is also employed in the construction of the Localized Orthogonal Decomposition and is a key feature of the approach. We prove that the method converges with second order in the energy norm, with a leading constant that does not depend on the scales at which the material parameters vary. We also illustrate the performance of the mass lumped method in a set of numerical experiments.
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