当前位置: X-MOL 学术arXiv.cs.NA › 论文详情
Our official English website, www.x-mol.net, welcomes your feedback! (Note: you will need to create a separate account there.)
Contrast-independent partially explicit time discretizations for multiscale wave problems
arXiv - CS - Numerical Analysis Pub Date : 2021-02-25 , DOI: arxiv-2102.13198
Eric T. Chung, Yalchin Efendiev, Wing Tat Leung, Petr N. Vabishchevich

In this work, we design and investigate contrast-independent partially explicit time discretizations for wave equations in heterogeneous high-contrast media. We consider multiscale problems, where the spatial heterogeneities are at subgrid level and are not resolved. In our previous work, we have introduced contrast-independent partially explicit time discretizations and applied to parabolic equations. The main idea of contrast-independent partially explicit time discretization is to split the spatial space into two components: contrast dependent (fast) and contrast independent (slow) spaces defined via multiscale space decomposition. Using this decomposition, our goal is further appropriately to introduce time splitting such that the resulting scheme is stable and can guarantee contrast-independent discretization under some suitable (reasonable) conditions. In this paper, we propose contrast-independent partially explicitly scheme for wave equations. The splitting requires a careful design. We prove that the proposed splitting is unconditionally stable under some suitable conditions formulated for the second space (slow). This condition requires some type of non-contrast dependent space and is easier to satisfy in the "slow" space. We present numerical results and show that the proposed methods provide results similar to implicit methods with the time step that is independent of the contrast.

中文翻译:

多尺度波动问题的与对比度无关的局部显式时间离散

在这项工作中,我们设计和研究非均质高对比度介质中波动方程的与对比度无关的局部显式时间离散。我们考虑了多尺度问题,其中空间异质性处于子网格级别并且没有得到解决。在我们以前的工作中,我们引入了与对比度无关的部分显式时间离散化,并将其应用于抛物线方程。不依赖于对比度的部分显式时间离散化的主要思想是将空间空间分为两个部分:通过多尺度空间分解定义的依赖于对比度的(快速)空间和不依赖于对比度的(慢速)空间。使用这种分解,我们的目标是进一步适当地引入时间分割,以使生成的方案稳定,并可以在某些合适(合理)的条件下保证对比度无关的离散化。在本文中,我们提出了波动方程的独立于对比度的部分显式方案。分割需要仔细的设计。我们证明,在为第二空间(慢速)制定的某些合适条件下,拟议的分裂是无条件稳定的。此条件需要某种类型的非对比度相关空间,并且在“慢速”空间中更容易满足。我们目前的数值结果,并表明,所提出的方法提供的结果类似于隐式方法,其时间步长与对比度无关。我们为波动方程提出了与对比度无关的部分显式方案。分割需要仔细的设计。我们证明,在为第二空间(慢速)制定的某些合适条件下,拟议的分裂是无条件稳定的。此条件需要某种类型的非对比度相关空间,并且在“慢速”空间中更容易满足。我们目前的数值结果,并表明,所提出的方法提供的结果类似于隐式方法,其时间步长与对比度无关。我们为波动方程提出了与对比度无关的部分显式方案。分割需要仔细的设计。我们证明,在为第二空间(慢速)制定的某些合适条件下,拟议的分裂是无条件稳定的。此条件需要某种类型的非对比度相关空间,并且在“慢速”空间中更容易满足。我们目前的数值结果,并表明,所提出的方法提供的结果类似于隐式方法,其时间步长与对比度无关。
更新日期:2021-03-01
down
wechat
bug