Radiation conditions for waves in periodic and stochastic media

周期性和随机介质中波的辐射条件

• 批准号: 431081410
• 负责人: Professor Dr. Ben Schweizer
• 金额: --
• 依托单位: Lehrstuhl I: Analysis
• 依托单位国家: 德国
• 项目类别: Research Grants
• 财政年份: 2019
• 资助国家: 德国
• 起止时间: 2018-12-31 至 2021-12-31
• 项目状态: 已结题
• 来源: https://gepris.dfg.de/gepris/projekt/431081410?language=en
• 关键词: Radiation; conditions; waves; periodic; stochastic

The project analyzes new radiation conditions for the Helmholtz equation and for the wave equation, we consider periodic and stochastic media. We emphasize that, in heterogeneous media, an artificial boundary should not be a non-reflecting boundary, since the heterogeneous medium in the outer domain creates reflections. For the Helmholtz equation, we want to improve a recently suggested scheme. The scheme demands that the solution is, in so called radiation boxes, a linear combination of outgoing Bloch-waves. The scheme can be transferred to the wave equation, where we can obtain a practical numerical scheme - at least in the homogenization limit. It is a crucial idea of this project to use first order correctors from homogenization theory to improve the numerical scheme. We analyze stochastic media in a third part of the project. We use the recently introduced Taylor-Bloch waves to transfer the above ideas of radiation boxes to the stochastic setting. Our aim is to analyze the new method for large wave-lengths and to test the new method numerically for moderate wave-lengths.

该项目分析了新的辐射条件的亥姆霍兹方程和波动方程，我们认为周期性和随机介质。我们强调，在非均匀介质中，人工边界不应该是无反射边界，因为外部区域的非均匀介质会产生反射。对于Helmholtz方程，我们想改进最近提出的一个方案。该计划要求的解决方案是，在所谓的辐射盒，一个线性组合的出射布洛赫波。该方案可以转移到波动方程，在那里我们可以得到一个实用的数值方案-至少在均匀化极限。利用均匀化理论中的一阶修正项对数值格式进行改进是本项目的一个重要思想。我们在项目的第三部分分析随机介质。我们使用最近引入的泰勒-布洛赫波转移到随机设置的辐射箱的上述想法。我们的目的是分析大波长的新方法，并测试新方法的数值中等波长。