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Helmholtz方程的新辐射条件以及波动方程，我们考虑周期性和随机介质。我们强调的是，在异质介质中，人造边界不应是非反射边界，因为外域中的异质介质会产生反射。对于Helmholtz方程，我们希望改善最近建议的方案。该方案要求该解决方案在所谓的辐射框中，是外向波动波的线性组合。该方案可以转移到波方程，我们可以在其中获得实用的数值方案 - 至少在均质化极限下。该项目是使用均化理论的一阶校正器来改善数值方案是一个至关重要的想法。我们在项目的第三部分中分析了随机媒体。我们使用最近引入的Taylor-Bloch波将上述辐射框的思想转移到随机设置中。我们的目的是分析大波长的新方法，并以数值测试中等波长的新方法。