Next-generation integral equation methods for wave scattering and propagation in periodic structures

周期性结构中波散射和传播的下一代积分方程方法

• 批准号: 1216656
• 负责人: Alexander Barnett
• 金额: $ 18万
• 依托单位: Dartmouth College
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2012
• 资助国家: 美国
• 起止时间: 2012-07-15 至 2015-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1216656&HistoricalAwards=false
• 关键词: Next; generation; integral; equation; methods

The investigator and supported graduate student will develop new integral equation algorithms to solve the Helmholtz equation in the context of time-harmonic wave scattering from complex periodic structures. These algorithms will be efficient, high-order accurate, mathematically rigorous, and, unlike many existing integral equation solvers, robust for all problem parameters. Building upon success in two dimensions, the project considers technologically important multilayer media and three dimensional doubly-periodic scatterers. The work includes developing new surface quadrature schemes, and the use of recent fast direct solvers to handle multiple incident angles.Basic science, engineering progress, and technology is increasingly reliant upon the guidance and control of waves by periodic structures on the scale of the wavelength. Examples include diffraction gratings, filters, photonic crystals and other nano-scale materials, cost-effective solar cells, microwave antennae, radar, sound absorbers, lithography and remote sensing. The computer algorithms proposed by the investigator will make the modeling and design of such devices more efficient, accurate, and reliable. Efficiency and robustness are paramount because predicting real-world device performance often requires thousands of solutions at different parameters. The societal benefits of more rapid modeling and design of such complex devices are many, including faster communication, and cheaper renewable energy. The investigator will release publicly-available software, and also will engage local rural high-school mathematics students with hands-on explorations in music, acoustics, waves, and computer signal analysis.

研究人员和支持的研究生将开发新的积分方程算法，以在复杂周期性结构的时谐波散射的背景下求解Helmholtz方程。这些算法将是有效的，高阶的准确性，数学上严格的，并且与许多现有的积分方程求解器不同，对于所有问题参数都有鲁棒。 该项目在两个维度上的成功基础上考虑了技术上重要的多层媒体和三维双周期散射器。这项工作包括开发新的表面正交方案，以及最新的快速直接求解器处理多个事件角度。基本科学，工程进步和技术越来越依赖于在波长规模上通过周期性结构对波浪进行的指导和控制。例子包括衍射光栅，过滤器，光子晶体和其他纳米尺度材料，具有成本效益的太阳能电池，微波天线，雷达，声音吸收器，光刻和遥感。 研究人员提出的计算机算法将使此类设备的建模和设计更有效，准确和可靠。 效率和鲁棒性至关重要，因为预测现实世界设备的性能通常需要以不同的参数为单位。 这种复杂设备的更快建模和设计的社会优势很多，包括更快的沟通和便宜的可再生能源。研究人员将发布公开可用的软件，并将通过音乐，声学，波浪和计算机信号分析中的动手探索与当地的农村高中数学学生互动。