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.

研究员和支持的研究生将开发新的积分方程算法，以解决复杂周期性结构的时谐波散射背景下的亥姆霍兹方程。这些算法将是高效的，高阶精度，数学上严格的，并且，不像许多现有的积分方程求解器，鲁棒的所有问题参数。 在二维成功的基础上，该项目考虑了技术上重要的多层介质和三维双周期散射体。工作包括开发新的表面求积方案，以及使用最近的快速直接求解器来处理多个入射角。基础科学、工程进展和技术越来越依赖于波长尺度上的周期性结构对波的引导和控制。例子包括衍射光栅、滤波器、光子晶体和其他纳米级材料、成本效益高的太阳能电池、微波天线、雷达、吸音器、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加高效，准确和可靠。 效率和鲁棒性至关重要，因为预测真实世界的设备性能通常需要不同参数的数千个解决方案。 更快地建模和设计这种复杂设备的社会效益很多，包括更快的通信和更便宜的可再生能源。研究人员将发布公开的软件，并将吸引当地农村高中数学学生参与音乐，声学，波浪和计算机信号分析的实践探索。