Optimized Domain Decomposition Methods for Wave Propagation in Complex Media

复杂介质中波传播的优化域分解方法

基本信息

批准号：
1908602
负责人：
Catalin Turc
金额：
$ 13.32万
依托单位：
New Jersey Institute of Technology
依托单位国家：
美国
项目类别：
Continuing Grant
财政年份：
2019
资助国家：
美国
起止时间：
2019-09-01 至 2022-08-31
项目状态：
已结题

来源：
https://www.nsf.gov/awardsearch/showAward?AWD_ID=1908602&HistoricalAwards=false
关键词：
Optimized Domain Decomposition Methods Wave

项目摘要

The propagation of electromagnetic or elastic waves in a medium is distorted by interfaces where the medium is discontinuous. This happens in many settings of great practical importance, involving devices for communications, optics, remote sensing, and geophysical exploration. To understand these interactions between waves and the complex structures of the media through which they move, which often involve multiple scatterers as well as multiple layers with different material properties, requires resolving the complicated reflections and transmissions that waves undergo in such environments. This in turn requires large-scale numerical simulations. The investigator develops and analyzes high-performance, efficient, accurate, and rapidly convergent algorithms for this class of problems. His recent work with colleagues resulted in the development of an efficient computational strategy that incorporates windowed Green's functions within the boundary integral equation approach for the simulation of interaction of waves with infinitely extending interfaces. This computational framework enables simulation of transmission and reflection of waves by periodic media at high frequencies. This project builds on these methods to enable high-fidelity simulations of waves propagating in engineering structures such as thin film solar cells and metasurfaces. Graduate students participate in the research.The investigator develops a family of algorithms that focus mainly on optimized Schwarz domain decomposition (DD) methods, incorporate carefully designed quasi-optimal transmission operators, and are amenable to simple yet effective preconditioning strategies. Combining the merits of direct and iterative solvers, this class of methods has emerged as a leading contender for solution of high-frequency wave propagation in complex media. The computational methodology underlying this work is based on boundary integral solvers that, whenever applicable, can produce solutions to partial differential equations with high-order accuracy and no numerical dispersion. The project leverages recent advances introduced by the investigator and collaborators in the boundary integral equation treatment of infinitely extending media (including periodic media) and dielectric composite media, combined with the modularity and parallelism inherent to DD methods, to enable simulations of realistic engineering structures such as complex photonic or electronic devices. The work affects a variety of areas of societal interest, including communication, remote sensing, seismology, and optics. A major part of the project with wide applications is the development of fast, highly accurate solvers for periodic metamaterials, and use of the resulting numerical tools in detailed investigation and design of photonic structures and metamaterials. Graduate students participate in the research and are trained in the field of high-performance scientific computing. Software packages for solution of boundary integral equations that can be used for teaching and research purposes are made available.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.

培养基中电磁或弹性波的传播被介质不连续的界面变形。这发生在许多实践意义的许多环境中，涉及通信，光学，遥感和地球物理探索的设备。要了解波浪和它们移动的介质的复杂结构之间的这些相互作用，这些介质通常涉及多个散点子以及具有不同材料特性的多个层，就需要解决在这种环境中波浪发生的复杂反射和传输。反过来，这需要大规模的数值模拟。研究人员针对此类问题开发和分析了高性能，有效，准确和快速收敛的算法。他最近与同事的工作导致了一种有效的计算策略的发展，该策略将窗口的格林功能纳入了边界积分方程方法中，以模拟与无限扩展接口的波的相互作用。该计算框架可以在高频下通过周期性介质对波的传输和反射进行模拟。该项目以这些方法为基础，以实现在工程结构（例如薄膜太阳能电池和元信息）中传播的波浪的高保真模拟。研究生参与了研究。研究人员开发了一种算法系列，主要关注精心设计的Schwarz域分解（DD）方法，并结合了精心设计的准最佳传输操作员，并且可以适应简单而有效但有效的预处理策略。结合了直接和迭代求解器的优点，这类方法已成为复杂介质中高频波传播解决方案的主要竞争者。这项工作基础的计算方法基于边界积分求解器，每当适用时，都可以为具有高阶精度的部分微分方程生成解决方案，并且无数值分散。该项目利用了研究人员和合作者在无限扩展媒体（包括定期媒体）和介电复合媒体的边界积分方程处理中提出的最新进展，并结合了DD方法固有的模块化和并行性，以启用现实工程结构（例如复杂的光电设备）等现实工程结构的模拟。这项工作会影响社会兴趣的各个领域，包括沟通，遥感，地震学和光学。该项目的主要应用是广泛应用的主要部分是开发用于周期性超材料的快速，高度精确的求解器，以及在光子结构和超材料的详细研究和设计中使用所得的数值工具。研究生参加了研究，并接受了高性能科学计算领域的培训。可以提供可用于教学和研究目的的边界积分方程解决方案的软件包。该奖项反映了NSF的法定任务，并被认为是值得通过基金会的知识分子优点和更广泛的影响审查标准通过评估来支持的。