Collaborative Research: Foundations of Solving Large Direct and Inverse Scattering Problems - Algorithm Analysis and System Support

合作研究：解决大型直接和逆散射问题的基础-算法分析和系统支持总结我们建议在基于集群的大型高端系统上开发和实施新的计算方法，以解决工业和军事应用中电磁学中的直接和逆问题。 我们将解决这一高端科学计算项目的两组重要和密切相关的技术问题。首先，该项目的目标问题是只能在高端系统中解决的大规模直接和逆散射问题。 这些问题特别涉及高波数的电磁波传播。用优化方法求解反问题的一个主要困难是不适定性和许多局部极小值的存在。提出了一种求解三维麦克斯韦方程组逆散射问题的新方法。该方法的关键是开发一种有效的正则化迭代线性化算法（关于波数的递归线性化）。 发展数值方法的一个挑战是处理大型结构化数据集。 解决目标问题的第二组技术问题与高端体系结构中缺乏系统支持以保持高持续性能ofcomputing有关，这是由于CPU与内存和I/O存储之间的速度差距越来越高。 这种挑战也可以在高端系统上的许多其他大型科学计算问题中找到。 该提案中与科学计算同等重要的目标是通过有效分配CPU和内存资源、建立高端架构的全局网络RAM系统以及提供特殊的系统处理程序来处理应用程序动态和意外的大内存需求，设计和构建有效的系统支持。该提案的智力优势来自几个方面。 (1)我们提出的数值方法将解决应用数学中的几个科学挑战，包括高波数的电磁波传播，逆问题的不适定性，以及多维大数据集的管理。(2)处理器和高端系统变得越来越复杂，这使得对执行行为的理解变得越来越困难。 我们提出的系统支持的基础上，硬件计数器和系统内核的仪器工具将解决系统的复杂性问题，并提供有见地的运行时系统信息的资源管理系统的低开销。 (3)为了有效地支持集群中的高持续性能和高生产率计算，我们的系统支持旨在实现几个重要的资源管理目标，如高内存利用率，低通信延迟和快速响应时间。 (4)虽然我们的系统将主要通过解决大型正问题和逆问题来测试，但我们的目标也是将其构建为通用系统，以便它将成为高端系统中许多其他大型科学应用的基本软件系统基础设施。（1）由于高性能系统的快速发展，计算电磁学已成为各种科学和工程学科中的一项基本的、蓬勃发展的技术，例如微波、毫米波、光学和声学。 我们的计算模型和集群系统支持将提供一个廉价和易于控制的结构/介质的"虚拟原型”，而不是昂贵，耗时的物理原型。 (2)拟议的系统资源管理工具和系统原型将在高端计算和系统界传播，供广泛使用。(3)研究成果将及时引入科学计算，并行计算和操作系统的本科和研究生课程开发。

Collaborative Research: Foundations of Solving Large Direct and Inverse Scattering Problems --- Algorithm Analysis and System SupportSummaryWe propose to develop and implement new computational methods on large cluster-based high-end systems for solving the direct and inverse problems in electromagnetics motivated by industrial and military applications. We will address two sets of important and closely related technical issues for this high-end scientific computing project. First, the targeted problems for the proposed project are large-scale direct and inverse scattering problems that can be only solved in high-end systems. These problems involveparticularly electromagnetic wave propagation with high wave numbers. A major difficulty for solving the inverse problems by an optimization method is the ill-posedness and the presence of many local minima. We propose a novel approach for solving the inverse medium scattering problem of Maxwell's equations in three dimensions. Crucial to the approach will be the development of an efficient regularized iterative linearization algorithm (recursive linearization with respect to the wave number). A challenge indeveloping our numerical methods is to deal with large and structured data sets. The second set of technical issues for solving the targeted problems is concerned with the lack of system support in high-end architectures to maintain high sustained performance ofcomputing due to increasingly high speed gap between the CPU and the memory and the I/O storage. This challenge can also be found in many other large scientific computation problems on high-end systems. An equivalently important objective to the scientific computing in this proposal is to design and build effective system support by effectively allocating both CPU and memory resources, by establishing a global network RAM system in high-end architecture, and by providing exceptional system handlers to deal with dynamic and unexpectedlylarge memory demands from applications.Intellectual merits of this proposal come from several aspects. (1) Our proposed numerical methods will address several scientific challenges in applied mathematics including electromagnetic wave propagation with high wave numbers, ill-posedness for inverse problems, and management of large data sets in multiple dimensions. (2) Processors and high-end systems have become increasingly complex, which makes the understanding of execution behavior more and more difficult. Our proposed system support based on both hardware counters and a system kernel instrumentation tool will address the system complexity issue, and provide insightful runtime system information for resource management systems with low overhead. (3) In order to effectively support high sustained performance and high productivity computing in clusters, our system support aims for several important resource management objectives, such as high memory utilization, low communication latency, and fast response time. (4) Although our system will be mainly tested by solving the large direct and inverse problems, it is also our aim to build it as a general purpose system so that it will become a fundamental software system infrastructure for many other large scientific applications in high-end systems.Broader impact of this proposal will be: (1) Due to the fast development of high performance systems, computational electromagnetics has become a fundamental, vigorously growing technology in diverse science and engineering disciplines, such asmicrowaves, millimeter waves, optics, and acoustics. Our computational models and cluster system support will provide an inexpensive and easily controllable ``virtual prototype" of the structures/media as opposed to costly, time-consuming physicalprototyping. (2) The proposed system resource management tools and system prototype will be disseminated in the high-end computing and systems community for a wide usage. (3) The research results will be timely introduced to both undergraduate and graduate curriculum development of scientific computing, parallel computing, and operating systems.