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

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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 physical prototyping. (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.