SPX: A Geometry and Architecture Agnostic Scalable Framework for N-body Problems with Oscillatory Potentials

电磁学和声学方程的解决方案使关键技术得以实现，如无线通信设备、无源和有源RF-ID、光学和高速设备、汽车中的声纳和雷达发射器、微波、医疗诊断和成像工具等。这些技术的进步有赖于对潜在的波动物理有足够详细的了解。鉴于几何复杂性的增加(更小和更复杂的特征)和更宽的工作波频率范围，这项任务越来越具有挑战性，因此需要更高的精度和细节才能实现最佳性能。这个项目的主要目标是通过数值方法和并行算法的协同研究，开发一个几何和结构不可知的可扩展框架，用于解决具有振荡(波)势的N体问题。在与领域科学家的合作下，将通过在电磁辐射、声学成像和纳米光子学方面的应用来展示所产生的框架的实用性。为了确保尽可能广泛地传播，拟议研究的结果，包括技术报告、代码、用户手册和测试案例，将通过一个专门的网站提供。该项目的跨学科性质将为本科生和研究生提供大量的机会，以培养横跨应用数学、高性能计算和电气工程的前沿研究。该项目中将开发的框架的关键使能是快速多极方法(FMM)的Helmholtz(振荡势)变体。虽然使用FMM快速求解拉普拉斯方程对几个学科产生了深远的影响，从引力物理到分子动力学，从地球物理到电气工程，但Helmholtz变体的算法和软件远远落后。利用大规模并行性，能够以前所未有的速度和规模评估振荡潜力，这构成了该项目的主要智力贡献。项目方法包括以下目标：(I)开发创新的自适应数值方案以克服FMM对振荡势的计算和存储瓶颈，(Ii)新的负载平衡和自动调整算法被优化以针对给定的问题实例和硬件体系结构实现高性能，(Iii)混合并行实现将利用任务并行性来减少通信开销并实现在新兴的分布式存储体系结构上的可移植性，以及(Iv)通过对一组不同的Helmholtz系统进行多尺度建模来评估所产生的软件的能力和性能。本项目中开发的数值方法和并行算法将在一个名为HFMM-XScale的开源软件中实现，该软件将被设计为一个模块化软件，便于集成到现有的特定领域求解器中。因此，HFMM-XScale预计将对研究界产生广泛影响。这一奖项反映了NSF的法定使命，并通过使用基金会的智力优势和更广泛的影响审查标准进行评估，被认为值得支持。

Solutions to equations governing electromagnetics and acoustics have enabled crucial technologies such as wireless communication devices, passive and active RF-IDs, optical and high-speed devices, sonar and radar emitters in automobiles, microwaves, medical diagnostic, and imaging tools, among several others. Advances in these technologies rely on understanding the underlying wave physics in sufficient detail. This task is increasingly challenging given the increase in geometric complexity (smaller and more complex features) and wider range of operating wave frequencies thereby requiring more precision and detail to achieve optimal performance. The primary goal of this project is to develop a geometry and architecture agnostic scalable framework for N-body problems with oscillatory (wave) potentials through synergistic research in both numerical methods and parallel algorithms. In collaboration with domain scientists, the resulting framework's utility will be demonstrated via applications in electromagnetic radiation, acoustic imaging, and nano-photonics. In order to ensure the widest possible dissemination, outcomes of the proposed research including technical reports, codes, user manuals and test cases will be made available through a dedicated website. The interdisciplinary nature of this project will provide ample opportunities to train undergraduate and graduate students in leading edge research that cuts across applied mathematics, high performance computing, and electrical engineering.The key enabler of the framework to be developed in this project is the Helmholtz (oscillatory potential) variant of the Fast Multipole Method (FMM). While rapid solution to Laplace equations using FMM has had a profound impact on several disciplines, from gravitational physics to molecular dynamics to geophysics to electrical engineering, the algorithms and software for the Helmholtz variant is lagging far behind. Leveraging massive parallelism to enable the evaluation of oscillatory potentials at unprecedented speed and scales forms the main intellectual contributions of this project. The project approach is comprised of the following objectives: (i) Development of an innovative adaptive numerical scheme to overcome the computational and memory bottlenecks of FMM for oscillatory potentials, (ii) Novel load balancing and auto-tuning algorithms optimized to achieve high performance for a given problem instance and hardware architecture, (iii) A hybrid parallel implementation that will leverage task parallelism to reduce communication overheads and achieve portability on emerging distributed memory architectures, and (iv) Evaluation of the capabilities and performance of the resulting software through multi-scale modeling of a diverse set of Helmholtz systems. The numerical methods and parallel algorithms developed in this project will be implemented in an open-source software called HFMM-XScale, which will be designed as a modular software for easy integration into existing domain specific solvers. As such, HFMM-XScale is anticipated to have a broad impact on the research community.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.