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

控制电磁学和声学方程的解决方案使无线通信设备、无源和有源射频识别、光学和高速设备、汽车声纳和雷达发射器、微波、医疗诊断和成像工具等关键技术成为可能。这些技术的进步依赖于充分详细地了解潜在的波物理。考虑到几何复杂性的增加（更小和更复杂的特征）和更宽的工作波频率范围，因此需要更高的精度和细节来实现最佳性能，这项任务越来越具有挑战性。该项目的主要目标是通过数值方法和并行算法的协同研究，为具有振荡（波）势的n体问题开发一个几何和结构不可知的可扩展框架。在与领域科学家的合作下，结果框架的效用将通过电磁辐射、声学成像和纳米光子学的应用来证明。为了确保尽可能广泛地传播，拟议的研究成果，包括技术报告、代码、用户手册和测试用例，将通过一个专门的网站提供。该项目的跨学科性质将为培养本科生和研究生在应用数学、高性能计算和电气工程领域的前沿研究提供充足的机会。在这个项目中开发的框架的关键促成因素是快速多极方法（FMM）的亥姆霍兹（振荡电位）变体。虽然利用FMM快速求解拉普拉斯方程对几个学科产生了深远的影响，从引力物理学到分子动力学，从地球物理学到电气工程，但亥姆霍兹变体的算法和软件远远落后。利用大规模的并行性，以前所未有的速度和规模评估振荡电位，形成了这个项目的主要智力贡献。项目方法包括以下目标：(i)开发一种创新的自适应数值方案，以克服振荡电位FMM的计算和内存瓶颈；（ii）新颖的负载平衡和自动调整算法，优化为给定问题实例和硬件架构实现高性能；（iii）混合并行实现，将利用任务并行性来减少通信开销，并在新兴的分布式内存架构上实现可移植性；（iv）通过对一组不同的亥姆霍兹系统进行多尺度建模，评估最终软件的能力和性能。在这个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，以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的影响。该奖项反映了美国国家科学基金会的法定使命，并通过使用基金会的知识价值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.