Collaborative Research: SI2-SSE: Software for integral equation solvers on manycore and heterogeneous architectures

我们建议开发和部署用于三维复杂几何中的边值问题的数学软件。库中的算法将基于积分方程式公式。该库将在由特殊加速器和多核架构组成的新型计算平台上进行扩展。积分方程组可以用来模拟许多具有重大社会影响的科学和工程问题。建议的模拟技术将在该项目中产生影响的三个示例应用是微流控芯片、生物分子静电学和等离子体物理。首先，微流控芯片是用于医疗诊断和药物设计的亚毫米大小的设备。以低成本优化这类设备的功能需要高效的计算机模拟工具，例如我们建议开发的工具。其次，了解DNA和蛋白质等生物分子的结构和功能在生物技术中至关重要。所提出的技术可用于解决双分子静电相互作用。第三，与聚变核反应堆相关的等离子体物理学包括复杂几何结构的静电相互作用，拟议的工作将使大规模三维模拟成为可能。该软件的主要特点是：(1)并行快速多极子方法，(2)高效的复杂几何建模技术，(3)简单的库接口，允许非专家使用所提出的软件，以及(4)在不同的体系结构上的可扩展性。几名博士后、研究生和本科生将参与该项目。其他教育活动将包括本科生的研究经验，利用NSF Reus等正在进行的项目。鼓励妇女、少数民族和代表性不足群体参与。

We propose to develop and deploy mathematical software for boundary-value problems in three-dimensional complex geometries. The algorithms in the library will be based on integral equation formulations. The library will be designed to scale on novel computing platforms that comprise special accelerators and manycore architectures. Integral equations can be used to conduct simulations on many problems in science and engineering with significant societal impact. Three example applications on which the proposed simulation technologies will have an impact in this project are microfluidic chips, biomolecular electrostatics, and plasma physics. First, microfluidic chips are submillimeter-sized devices used for medical diagnosis and drug design. Optimizing the function of such devices at low cost requires efficient computer simulation tools, such as the ones we propose to develop. Second, understanding the structure and function of biomolecules such as DNA and proteins is crucial in biotechnology. The proposed technologies can be used to resolve bimolecular electrostatic interactions. Third, plasma physics, which is related to fusion nuclear reactors, includes electrostatic interactions in complex geometries, and the proposed work will enable large-scale three-dimensional simulations. The key features of the proposed software are: (1) parallel fast multipole methods, (2) efficient geometric modeling techniques for complex geometries, (3) simple library interfaces that allow use of the proposed software by non-experts, and (4) scalability on heterogeneous architectures.Along with our research activities, an educational and dissemination program will be designed to communicate the results of this work to students and researchers. Several postdoctoral, graduate, and undergraduate students will be involved with the project. Additional educational activities will include research experiences for undergraduates, leveraging ongoing programs such as NSF REUs. We will encourage participation by women, minorities, and underrepresented groups.