权益分类	功能权益	普通用户	{{item.name}}会员
{{category.name}}	{{benefitItem.name}}

Collaborative Research: On Some Fundamental Computational Issues in Simulating Interaction Models

协作研究：模拟交互模型中的一些基本计算问题

基本信息

批准号：
2012451
负责人：
Jingfang Huang
金额：
$ 19.96万
依托单位：
University of North Carolina at Chapel Hill
依托单位国家：
美国
项目类别：
Continuing Grant
财政年份：
2020
资助国家：
美国
起止时间：
2020-08-15 至 2024-07-31
项目状态：
已结题

来源：
https://www.nsf.gov/awardsearch/showAward?AWD_ID=2012451&HistoricalAwards=false
关键词：
Collaborative Research Some Fundamental Computational

项目摘要

This project will investigate some fundamental computational issues for mathematical interaction models arising from scientific and engineering applications. Examples of these models include the electromagnetic and gravitational interactions in physics, interactions between molecules or cells in biology, and more general fractional differential equations and network models in material science, quantum theory, and social science. It is evident that modern interaction models are becoming more complex and demanding more accurate and efficient computational methods to handle the large scale interactions on high-performance computers. This project will (1) introduce novel representations of interaction models that are suitable for accelerated computation, (2) design efficient algorithms for interaction evaluations, (3) develop advanced open source tools, and (4) apply them to applications in nano-photonic devices, remote sensing, and medical imaging devices. This project will also train graduate students, including those from under-represented groups in STEM fields. This project will support one graduate per year for all 3 years on one campus and one graduate per year for years 2 and 3 on the other campus. In most interaction models, kernels usually depend on the spatial or temporal locations that may include the contributions from the interfaces between different materials. They may even depend on the given density functions at both the source and target locations. It is critical to find suitably compressed kernel representations for easier analysis and accelerated computation. This project will start from the optimal representations of the layered media Green’s functions for acoustic and electromagnetic waves that are spatially variant due to the contributions from the layer interfaces. These will be found through optimal integration contours and the corresponding discretized basis functions. The PIs will also generalize the partial-wave and plane-wave frame representations of the Laplace layer potentials to Yukawa, Helmholtz, and layered media potentials. The result will lead to better compressed density, kernel, and potential representations of more challenging non-local models in physics, biology, material science, social science, and image analysis. The PIs will develop effective numerical schemes for computing the compressible features and accelerating their algebraic operations by utilizing a multi-resolution framework to identify the interaction kernel features at different scales. The project also aims to create advanced open source software packages for the commonly used Laplace, Yukawa, and Helmholtz equations. Finally, through collaborations with application domain scientists and engineers, the numerical tools will be used in the design of optimal nano-photonic devices such as passive cooling devices, which may lead to a reduced carbon footprint and help socioeconomically disadvantaged communities lower their energy bills.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.

该项目将研究科学和工程应用中产生的数学交互模型的一些基本计算问题。这些模型的例子包括物理学中的电磁和引力相互作用、生物学中分子或细胞之间的相互作用，以及材料科学、量子理论和社会科学中更一般的分数阶微分方程和网络模型。显然，现代交互模型变得越来越复杂，需要更准确、更高效的计算方法来处理高性能计算机上的大规模交互。该项目将（1）引入适合加速计算的交互模型的新颖表示，（2）设计用于交互评估的有效算法，（3）开发先进的开源工具，以及（4）将它们应用于纳米光子设备、遥感和医学成像设备中的应用。该项目还将培训研究生，包括来自 STEM 领域代表性不足群体的研究生。该项目将在一个校区每年资助一名毕业生整个 3 年，并在另一个校区每年支持一名毕业生第 2 年和第 3 年。在大多数相互作用模型中，内核通常取决于空间或时间位置，其中可能包括不同材料之间界面的贡献。它们甚至可能取决于源位置和目标位置处给定的密度函数。找到适当压缩的内核表示以便于分析和加速计算至关重要。该项目将从声波和电磁波的层状介质格林函数的最佳表示开始，这些波和电磁波由于层界面的贡献而在空间上发生变化。这些将通过最佳积分轮廓和相应的离散基函数找到。 PI 还将把拉普拉斯层势的部分波和平面波框架表示推广到汤川势、亥姆霍兹势和分层介质势。结果将带来更好的压缩密度、内核以及物理、生物学、材料科学、社会科学和图像分析中更具挑战性的非局域模型的潜在表示。 PI 将开发有效的数值方案来计算可压缩特征，并通过利用多分辨率框架来识别不同尺度的交互核特征来加速其代数运算。该项目还旨在为常用的拉普拉斯、汤川和亥姆霍兹方程创建先进的开源软件包。最后，通过与应用领域科学家和工程师的合作，数值工具将用于设计最佳纳米光子设备，例如无源冷却设备，这可能会减少碳足迹，并帮助社会经济弱势社区降低能源费用。该奖项反映了 NSF 的法定使命，并通过使用基金会的智力价值和更广泛的影响进行评估，被认为值得支持审查标准。