CAREER: Towards General-Purpose, High-Order Integral Equation Methods for Computer Simulation in Engineering: Analysis, Algorithm Design, and Applications
职业:面向工程计算机仿真的通用高阶积分方程方法:分析、算法设计和应用
基本信息
- 批准号:1654756
- 负责人:
- 金额:$ 40万
- 依托单位:
- 依托单位国家:美国
- 项目类别:Continuing Grant
- 财政年份:2017
- 资助国家:美国
- 起止时间:2017-08-15 至 2023-07-31
- 项目状态:已结题
- 来源:
- 关键词:
项目摘要
Numerical simulation has become an essential tool in nearly all areas of science and engineering, ranging from engine design to naval architecture, and from personalized medicine to city planning. Yet, the efficient solution of large-scale, globally coupled (so-called elliptic) computational problems arising in these application areas remains a major challenge. Although integral equation (IE) methods for numerical simulation typically have optimally low cost when applied to common problems in science and engineering, their impact has been limited to a small handful of applications by technical obstacles. The purpose of this project is to take important steps to remove these obstacles. First, the project will develop novel numerical and symbolic algorithms to reduce the amount of method design and implementation work required when adapting IE methods to new classes of applications. This will make the associated cost savings of these methods more broadly accessible. Second, the project will design, implement, and analyze parallel algorithms to enable the nation's large-scale computing resources to be used in conjunction with IE methods. Their increased computational efficiency will facilitate the study of models with increased fidelity and higher accuracy. Third, the project will extend the set of problems that can be attacked with IE methods to those including volume (and not just surface) data while using highly accurate geometric representations. Fourth, it will provide a theoretical understanding and practical methods for automatic control of numerical error in these methods. Lastly, the project will demonstrate the new methods and their use in the mathematically and numerically challenging context of fluid dynamics. To foster an understanding of the power of these kinds of computational tools in the next generation of the nation's workforce, this project will employ a day-long experience for students in their formative middle-school years. This experience will convey that computer modeling and simulation can help understand the world by testing the predictive power of simple, mechanistic models. Through its reliance on self-contained, hands-on computer experiments, the experience will be interactive and visually engaging, require little mathematics preparation, and easily establish connections with real-world applications of computing. The program focuses on creating engagement and interest, with the goal of promoting career and educational choices in mathematics and computing. Integral equation (IE) methods for computer simulation typically have optimally low cost, but their impact has been limited to a handful of applications by technical obstacles. The purpose of this research is to take important steps to remove these obstacles, by providing: 1. high-order singular quadrature and infrastructure for fast multipole methods for the evaluation of layer potentials with general, symbolically given kernels in complex geometry, 2. scalable and efficient distributed-memory parallel algorithms for the use of IE methods in large-scale applications, 3. design and analysis of high-order numerical methods for volume potentials in complex geometry as needed by inhomogeneous partial differential equations, 4. theory and methods for automatic adaptive mesh refinement based on a-posteriori error estimates, and 5. a demonstration of the capabilities of the developed methods and algorithms in the context of the incompressible Navier-Stokes equations, including high-order finite-element-method and IE coupling.
数值模拟已经成为几乎所有科学和工程领域的重要工具,从发动机设计到海军建筑,从个性化医疗到城市规划。然而,在这些应用领域中产生的大规模,全球耦合(所谓的椭圆)计算问题的有效解决方案仍然是一个重大的挑战。虽然积分方程(IE)方法的数值模拟通常具有最佳的低成本时,应用于科学和工程中的常见问题,其影响已被限制在少数应用的技术障碍。该项目的目的是采取重要步骤消除这些障碍。首先,该项目将开发新的数值和符号算法,以减少方法设计和实施工作的量时,需要适应IE方法的新类别的应用程序。这将使这些方法的相关成本节约更广泛地得到利用。其次,该项目将设计,实现和分析并行算法,使国家的大规模计算资源与IE方法结合使用。它们提高的计算效率将有助于研究具有更高保真度和更高准确性的模型。第三,该项目将扩展可以用IE方法攻击的问题集,包括体积(而不仅仅是表面)数据,同时使用高度精确的几何表示。第四,为这些方法中的数值误差自动控制提供理论认识和实用方法。最后,该项目将展示新方法及其在流体动力学的数学和数值挑战背景下的使用。为了促进对这些计算工具在国家下一代劳动力中的力量的理解,该项目将在学生的中学阶段为他们提供为期一天的体验。这种经验将传达计算机建模和仿真可以通过测试简单的机械模型的预测能力来帮助理解世界。通过其依赖于独立的,动手的计算机实验,经验将是互动的和视觉上的吸引力,需要很少的数学准备,并很容易建立与现实世界的计算应用程序的连接。该计划的重点是创造参与和兴趣,以促进数学和计算的职业和教育选择的目标。用于计算机模拟的积分方程(IE)方法通常具有最优的低成本,但由于技术障碍,其影响仅限于少数应用。 本研究的目的是采取重要步骤,以消除这些障碍,通过提供:1。高阶奇异求积和快速多极子方法的基础设施,用于评估层电位,具有复杂几何中的一般性,象征性地给出内核,2.可扩展和高效的分布式内存并行算法,用于在大规模应用中使用IE方法,3。非齐次偏微分方程所需要的复杂几何体势的高阶数值方法的设计和分析,4.基于后验误差估计的自动自适应网格细化的理论和方法; 5.在不可压缩Navier-Stokes方程的背景下,包括高阶有限元法和IE耦合的开发的方法和算法的能力的演示。
项目成果
期刊论文数量(6)
专著数量(0)
科研奖励数量(0)
会议论文数量(0)
专利数量(0)
Conformal Mapping via a Density Correspondence for the Double-Layer Potential
通过双层势的密度对应进行共形映射
- DOI:10.1137/18m1174982
- 发表时间:2018
- 期刊:
- 影响因子:3.1
- 作者:Wala, Matt;Klöckner, Andreas
- 通讯作者:Klöckner, Andreas
An Integral Equation Method for the Cahn-Hilliard Equation in the Wetting Problem
- DOI:10.1016/j.jcp.2020.109521
- 发表时间:2019-04
- 期刊:
- 影响因子:0
- 作者:Xiaoyu Wei;Shidong Jiang;A. Klöckner;Xiaoping Wang
- 通讯作者:Xiaoyu Wei;Shidong Jiang;A. Klöckner;Xiaoping Wang
A fast algorithm with error bounds for Quadrature by Expansion
一种具有误差范围的展开求积的快速算法
- DOI:10.1016/j.jcp.2018.05.006
- 发表时间:2018
- 期刊:
- 影响因子:4.1
- 作者:Wala, Matt;Klöckner, Andreas
- 通讯作者:Klöckner, Andreas
A fast algorithm for Quadrature by Expansion in three dimensions
三维展开求积的快速算法
- DOI:10.1016/j.jcp.2019.03.024
- 发表时间:2019
- 期刊:
- 影响因子:4.1
- 作者:Wala, Matt;Klöckner, Andreas
- 通讯作者:Klöckner, Andreas
Optimization of fast algorithms for global Quadrature by Expansion using target-specific expansions
- DOI:10.1016/j.jcp.2019.108976
- 发表时间:2018-11
- 期刊:
- 影响因子:0
- 作者:Matt Wala;A. Klöckner
- 通讯作者:Matt Wala;A. Klöckner
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Andreas Kloeckner其他文献
Andreas Kloeckner的其他文献
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{{ truncateString('Andreas Kloeckner', 18)}}的其他基金
SHF: Small: Collaborative Research: Transform-to-Perform: Languages, Algorithms, and Solvers for Nonlocal Operators
SHF:小型:协作研究:从转换到执行:非本地算子的语言、算法和求解器
- 批准号:
1911019 - 财政年份:2019
- 资助金额:
$ 40万 - 项目类别:
Standard Grant
Elements: Transformation-Based High-Performance Computing in Dynamic Languages
要素:动态语言中基于转换的高性能计算
- 批准号:
1931577 - 财政年份:2019
- 资助金额:
$ 40万 - 项目类别:
Standard Grant
Small: Collaborative Research: Transform-to-Perform: Languages, Algorithms, and Code Transformations for High-Performance FEM
小:协作研究:从转换到执行:高性能 FEM 的语言、算法和代码转换
- 批准号:
1524433 - 财政年份:2015
- 资助金额:
$ 40万 - 项目类别:
Standard Grant
Collaborative Research: Efficient High-Order Parallel Algorithms for Large-Scale Photonics Simulation
协作研究:大规模光子学仿真的高效高阶并行算法
- 批准号:
1418961 - 财政年份:2014
- 资助金额:
$ 40万 - 项目类别:
Continuing Grant
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