CAREER: Predictive Simulations of Complex Kinetic Systems

职业：复杂运动系统的预测模拟

基本信息

批准号：
1654152
负责人：
Jingwei Hu
金额：
$ 40万
依托单位：
Purdue University
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：
2017-09-01 至 2021-11-30
项目状态：
已结题

来源：
https://www.nsf.gov/awardsearch/showAward?AWD_ID=1654152&HistoricalAwards=false
关键词：
CAREER Predictive Simulations Complex Kinetic

项目摘要

This project aims to build an integrated program of research and education focused on advances in predictive simulations of complex kinetic systems. Such systems are comprised of a large number of particles in random motion and are best described by the Boltzmann and related kinetic equations. In practical applications, there are many sources of uncertainties that can arise in kinetic systems: imprecise measurements for initial and boundary conditions, incomplete knowledge of the fundamental interaction mechanism between particles, and so on. Understanding the impact of these uncertainties is critical to the simulations of the complex kinetic systems, and will allow scientists and engineers to obtain more reliable predictions and perform better risk assessment. Due to the unique challenges arising in kinetic equations, such as multiple scales, high dimensionality, and positivity, very few existing generic uncertainty quantification (UQ) algorithms can be applied directly. To bridge this gap, the research objective of this project is to develop highly efficient stochastic and multiscale numerical methods for Boltzmann-like kinetic equations. A parallel educational objective is to create innovative opportunities for students at all levels to improve science, technology, engineering, and mathematics (STEM) education and promote career interest in these disciplines, especially among female students. Specifically, we will pursue four research and educational aims: 1) develop stochastic asymptotic-preserving methods for multiscale kinetic equations; 2) construct high performance stochastic algorithms for the Boltzmann collision operator; 3) design physics-preserving UQ algorithms for kinetic systems; and 4) create education and outreach activities for students through undergraduate STEM classroom innovation; graduate curriculum development in kinetic theory; graduate and undergraduate mentoring; and organizing an after-school math research program for high school girls and family math/science nights at middle and elementary schools.

该项目旨在建立一个集成的研究和教育计划，重点介绍复杂动力学系统的预测模拟的进步。这样的系统由随机运动中的大量粒子组成，并且最好由Boltzmann和相关动力学方程描述。在实际应用中，动力学系统中可能出现许多不确定性来源：初始和边界条件的不精确测量，对粒子之间的基本相互作用机制的了解不完整等等。了解这些不确定性的影响对于复杂动力学系统的模拟至关重要，并且将使科学家和工程师能够获得更可靠的预测并进行更好的风险评估。由于动力学方程式产生的独特挑战，例如多个量表，高维度和积极性，因此很少直接应用现有的通用不确定性量化（UQ）算法。为了弥合这一差距，该项目的研究目标是为Boltzmann样动力学方程开发高效的随机和多尺度数值方法。一个平行的教育目标是为各级学生创造创新的机会，以改善科学，技术，工程和数学（STEM）教育，并促进对这些学科的职业兴趣，尤其是在女学生中。具体而言，我们将追求四个研究和教育目标：1）为多尺度动力学方程开发随机渐近保护方法； 2）构造玻尔兹曼碰撞操作员的高性能随机算法； 3）设计具有动力学系统的物理性uq算法； 4）通过本科STEM课堂创新为学生创建教育和外展活动；动力学理论的研究生课程发展；研究生和本科指导；并在中学和小学组织一项针对高中女生和家庭数学/科学之夜的课后数学研究计划。