Path Integral Monte Carlo Methods for Computing Polarizability Tensors of Nano-materials and Electrical Impedance Tomography

计算纳米材料极化张量和电阻抗断层扫描的路径积分蒙特卡罗方法

• 批准号: 1719303
• 负责人: Wei Cai
• 金额: $ 18.25万
• 依托单位: University of North Carolina at Charlotte
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2017
• 资助国家: 美国
• 起止时间: 2017-08-15 至 2017-11-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1719303&HistoricalAwards=false
• 关键词: Path; Integral; Monte; Carlo; Methods

This research project aims to develop improved efficient numerical methods for two application areas: highly accurate simulation of the electric and magnetic properties of nanometer-scale materials, and electrical impedance tomography. In both areas, numerical computations with traditional methods are challenging, if not impossible. This project aims to develop novel computational methods based on probabilistic representations of solutions to the partial differential equations under study. Results of the project are expected to have wide applicability, from the development of solar cells to the detection of cancer.This project concerns the development of highly accurate and efficient numerical methods to simulate the electric and magnetic polarizability tensors of nanoparticles of complex shapes as in nanowires, quantum dots, and DNA, and fast algorithms for electrical impedance tomography (EIT). Due to the geometric complexities of nanoparticles, numerical computations with traditional mesh-based discretization methods such as finite element and boundary element methods face great challenges, if not impossibility. To meet these challenges, in this project, path integral Monte Carlo (PIMC) methods, based on Feynman-Kac probabilistic representations of solutions to partial differential equations, will be studied for material science applications as well as EIT problems. Compared with traditional grid-based numerical methods, the PIMC methods offer the capability of handling objects with highly irregular geometries arising from materials science applications on the one hand, and provide local solutions of partial differential equations over electrodes in forward problems in EIT on the other hand.

该研究项目旨在为两个应用领域开发改进的有效数值方法：高度准确地模拟纳米尺度材料的电和磁性特性，以及电阻抗层析成像。 在这两个领域，使用传统方法的数值计算是具有挑战性的，即使不是不可能的。 该项目旨在根据研究的部分微分方程的解决方案的概率表示开发新的计算方法。 从太阳能电池的发展到检测癌症的结果，该项目的结果预计将具有广泛的适用性。该项目涉及高度准确，高效的数值方法的发展，以模拟复杂形状的纳米颗粒的电和磁性极化量张量，如纳米层，量子点，量子点以及快速的Algorital（Electical and Impogrions）（Elgoricalssmogrions）（以Elgorictance）（Elgoricalssmogrions）。由于纳米颗粒的几何复杂性，具有传统基于网格的离散方法（例如有限元和边界元素方法）的数值计算将面临巨大的挑战，即使不是不可能的挑战。为了应对这些挑战，在这个项目中，将根据材料科学应用以及EIT问题研究基于Feynman-KAC概率的概率表示，基于FEYNMAN-KAC概率代表的路径积分蒙特卡洛（PIMC）方法。与传统的基于网格的数值方法相比，PIMC方法一方面提供了具有高度不规则的几何形状的物体的能力，一方面是由材料科学应用引起的，并提供了局部微分方程的局部解决方案，而不是另一方面的EIT中的电极中的电极中的电极。