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: 1764187
• 负责人: Wei Cai
• 金额: $ 18.25万
• 依托单位: Southern Methodist University
• 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: 2017-09-08 至 2020-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1764187&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高效数值方法：纳米级材料的电学和磁学特性的高精度模拟以及电阻抗断层扫描。 在这两个领域，使用传统方法进行数值计算即使不是不可能，也是具有挑战性的。 该项目旨在开发基于所研究的偏微分方程解的概率表示的新颖计算方法。 该项目的结果预计将具有广泛的适用性，从太阳能电池的开发到癌症的检测。该项目涉及开发高精度和高效的数值方法来模拟复杂形状纳米颗粒的电和磁极化张量，例如纳米线、量子点和 DNA，以及电阻抗断层扫描 (EIT) 的快速算法。由于纳米粒子的几何复杂性，传统的基于网格的离散方法（例如有限元和边界元方法）的数值计算即使不是不可能，也面临着巨大的挑战。为了应对这些挑战，在本项目中，将研究基于偏微分方程解的 Feynman-Kac 概率表示的路径积分蒙特卡罗 (PIMC) 方法，用于材料科学应用以及 EIT 问题。与传统的基于网格的数值方法相比，PIMC方法一方面能够处理材料科学应用中产生的高度不规则几何形状的物体，另一方面在EIT中的正向问题中提供电极偏微分方程的局部解手。

项目成果

Clusters of lysozyme in aqueous solutions

水溶液中的溶菌酶簇

• DOI: 10.1103/physreve.98.032419
• 发表时间: 2018-09
• 期刊: Physical Review E
• 影响因子: 2.4
• 作者: Baumketner, A.;Cai, W.
• 通讯作者: Cai, W.

Discovering variable fractional orders of advection–dispersion equations from field data using multi-fidelity Bayesian optimization

使用多保真贝叶斯优化从现场数据发现平流离散方程的可变分数阶

• DOI: 10.1016/j.jcp.2017.07.052
• 发表时间: 2017-11
• 期刊: Journal of Computational Physics
• 影响因子: 4.1
• 作者: Pang, Guofei;Perdikaris, Paris;Cai, Wei;Karniadakis, George Em
• 通讯作者: Karniadakis, George Em

Exponential Convergence for Multipole and Local Expansions and Their Translations for Sources in Layered Media: Two-Dimensional Acoustic Wave

多极子和局域展开式的指数收敛性及其对层状介质中源的转换：二维声波

• DOI: 10.1137/19m1268033
• 发表时间: 2020-05-12
• 期刊: SIAM J. Numer. Anal.
• 作者: Wenzhong Zhang;Bo Wang;W. Cai
• 通讯作者: W. Cai

What is the fractional Laplacian? A comparative review with new results

什么是分数拉普拉斯算子？

• DOI: 10.1016/j.jcp.2019.109009
• 发表时间: 2018-01-29
• 期刊: J. Comput. Phys.
• 作者: A. Lischke;G. Pang;Mamikon A. Gulian;Fangying Song;Christian A. Glusa;Xiaoning Zheng;Zhiping Mao;W
• 通讯作者: W