A path integral Monte Carlo (PIMC) method based on Feynman-Kac formula for electrical impedance tomography

被引：1

作者：

Ding, Cuiyang ^{[1
]}

Zhou, Yijing ^{[2
]}

Cai, Wei ^{[3
]}

Zeng, Xuan ^{[1
]}

Yan, Changhao ^{[1
]}

机构：

[1] Fudan Univ, Sch Microelect, State Key Lab ASIC & Syst, Shanghai, Peoples R China

[2] Univ North Carolina Charlotte, Dept Math & Stat, Charlotte, NC 28223 USA

[3] Southern Methodist Univ, Dept Math, Dallas, TX 75275 USA

来源：

JOURNAL OF COMPUTATIONAL PHYSICS | 2023年 / 476卷

基金：

中国国家自然科学基金; 美国国家科学基金会;

关键词：

EIT; Reflecting Brownian motion; Boundary local time; Feynman-Kac formula; Laplace equation; Mixed boundary problem; BOUNDARY-VALUE PROBLEM; SPHERES ALGORITHM; UNIQUENESS; EQUATIONS; WALK;

D O I：

10.1016/j.jcp.2022.111862

中图分类号：

TP39 [计算机的应用];

学科分类号：

081203 ; 0835 ;

摘要：

A path integral Monte Carlo method (PIMC) based on a Feynman-Kac formula for the Laplace equation with mixed boundary conditions is proposed to solve the forward problem of the electrical impedance tomography (EIT). The forward problem is an important part of iterative algorithms of the inverse EIT problem, and the proposed PIMC provides a local solution to find the potentials and currents on individual electrodes. Improved techniques are proposed to compute with better accuracy both the local time of reflecting Brownian motions (RBMs) and the Feynman-Kac formula for mixed boundary problems of the Laplace equation. Accurate voltage-to-current maps on the electrodes of a model 3-D EIT problem with eight electrodes are obtained by solving a mixed boundary problem with the proposed PIMC method. (c) 2022 Elsevier Inc. All rights reserved.

引用

页数：19

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