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

DOI10.1016/j.jcp.2022.111862OpenAlexW4313561036MaRDI QIDQ2681096

Changhao Yan, Yijing Zhou, Cuiyang Ding, Wei Cai, Xuan Zeng

Publication date: 10 February 2023

Published in: Journal of Computational Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jcp.2022.111862

zbMATH Keywords

Laplace equationFeynman-Kac formulareflecting Brownian motionmixed boundary problemEITboundary local time

Mathematics Subject Classification ID

Markov processes (60Jxx) Miscellaneous topics in partial differential equations (35Rxx) Elliptic equations and elliptic systems (35Jxx)

Cites Work

• Numerical solution of the Robin problem of Laplace equations with a Feynman-Kac formula and reflecting Brownian motions
• Walk-on-spheres algorithm for solving third boundary value problem
• Accuracy and efficiency in computing electrostatic potential for an ion channel model in layered dielectric/electrolyte media
• Computation of the local time of reflecting Brownian motion and the probabilistic representation of the Neumann problem
• Stochastic differential equations with reflecting boundary condition in convex regions
• The probabilistic solution of the third boundary value problem for second order elliptic equations
• A partially reflecting random walk on spheres algorithm for electrical impedance tomography
• On an inverse boundary value problem
• A Parallel Method for Solving Laplace Equations with Dirichlet Data Using Local Boundary Integral Equations and Random Walks
• Monte Carlo approximations of the Neumann problem
• A Backprojection Algorithm for Electrical Impedance Imaging
• Green, Brown, and Probability and Brownian Motion on the Line
• Some Continuous Monte Carlo Methods for the Dirichlet Problem
• Stochastic differential equations with reflecting boundary conditions
• A uniqueness theorem for an inverse boundary value problem in electrical prospection
• Existence and Uniqueness for Electrode Models for Electric Current Computed Tomography
• Electrical Impedance Tomography
• Statistical inversion and Monte Carlo sampling methods in electrical impedance tomography
• Stable determination of conductivity by boundary measurements
• Electrical impedance tomography
• Integral Formulation of the Boundary Value Problems and the Method of Random Walk on Spheres
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