A path integral Monte Carlo (PIMC) method based on Feynman-Kac formula for electrical impedance tomography. (English) Zbl 07652777
Summary: 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.
MSC:
| 35Rxx | Miscellaneous topics in partial differential equations |
| 60Jxx | Markov processes |
| 35Jxx | Elliptic equations and elliptic systems |
Keywords:
EIT; reflecting Brownian motion; boundary local time; Feynman-Kac formula; Laplace equation; mixed boundary problemReferences:
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