skip to main content

Title: An integral equation method for the Cahn-Hilliard equation in the wetting problem
Authors:
; ; ;
Award ID(s):
1654756
Publication Date:
NSF-PAR ID:
10174253
Journal Name:
Journal of Computational Physics
Volume:
419
Issue:
C
Page Range or eLocation-ID:
109521
ISSN:
0021-9991
Sponsoring Org:
National Science Foundation
More Like this
  1. Optical tomography is the process of reconstructing the optical properties of biological tissue using measurements of incoming and outgoing light intensity at the tissue boundary. Mathematically, light propagation is modeled by the radiative transfer equation (RTE), and optical tomography amounts to reconstructing the scattering coefficient in the RTE using the boundary measurements. In the strong scattering regime, the RTE is asymptotically equivalent to the diffusion equation (DE), and the inverse problem becomes reconstructing the diffusion coefficient using Dirichlet and Neumann data on the boundary. We study this problem in the Bayesian framework, meaning that we examine the posterior distribution ofmore »the scattering coefficient after the measurements have been taken. However, sampling from this distribution is computationally expensive, since to evaluate each Markov Chain Monte Carlo (MCMC) sample, one needs to run the RTE solvers multiple times. We therefore propose the DE-assisted two-level MCMC technique, in which bad samples are filtered out using DE solvers that are significantly cheaper than RTE solvers. This allows us to make sampling from the RTE posterior distribution computationally feasible.« less