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Solving the inverse three-dimensional continuous model of electrical resistance tomography using the method of fundamental solutions and the Markov chain Monte Carlo approach.

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Academic year: 2019

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Figure 1.1: (exact inner derivative (functions ofand(a, d, g) The absolute errors between the MFS and exact interior solutions uMF S(0.6, θ, φ) uExact(0.6, θ, φ),(b, e, h) the absolute errors between the MFS and exact outer derivative∂u/∂nMF S)(1, θ, φ) and (∂u/∂nExact)(1, θ, φ), and (c, f, i) the absolute errors between the MFS and∂u/∂nMF S)(0.5, θ, φ) and (∂u/∂nExact)(0.5, θ, φ), for M = N = {8, 16, 32}, as φ/(2π) and θ/π.
Figure 1.2: The MFS outer derivative (∂u/∂n)MF SOuter(1, θ, φ), as a function of φ/(2π) and θ/π, for (a)M = N = 8, (b) M = N = 16, (c) M = N = 32, (d) M = N = 64, when R = 5 and ηI = 0.6.
Figure 1.3: Star-shaped model reconstruction: The exact inner ellipsoid and the fitted ellipsoids afterK = 80 iterations.
Figure 1.4: Credible intervals for various cross-sections ((a) θ =π14, (b) θ = 3π14 , (c) θ = 6π14 , (d) θ = 8π14e) θ = 11π14 , and (f) θ = 13π14 and (φ)j=1,15 ∈ [0, 2π), for Experiment 2.
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