Solving the complete-electrode direct model of ERT using the boundary element method and the method of fundamental solutions

Abstract

Abstract. This paper discusses solving the forward problem for electrical resistance tomography (ERT). The mathematical model is governed by Laplace's equation with the most general boundary conditions forming the so-called completeelectrode model (CEM). We examine this problem in simply-connected and multiply -connected domains (rigid inclusion, cavity and composite bi-material). This direct problem is solved numerically using the boundary element method (BEM) and the method of fundamental solutions (MFS). The resulting BEM and MFS solutions are compared in terms of accuracy, convergence and stability. Anticipating the findings, we report that the BEM provides a convergent and stable solution, whilst the MFS places some restrictions on the number and location of the source points.

Inclusion boundary reconstruction and sensitivity analysis in electrical impedance tomography

“…where r = |r| is the scalar displacement, t ∈ [−1, 1] is the local coordinate at the segment Γ n k , and α and β denotes the angles between the displacement vector r and the boundary elements Γ n−1 k and Γ n k , respectively. Substitute (26) into (25), the derivative of the EIT measurement with respect to the two dimensional vertex displacement is…”

“…Although, more accurate solutions can be obtained by using a higher order numerical method, e.g. the Galerkin BEM [24] or the p-FEM [25], or the Method of Fundamental Solutions (MFS) [26], they will not be discussed in this paper. Later, the presented BEM with constant boundary elements is proved to be good enough for the inclusion reconstruction.…”

Comparison of the Boundary Element Method and the Method of Fundamental Solutions for Analysis of Potential and Elasticity Problems in Convex and Concave Domains

“…Similar to the BEM, the MFS technique can be particularly useful for the analysis of acoustic problems, Godinho et al [37] and Godinho and Soares [38] while the formulation of the MFS is simpler than the BEM. Dyhoum et al [39] investigated several EIT (electrical impedance tomography) problems and found the BEM more convergent and stable in comparison with the MFS, which imposed some restriction on the arrangement of source points. Liravi et al [40] analysed elastodynamics behaviour of solid structure, e.g., cylinder and a thin circular shell located in the soil.…”