Study of the Boundary Element Method for the Direct Problem of Electrical Impedance Tomography

The main objective of this paper is to contribute to the development of a reconstruction method for the electrical impedance tomography (EIT) problem using the boundary element method (BEM). The idea is to adopt BEM to improve the performance of the solution of the direct problem. The EIT problem is generally formulated as an inverse problem and the approach to its solution consists in minimizing an error functional that confronts two different models of the same problem, one calculated from a numerical method and another experimentally obtained. An iterative process is performed until the global minimum (sought image) of the error functional has been reached. Therefore, the direct problem is solved many times to reconstruct the image, and the improvement of its performance is essential to obtain solutions in viable time. BEM can provide this benefit since it effectively reduces the dimension of the numerical problem and, consequently, results in a considerable reduction in the number of variables required for the solution. Tests with the developed BEM algorithm considering a two-dimensional domain with piecewise constant conductivities, synthetic data for the experimental setup and different values and distribution of the contrast have been performed. The numerical results have shown that the method is quite promising.