| Abstract: |
| Electric Impedance Tomography (EIT) is a method that allows us to reconstruct the inner body by measuring a patient`s response to electric potential applied to the skin. Mathematically this is a Dirichlet to Neumann problem which can be recast as a d-bar problem. Remarkably, the same d-bar problem appears in the scattering treatment of members of the Davey-Stewartson (DS) family of equations.
One of the best-known models of multidimensional integrable systems, DS appears as a two-dimensional generalisation of the infamous nonlinear Schr\odinger equation. It finds various applications in physics, where in general it models the interaction of long and short waves.
In this paper, we present analytical results allowing numerical treatment based on spectral methods for both DS and EIT problems and discuss implementation on graphical processing units (GPUs). Our findings offer the possibility of significant improvements in the speed, cost, and accuracy of medical imaging done with EIT, with further applications in a wide range of areas in physics. |
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