This project is concerned with the mathematical reconstruction problem of identifying the unknown conductivity (diffusion) coefficient in an elliptic equation, given full or partial measurements of the Dirichlet to Neumann map on the boundary. This is a nonlinear problem. The potential is calculated by extending the boundary data into the domain. A basis using sinusoids in the angular direction and polynomials in the radial direction is used to for expressing the extensions. The inner products of the gradients of the harmonic basis functions then act as the basis set for expanding the conductivity. The numerical tests of convergence in the expansion is studied as the number of basis functions is increased, for the problem on the unit disk in two dimensions.
Worcester Polytechnic Institute
Major Qualifying Project
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