Determination of the diffusion coefficient

The multilevel algorithm for the solution of the inverse problem for the diffusion equation by an optimization method using the Laguerre functions is considered. Numerical simulations are carried out for Maxwell's equations in 1-dimensional setting in diffusion approximations. Spatial distributions of conductivity of the medium are determined from a known solution in some point. A function of the Laguerre harmonics is minimized. Minimizations are performed by Newton and the conjugate gradient method. The influence of form and spectrum of the source of electromagnetic waves on the accuracy of solution of the inverse problem is investigated. The accuracy of the solution of the inverse problem when using multilevel algorithm and the conventional one-level algorithm are compared.