The inverse scattering problem is converted to an operator equation F(Γ)=f, which consists of the far field operator F, the measured far field data f and the shape Γ of the unknown obstacle. Using the Levenberg-Marquardt method and the derivative of F on Γ, in-troduced by A. Kirsh, this equation is solved and the shape Γ is determined. The numerical results show that this algorithm is practical and efficient.

A variational formula combining mixed finite element method with discontinuous finite element method is derived for solving the two group neutron diffusion equation in 2D. According to the variational formula, a numerical test is given whose result proves that the variational formula is reasonable and practicable. In order to improve the precision of the calculation, there are more to be studied.

Results of existence,uniqueness and stability recovering the domain from a measured data of Poisson equation are obtained.The results of determining the shape of unknown domain are proven with Sobolev theory and the fundamental solution of Poisson equation.

In this paper the formulae of the collision probobilities for the isotro-pic two-dimensional neutron transport problem on the mixed region consisting of rectangular or triangle cells are given. Based on these formulae the code has been developed and applied to tow-dimensional mixed cells calculations. The calculated results show good agreement with those of Montecalo method and conservation principles.