Direct solver for an inverse problem of the type of the transmission

The purpose of this paper is to control a temperature of a material Ω₀ when the domain Ω₀ is occupied by a dangerous material and one can not directly control its temperature. To do so, we set two materials Ω _i (i = 1,2) outside Ω₀ in order to control the temperature of Ω₀ From this point of view, an inverse problem which decide the boundary value of Ω _i (i = 1,2) from the information of the interior Ω₀ is derived. In this paper the direct solver for solving the inverse problem will be shown and itstechnique is based on the domain decomposition and succcessive elimination of lines which we call SEL.