We shall now discuss some details of Nishimura & Kobayashi's approach. The description will be mainly for 2D cases for the purpose of simplicity. The corresponding 3D results are obtained in a similar manner, and are available in the literature.
Nishimura & Kobayashi considered the simplest case where the crack S consists of one single segment and the measurement of is made on the whole exterior boundary (). To start with we shall describe their method of solving direct crack problems, because they use a direct problem solver in an iterative manner to solve inverse problems.