非破壊検査の数理(<特集>逆問題)

抄録

We discuss the mathematical analysis in non-destructive techniques and stress the role. For the account, we take one problem of determining subboundaries by means of a stationary heat conduction process. A part of boundary is unknown to be determined from measurements of temperature and heat flux on the rest subboundary. In this problem, we distinguish two schemes: (A) Original continuous forward problem=Discretized forward problem=Inverse problem to the discretized forward problem. (B) Original continuous forward problem=Inverse problem to the continuous forward problem=Discretized inverse problem. As for the second step in the scheme (B), we show the uniqueness and stability for our inverse problem and point usefulness of such results for numerical computations. We assert that the mathematical analysis should eventually synthesize these two schemes.