We consider an inverse problem for finding the anomaly of discontinuous electrical conductivity by one current-voltage observation. We develop a real-time algorithm for determining the location of the anomaly. This new idea is based on the observation of the pattern of a simple weighted combination of the input current and the output voltage. Combined with an estimation of size, this algorithm gives a good initial guess for Newton-type schemes. We give a rigorous proof for the location search algorithm. Both the mathematical analysis and its numerical implementation indicate our location search algorithm is very fast, stable, and efficient.
All Science Journal Classification (ASJC) codes
- Applied Mathematics