On the convergence of the finite integration technique for the anisotropic boundary value problem of magnetic tomography

The reconstruction of a current distribution from measurements of the magnetic field is an important problem of current research in inverse problems. Here, we study an appropriate solution to the forward problem, i.e. the calculation of a current distribution given some resistance or conductivity distribution, respectively, and prescribed boundary currents. We briefly describe the well‐known solution of the continuous problem, then employ the finite integration technique as developed by Weiland et al . since 1977 for the solution of the problem. Since this method can be physically realized it offers the possibility to develop special tests in the area of inverse problems. Our main point is to provide a new and rigorous study of convergence for the boundary value problem under consideration. In particular, we will show how the arguments which are used in the proof of the continuous case can be carried over to study the finite‐dimensional numerical scheme. Finally, we will describe a program package which has been developed for the numerical implementation of the scheme using Matlab.