Recovering the location and intensity a point source for an advection-dispersion-reaction equation is studied with the use of two point wise measurements situated one upstream and the other downstream with respect to the source. The equation is furnished with the initial and boundary conditions of the Neumann or Dirichlet type. This inverse problem is a classical problem studied in many articles in both the one-dimensional and multi-dimensional cases. However, the most part of them is based on reducing the problem to an optimal control problem and minimizing the corresponding cost functional. As a rule, it requires large computational facilities and does not always lead to a desired result. We expose some theoretical results, in particular, an explicit asymptotic formula for determining the source location. Next, a numerical algorithm is constructed and the results of numerical experiments are described. The numerical algorithm for determination of the source location and a solution to the inverse problem is justified with the use of the above-mentioned asymptotic formula. The intensity is defined with the use of the Duhamel formula. The numerical realization relies on the finite element method and the finite difference method for the corresponding system of ordinary differential equations. The numerical experiments demonstrate a good computational performance.
Volume 11 | 01-Special Issue
Pages: 496-510