On the Inverse Point-Source Problem of the Poisson Equation

Abstract

In this work a basic inverse heat conduction problem of a simple 2-D model with steady state heat source is taken into view. The physical problem is for a square region with uniform thermophysical properties and a point heat source of unit magnitude. To obtain boundary data temperature probes are placed at the midpoints of the sides of the square domain. The objective of the inverse problem is to estimate the coordinates of the point source with the least amount of data. Initially the inverse problem is analyzed to determine the main causes that render the problem ill conditioned. As for the solution among the methods that has been tried so far the best results are obtained from a backpropagating ANN with four-probe data. When white Gaussian noise is added to the measurements no catastrophic failure has been observed.