Application of equation regulation method to the solution of inverse problems in multiphase materials (Q1321886)

We propose a new method of determining local material properties of multiphase composites given the experimentally measured displacements and known traction boundary conditions. In the proposed method, an ``observation'' term is added to the original differential equation, and the modified equation is solved in terms of a regulation parameter. We call this approach the equation regulation method. By appropriately adjusting the value of the regulation parameter based on the noise level in the input data, we get faster convergence and improved stability than prevailing methods of solving the inverse problem in elliptic ordinary differential equations.