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

In this paper, 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 (ER) 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. Several numerical examples to the solution of this non-linear problem with continuous and discontinuous coefficient functions are given to show the accuracy and reliability of the proposed method.