Search

Abstract: This work studies the inverse problem of reconstructing a time-dependent heat source in the heat conduction equation using the temperature measurement specified at an internal point. Problems of this type have important applications in several fields of applied science. By the Green’s function method, the inverse problem is reduced to an operator equation of the first kind which is known to be ill-posed. The uniqueness of the solution for the inverse problem is obtained by the contraction mapping principle. A numerical algorithm on the basis of the Landweber iteration is designed to deal with the operator equation and some typical numerical experiments are also performed in the paper. The numerical results show that the proposed method is stable and the unknown heat source is recovered very well. [Copyright &y& Elsevier]

Abstract: This paper presents an iterative alternating algorithm for solving an inverse problem in linear elasticity. A relaxation procedure is developed in order to increase the rate of convergence of the algorithm and two selection criteria for the variable relaxation factors are provided. The boundary element method is used in order to implement numerically the constructing algorithm. We discuss this implementation, mention the use of Krylov methods to solve the obtained linear algebraic systems of equations and investigate the convergence and the stability when the data is perturbed by noise. [Copyright &y& Elsevier]