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.

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In this paper, we discuss an inverse problem of determining a part of the boundary of the depletion region of semiconductor devices. The existence of the unique solution is proved. The unknown boundaries as well as unknown potentials are parameterized by h i t e elements. Decoupling the discretized Laplace equation from the boundary conditions, we derive two algorithms to solves this problems. The obtained nonlinear systems of algebraic equations are solved by quasi-Newton methods. Numerical experiments, including comparisons of the behaviour of the proposed algorithms when applied to two-dimensional inverse boundary problems, are reported.

International audienceIn this paper, we propose a shape optimization formulation for a problem modeling a process of welding. We show the existence of an optimal solution. The finite element method is used for the discretization of the problem. The discrete problem is solved by an identification technique using a parameterization of the weld pool by Bézier curves and Genetic algorithms

In this paper, a bilateral free boundaries problem is considered. This kind of inverse problems appears in the theory of semiconductors and multi‐phase problems. Using a shape functional and some regularization terms, an optimal control problem is formulated. In addition, we prove its solution existence. The first optimality conditions and the shape gradient are computed. With the finite element method, we write the discrete version of the optimal control problem. To design our proposed scheme, we based on the conjugate gradient, where we use the genetic algorithm to find the best initial guess for the gradient method. At each mesh regeneration, we perform a mesh refinement in order to avoid any domain singularities. Some numerical examples are shown to demonstrate the validity of the theoretical results and to prove the robustness and efficiency of the proposed scheme, especially to identify free boundaries with jump points.