Numerical method for solving a class of nonlinear elliptic inverse problems

AbstractThis paper discusses a method to solve a family of nonlinear inverse problems with Cauchy conditions on a part of the boundary and no condition at all on another part. An iterative boundary element procedure is proposed. The scheme uses a dynamically estimated relaxation parameter on the under-specified boundary. Various types of convergence, boundary condition formulations and effects of added small perturbations into the input data are investigated. The numerical results show that the method produces a stable reasonably approximate solution

Development of Numerical Method for Optimizing Silicon Solar Cell Efficiency

This paper presents a development of numerical method to determine and optimize the photocurrent densities in silicon solar cell. This method is based on finite difference algorithm to resolve the continuity and Poisson equations of minority charge carriers in p-n junction regions by using Thoma’s algorithm to resolve the tridiagonal matrix. These equations include several physical parameters as the absorption coefficient and the reflection one of the material under the sunlight irradiation of AM1.5 solar spectrum. In this work, we study the effect of various parameters such as thickness and doping concentration of the (emitter, base) layers on crystalline silicon solar cell perfomance. The obtained results show that the optimum energy conversion efficiency is 22.16 % with the following electrical parameters solar cell Voc = 0.62 V and Jph = 43.20 mA · cm – 2. These results are compared with experimental data and show a good agreement of our developped method

Adaptive mesh techniques based on a posteriori error estimates for an inverse Cauchy problem

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The Local Representation Formula of Solution for the Perturbed Controlled Differential Equation with Delay and Discontinuous Initial Condition

For the perturbed controlled nonlinear delay differential equation with the discontinuous initial condition, a formula of the analytic representation of solution is proved in the left neighborhood of the endpoint of the main interval. In the formula, the effects of perturbations of the delay parameter, the initial vector, the initial and control functions are detected

On a numerical approximation of a highly nonlinear parabolic inverse problem in hydrology

International audienceIn this paper, we consider an inverse problem in hydrology governed by a highly nonlinear parabolic equation called Richards equation. This inverse problem consists to determine a set of hydrological parameters describing the flow of water in porous media, from some additional observations on pressure. We propose an approximation method of this problem based on its optimal control formulation and a temporal discretization of its state problem. The obtained discrete nonlinear state problem is approached by the finite difference method and solved by Picard's method. Then, for the resolution of the discrete associated optimization problem, we opt for an evolutionary algorithm. Finally, we give some numerical results showing the efficiency of the proposed approach

On a numerical shape optimization approach for a class of free boundary problems

This paper is devoted to a numerical method for the approximation of a class of free boundary problems of Bernoulli's type, reformulated as optimal shape design problems with appropriate shape functionals. We show the existence of the shape derivative of the cost functional on a class of admissible domains and compute its shape derivative by using the formula proposed in [5, 6], that is, by means of support functions. On the numerical level, this allows us to avoid the tedious computations of the method based on vector fields. A gradient method combined with boundary element method are performed for the approximation of this problem, in order to overcome the re-meshing task required by the finite element method. Finally, we present some numerical results and simulations concerning practical applications, showing the effectiveness of the proposed approach

On a numerical shape optimization approach for a class of free boundary problems

This paper is devoted to a numerical method for the approximation of a class of free boundary problems of Bernoulli's type, reformulated as optimal shape design problems with appropriate shape functionals. We show the existence of the shape derivative of the cost functional on a class of admissible domains and compute its shape derivative by using the formula proposed in [5, 6], that is, by means of support functions. On the numerical level, this allows us to avoid the tedious computations of the method based on vector fields. A gradient method combined with boundary element method are performed for the approximation of this problem, in order to overcome the re-meshing task required by the finite element method. Finally, we present some numerical results and simulations concerning practical applications, showing the effectiveness of the proposed approach