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

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 of 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

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

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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

Homogenization of parabolic nonlinear coupled problem in heat exchange

International audienceThis work deals with the homogenization of heat transfer nonlinear parabolic problem in a periodic composite medium consisting in two-component (fluid/solid). This problem presents some difficulties due to the presence of a nonlinear Neumann condition modeling a radiative heat transfer on the interface between the two parts of the medium and to the fact that the problem is strongly coupled. In order to justify rigorously the homogenization process, we use two scale convergence. For this, we show first the existence and uniqueness of the homogenization problem by topological degree of Leray-Schauder, Then we establish the two scale convergence, and identify the limit problems

Non-smooth classification model based on new smoothing technique

International audienceThis work describes a framework for solving support vector machine with kernel (SVMK). Recently, it has been proved that the use of non-smooth loss function for supervised learning problem gives more efficient results [1]. This gives the idea of solving the SVMK problem based on hinge loss function. However, the hinge loss function is non-differentiable (we can’t use the standard optimization methods to minimize the empirical risk). To overcome this difficulty, a special smoothing technique for the hinge loss is proposed. Thus, the obtained smooth problem combined with Tikhonov regularization is solved using a stochastic gradient descent method. Finally, some numerical experiments on academic and real-life datasets are presented to show the efficiency of the proposed approach