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This paper outlines a new approach to identify a source term of a 2D elliptic equation for anisotropic nonhomogenous media. The proposed methodology is based on the minimization of an objective function representing differences between the measured potential and those calculated by using the discontinuous dual reciprocity boundary element method, the measurements are required to render a unique solution and supposed to be pointwise in the problem domain. Since the additional data may be contaminated by measurement noises or the numerical computing errors, we adopt a regularizing Levenberg–Marquardt method to solve the nonlinear least-squares problem attained from the inverse source problem. The numerical performance of the proposed approach is studied at the end for both geometries: smooth and piecewise smooth one. The results show a very good agreement with the analytical solutions under exact and noisy data.

In this work, a numerical bi-dimensional simulation of heat distribution in the human eye is investigated. A dual reciprocity boundary element method (DRBEM) is applied to obtain the heat distribution in the human eye. The non-overlapping Dirichlet-Neumann domain decomposition method combined with DRBEM is used to find a more accurate representation of heat distribution in the human eye presented for two, three and four subdomains. The result obtained are compared with literature experimental and numerical studies. The simulations of proposed algorithms describe with sufficient accuracy the heat distribution in the human eye.

The purpose of this work is to identify a Robin coefficient from available measurements on the accessible part of the boundary. After recasting the inverse problem as an optimization problem, we study the issue of identifiability, stability, and identification. For the reconstruction process, two regularized algorithms are designed, and the forward problem is approximated using the discontinuous dual reciprocity method. The accuracy of the proposed approaches is tested in the case of noise–free and noisy data and the findings are very promising and encouraging.