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Finite element solution of the nonlinear Poisson equation for semiconductor devices using the fixed-point iteration method Abstract. A novel numerical approach for the solution of Troesch's problem is presented. The underlying strategy is based on embedding the Green's function in Picard's fixed point iteration.Numerical results show highly accurate approximations compared with both the analyticalsolutions and/or existing numerical solutions in the literature. Convergence of the iterative scheme is established and it is shown that the rate of convergence increases as the magnitude of the eigenvalues increases.

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