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Exact and numerical solutions of Poisson equation for electrostatic potential problems. (English) Zbl 1152.78306

Summary: Homotopy perturbation method (HPM) and boundary element method (BEM) for calculating the exact and numerical solutions of Poisson equation with appropriate boundary and initial conditions are presented. Exact solutions of electrostatic potential problems defined by Poisson equation are found using HPM given boundary and initial conditions. The same problems are also solved using the BEM. The cell integration approach is used for solving Poisson equation by BEM. The problem region containing the charge density is subdivided into triangular elements. In addition, this paper presents a numerical comparison with the HPM and BEM.

MSC:

78A30 Electro- and magnetostatics
78M15 Boundary element methods applied to problems in optics and electromagnetic theory
78A25 Electromagnetic theory (general)
65R20 Numerical methods for integral equations
78M25 Numerical methods in optics (MSC2010)
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