Semi-analytical solution of Poisson’s equation in bounded domain

Abstract

Poisson's equation is very important in electrostatics, mechanical engineering and theoretical physics. The novel semi-analytical, scaled boundary finite element method (sbfem), is applied to solve Poisson's equation with Dirichlet and Neumann boundary conditions in the bounded domain. The sbfem weakens the governing differential equation in the circumferential direction and solves the weakened equation analytically in the radial direction, combining the advantages of the finite element method and the boundary element method. Three examples demonstrate the excellent computational accuracy and efficiency of the sbfem approach, revealing the great potential of this method to solve more complex engineering problems. © Austral. Mathematical Soc. 2010.