Calculation of Green's Function for Poisson's Equation in Plane Polar Coordinates

Abstract

A new calculation of Green's function for Poisson's equation in plane polar coordinates is presented. The method consists in first calculating the solution to the simpler problem, but with the same Green's function, that is obtained with the homogenization of the boundary conditions and then inferring Green's function by comparing this calculated solution with Green's solution formula. Depending on how the solution to the simplified problem is calculated, Green's function may result as an integral or an infinite series, but it is finally presented in a closed form, because it is possible to calculate the integral or the sum of this series.

Keywords

• Green's function
• Poisson
• plane polar coordinates
• disc sector
• closed form
• Dirichlet