Electric Field Computations Using Axial Green Function Method on Refined Axial Lines

The axial Green function method (AGM) uses so-called axial lines, which are parallel to axes and look like grids in the finite-difference method. These axial lines can easily be constructed in complicated domains compared to meshes in the FEM, because they are only parallel to axes no matter what the geometry of the problem domain is. The objective of this paper is laid on the computations of the electric potential problems with singularities, which can be caused by a nonsmooth boundary, discontinuous boundary values, and different types of boundary values. In the vicinity of the singularities, we select singular subdomains on which the axial lines can be independently refined. It is shown that the axial line refinements on subdomains near the singularities enable us to calculate the accurate and efficient electric field when using the AGM.