Electric Field Computation in Unbounded Domain Using Axial Green Function Method

Since the numerical computation in unbounded domains has many limitations using the traditional discretization methods, it is necessary to develop an efficient method that can handle the infinite boundary problem. The axial Green function method (AGM) is eligible to implant the prescribed asymptotic behavior of the solution at the far field into the bounded computational domain. The axial line in AGM plays a key role in discretizing the differential equation in association with 1-D Green function. In case of unbounded domain, we have to consider the infinite axial line that is a half-infinite line parallel to an axis. We define a particular type of 1-D Green function on this infinite axial line corresponding to the elliptic problem, which is called the infinite axial Green function. Based on the new feature of this Green function, we derive the representation formula of the solution on the infinite axial line. Using this formula, we can translate the far-field asymptotic behavior with undetermined coefficient into the forcing term in the bounded computational domain. The efficiency and accuracy of this approach are fully investigated by taking numerical examples.