Electrostatic Boundary Integral Method for 3D Structures in a Layered Conducting Medium

An integral equation formulation is presented for the modeling of the electrostatic fields surrounding arbitrary three-dimensional structures situated in a conducting layered medium. The layered Green's function for the electrostatic potential and the tensor Green's function for the gradient potential are derived. Closed forms for the 3D layered Green's functions are generated using a discrete complex image method (DCIM) approximation. Improved accuracy of the DCIM approximation is achieved using optimization for the computation of the DCIM poles and residues. The problem is discretized via a high-order locally corrected Nyström method with curvilinear cells. Several examples are shown that demonstrate the accuracy of the DCIM approximation for layered media with disparate layer spacing and conductivities for arbitrary 3D geometries.