arXiv subjects
Publications and source records attributed to Richard Hollos.
We derive formulas for the matrix elements of the two dimensional square lattice Green function along the diagonal, and along the coordinate axes. We also give an asymptotic formula for the diagonal elements.
We show how to use the lattice Green function to calculate capacitances in two dimensions with boundary conditions at infinity. It is shown how to calculate coefficients of capacitance and induction from the lattice Green function. A general analysis of two arbitrary conductors is carried out. It is shown how the calculations can be simplified in the case of identical conductors when certain symmetry conditions are met. Example calculations for a parallel and coplanar stripline are shown. The use of the two conductor formulas for the case of three or more conductors is discussed.
We derive formulas for the matrix elements of the lattice Green function for the discrete Poisson equation on an infinite square lattice. The partial difference equation for the matrix elements is solved by reducing it to a series of first order difference equations, which can then be solved sequentially. These formulas are useful in solving two dimensional Poisson equation problems using the finite difference approximation.