Author(s)

R.P. Shaw, G. Manolis & G.S. Gipsoif

Abstract

The 2-D free-space Green's function and BIE for a Poisson equation with linearly varying conductivity in two directions R.P. Shaw/ G. Manolis,* G.S. Gipsoif ^Aristotle University, Thessaloniki, Greece 'Oklahoma State University, Stillwater, OK 74074, USA ABSTRACT: The fundamental Green's function for a two dimensional Poisson equation with linearly varying conductivities in both directions is found by an approach analogous to that used previously for a single direction variation. These Green's functions are the basis for boundary integral equation formulations on which boundary element methods are based. INTRODUCTION: Consider a variable conductivity Poisson equation, V(2)#{K(x,y)V(2)U(x,y)}= - Q(x,y) [1] where V#) represents the two dimensional del operator. This equation holds in a two dimensional domain, V(2>(x,y) bounded by a one dimensional curve, S(i)(s), where s is an arclength coordinate. Such equations represent mathematical models for many

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