Analytic solutions of a multi-interface transmission problem and crack approximation

Analytic solutions to the Laplace equation in annulus and disc are combined with transmission conditions to find analytic solutions for transmission p roblems with multiple concentric circular interfaces. Coefficients are foun d rapidly by solving 2 x 2 linear systems for each interface. This makes th em very suitable as test cases for inverse problem solvers. The special cas e of two very close interfaces is used to quantitatively test crack jump co nditions which result from combining transmission conditions at the two int erfaces into approximate conditions at a single interface. The quality of t he approximation depends on whether the crack is resistive or conductive.