An algorithm for the electromagnetic scattering due to an axially symmetric body with an impedance boundary condition

Let B be a body in R³ and let S denote the boundary of B. The surface S is described by $\text{S = {(x, y, z): (x}{}^2\text{+ y}{}^2\text{)}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{= f(z), ?1 ? z ? 1}}$, where f is an analytic function that is real and positive on (?1, 1) and f(±1) = 0. An algorithm is described for computing the scattered field due to a plane wave incident field, under Leontovich boundary conditions. The Galerkin method of solution used here leads to a block diagonal matrix involving 2M + 1 blocks, each block being of order 2(2N + 1). If, e.g., N = O(M²), the computed scattered field is accurate to within an error bounded by $\text{Ce}{}^{\mathrm{<mtext>?cN</mtext><mtext>1</mtext><mtext>2</mtext>}}$, where C and c are positive constants depending only on f.