 
Summary: AN INTEGRAL EQUATION METHOD FOR THE
ELECTROMAGNETIC SCATTERING FROM A SCATTERER ON AN
ABSORBING PLANE
Habib Ammari and Chiraz LatiriGrouz
Consider a timeharmonic electromagnetic plane wave incident on a scatterer on a grounded ab
sorbing plane modelized as an infinite impedance plane. In this paper, a new integral representation
formula is rigorously derived. Existence and uniqueness of weak solutions for the model problem are
also established. The proof of existence is based on an extension of the Hodge decomposition tech
nique to open boundaries. The results reported in this paper form a basis for numerical solutions of
the electromagnetic scattering problem from a scatterer on an absorbing plane.
Key words. Leontovich boundary condition, infinite absorbing plane, open boundaries, integral
equations, Hodge decomposition, existence and uniqueness
AMS(MOS) subject classifications. 35Q60, 78A45, 35J20
1 Introduction
The Leontovich boundary condition on an infinite plane came into use in the early 40's. It was used in
connection with ground wave propagation over the earth. Since then it has became an essential tool
for modeling a surface for which a local surface impedance can be identified. The reader is referred
to [15], [7], [8], [11], and [12] for significant mathematical results on the Leontovich boundary value
problem.
In this paper we consider the following problem. A flash lightning propagates in the air and is
