ON THE SOLUTION OF TIME-HARMONIC SCATTERING PROBLEMS FOR MAXWELLS EQUATIONS

This paper deals with the scattering of a monochromatic electromagneti c wave by a perfect conductor surrounded by a locally inhomogeneous me dium. The direct numerical solution of this problem by a finite-elemen t method requires special edge elements. The aim of the present paper is to give an equivalent formulation of the problem well suited for bo th easy theoretical investigation and numerical implementation. Follow ing a well-known idea, this formulation is obtained by adding a regula rizing term such as ''grad div'' in the time-harmonic Maxwell equation s, which leads us to solve an elliptic problem similar to the vector H elmholtz equation instead of Maxwell's equation. The numerical treatme nt of this new formulation requires only standard Lagrange finite elem ents. A unified approach, which is valid for the equations satisfied b y either the electric or the magnetic field, is presented. It applies for a conductor with a Lipschitz-continuous boundary surrounded by a d issipative or nondissipative medium whose electromagnetic coefficients (permittivity and permeability) may be irregular. A family of scatter ing problems is defined, that is, the classical problem (which follows from Maxwell's equations) and the so-called ''regularized problem'' o btained by adding a regularizing term in Maxwell's equations. These pr oblems are shown to be well posed and to have the same solution. An in tegral representation technique is described.