Mathematical Foundations for the Boundary-Field Equation Methods in Acoustic and Electromagnetic Scattering

Abstract

The essence of the boundary-field equation method is the reduction of the boundary value problem under consideration to an equivalent nonlocal boundary value problem in a bounded domain by using boundary integral equations. The latter can then be treated by the standard variational method including its numerical approximations. In this paper, various formulations of the nonlocal boundary value problems will be given for the Helmholtz equation as well as for the timeharmonic Maxwell equations. Emphasis will be placed upon the variational formulation for the method and mathematical foundations for the solution procedure. Some numerical experiments are included for a model problem in electromagnetic scattering.