Quadratic functional and integral equations for the harmonic Maxwell’s equations in exterior domains. (Fonctionnelle quadratique et équations intégrales pour les équations de Maxwell harmoniques en domaine extérieur.) (French. Abridged English version) Zbl 0858.65126

Summary: We exhibit a quadratic functional for the harmonic Maxwell equations in exterior domain. The functional reaches its unique minimum in the space of out-going and/or in-going solution at the out-going solutions with absorbing boundary condition. It gives a “natural” Hilbertian framework to this problem. It is possible to compute explicitly all the terms of the functional to obtain a mixed integral system. Simple algorithms solve the system.


65Z05 Applications to the sciences
35Q60 PDEs in connection with optics and electromagnetic theory
78A25 Electromagnetic theory (general)
65N38 Boundary element methods for boundary value problems involving PDEs