Generalized combined field integral equations for the iterative solution of the three-dimensional helmholtz equation

Abstract

This paper addresses the derivation of new second-kind Fredholm combined field integral equations for the Krylov iterative solution of tridimensional acoustic scattering problems by a smooth closed surface. These integral equations need the introduction of suitable tangential square-root operators to regularize the formulations. Existence and uniqueness occur for these formulations. They can be interpreted as generalizations of the well-known Brakhage-Werner [A. Brakhage and P. Werner, Arch. Math. 16 (1965) 325-329] and Combined Field Integral Equations (CFIE) [R.F. Harrington and J.R. Mautz, Arch. Elektron. Übertragungstech (AEÜ) 32 (1978) 157-164]. Finally, some numerical experiments are performed to test their efficiency. © EDP Sciences,.