Generalized Combined Field Integral Equations for the Iterative Solution of the Three-Dimensional Helmholtz Equation

Xavier Antoine (1, 2) , Marion Darbas (3)

1 CORIDA - Robust control of infinite dimensional systems and applications
2 IECN - Institut Élie Cartan de Nancy
3 LAMFA - Laboratoire Amiénois de Mathématique Fondamentale et Appliquée

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.

Mots clés: Acoustic scattering; Helmholtz equation; second-kind Fredholm integral equation; Krylov iterative solution

Domaines: Analyse numérique [math.NA]

Xavier Antoine, Marion Darbas. Generalized Combined Field Integral Equations for the Iterative Solution of the Three-Dimensional Helmholtz Equation. ESAIM: Mathematical Modelling and Numerical Analysis, 2007, 41 (1), pp.147-167. ⟨hal-00141047⟩