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2 results

  • Generalized combined field integral equationsfor the iterative solution of the three-dimensional Helmholtz equation

  • Xavier Antoine, Marion Darbas
  • Journal:
    ESAIM: Mathematical Modelling and Numerical Analysis / Volume 41 / Issue 1 / January 2007
    Published online by Cambridge University Press:
    26 April 2007, pp. 147-167
    Print publication:
    January 2007

  • 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 integralequations need the introduction of suitable tangential square-root operators to regularize the formulations. Existence and uniqueness occur for these formulations. They can be interpreted asgeneralizations 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.