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Original Articles

An integral preconditioner for solving the two-dimensional scattering transmission problem using integral equations

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Pages 1473-1490 | Received 26 May 2006, Accepted 14 Jan 2007, Published online: 01 Sep 2008

References

  • Amini , S. and Kirkup , S. M. 1995 . Solution of Helmholtz equation in exterior domain by elementary boundary integral equations . J. Comput. Phys. , 118 : 208 – 221 .
  • Antoine , X. and Darbas , M. 2005 . Alternative integral equations for the iterative solution of acoustic scattering problems . Quart. J. Mech. Appl. Math. , 58 ( 1 ) : 107 – 128 .
  • Antoine , X. and Darbas , M. 2006 . Generalized combined field integral equations for the iterative solution of the three-dimensional Helmholtz equation . ESAIM-Math. Model. Num. , 41 : 147 – 167 .
  • Antoine , X. , Barucq , H. and Vernhet , L. 2001 . High-frequency asymptotic analysis of a dissipative transmission problem resulting in generalized impedance boundary conditions . Asympt. Anal. , 26 ( 3–4 ) : 257 – 283 .
  • Antoine , X. , Bendali , A. and Darbas , M. 2004 . Analytic preconditioners for the electric field integral equation . Int. J. Numer. Meth. Eng. , 61 : 1310 – 1331 .
  • Antoine , X. , Bendali , A. and Darbas , M. 2005 . Analytic preconditioners for the boundary integral solution of the scattering of acoustic waves by open surfaces . J. Comput. Acoust. , 13 ( 3 ) : 477 – 498 . Special Issue on Innovative Computational Methods for Wave Propagation
  • Bendali , A. and Souilah , M. 1994 . Consistency estimates for a double-layer potential and application to the numerical analysis of the boundary-element approximation of acoustic scattering by a penetrable object . Math. Comp. , 62 : 65
  • Carpinteri , B. , Duff , I. S. and Giraud , L. 2000 . Sparse pattern selection strategies for robust Frobenius-norm minimization preconditioners in electromagnetism . Numer. Linear Algebra Appl. , 7 : 667 – 685 .
  • Chazarain , J. and Piriou , A. 1982 . Introduction to the Theory of Linear Partial Differential Equations , Amsterdam/New-York : North-Holland .
  • Chen , K. 2005 . Matrix Preconditioning Techniques and Applications, Cambridge Monographs on Applied and Computational Mathematics . 19
  • Chen , G. and Zhou , J. 1992 . Boundary Element Methods, Computational Mathematics and Applications , Academic Press .
  • Chew , W. C. , Jin , J.-M. , Michielssen , E. and Song , J. 2001 . Fast and Efficient Algorithms in Computational Electromagnetics , Norwood : Artech House Antennas and Propagation Library .
  • Christiansen , S. H. 2002 . Résolution des Equations Intégrales pour la Diffraction d'Ondes Acoustiques et Electromagnétiques, Stabilisation d'Algorithmes Itératifs et Aspects de l'Analyse Numérique , France : Thèse de Doctorat de l'Ecole Polytechnique .
  • Christiansen , S. H. and Nédélec , J. C. 2000 . Des préconditionneurs pour la résolution numérique des équations intégrales de frontière de l'acoustique . C.R. Acad. Sci. Paris, Sér. I , 330 ( 7 ) : 617 – 622 .
  • Christiansen , S. H. and Nédélec , J. C. 2002 . A preconditioner for the electric field integral equation based on Calderon formulas . SIAM J. Numer. Anal. , 40 ( 3 ) : 1100 – 1135 .
  • Colton , D. and Kress , R. 1983 . Integral Equations in Scattering Theory, Pure and Applied Mathematics , New York : Wiley and Sons .
  • Colton , D. and Kress , R. 1998 . “ Inverse Acoustic and Electromagnetic Scattering Theory ” . In Applied Mathematical Sciences , 2 , Vol. 93 , Berlin : Springer-Verlag .
  • Darbas , M. 2004 . Préconditionneurs Analytiques de type Calderón pour les Formulations Intégrales des Problèmes de Diffraction d'Ondes , INSA Toulouse . Thèse de Doctorat
  • Joannopoulos , J. D. , Meade , R. , Joshua , D. and Winn , N. 1995 . Photonic Crystals: Molding the Flow of Light , Princeton University Press .
  • Kechroud , R. , Soulaimani , A. , Saad , Y. and Gowda , S. 2004 . Preconditioning techniques for the solution of the Helmholtz equation by the finite element method . Math. Comput. Simul. , 65 ( 4–5 ) : 303 – 321 .
  • Kleinman , R. E. and Martin , P. A. 1988 . On single integral equations for the transmission problem of acoustics . SIAM J. Appl. Math. , 48 : 307 – 325 .
  • Kress , R. 1985 . Minimizing the condition number of boundary integral operators in acoustic and electromagnetic scattering . Quart. J. Mech. Appl. Math. , 38 ( 2 ) : 323 – 341 .
  • Lee , J. , Zhang , J. and Lu , C. C. 2004 . Sparse inverse preconditioning of multilevel fast multipole algorithm for hybrid integral equations in electromagnetism . IEEE Trans. Antennas Propagation , 52 ( 9 ) : 2277 – 2286 .
  • Levadoux , D. 2001 . Etude d'une Equation Intégrale Adaptée à la Résolution Haute-Fréquence de l'Equation d'Helmholtz France Thèse de Doctorat de l'Université Paris VI
  • McLean , W. 2000 . Strongly Elliptic Systems and Boundary Integral Equations , Cambridge : Cambridge University Press .
  • Nédélec , J. C. 1982 . Integral equations with non-integrable kernels . Integ. Equ. Oper. Theory , 5 : 561 – 572 .
  • Ossandrón Véliz , S. E. 2006 . Mathematical modeling, numerical analysis and computational simulation of complex phenomena of propagation of acoustic, elastic and electromagnetic waves , Chili : Ecole Polytechnique, France and Facultad de Ingenieria, Pontificia Universidad Catolica de Chile . Ph.D. thesis
  • Saad , Y. 1996 . Iterative Methods for Sparse Linear Systems , Boston : PWS Pub. Co .
  • Sakoda , K. 2005 . Optical Properties of Photonic Crystals , Springer-Verlag .
  • Sertel , K. and Volakis , J. L. 2000 . Incomplete LU preconditioner for FMM implementation . Microwave Opt. Technol. Lett. , 26 : 265 – 267 .
  • Steinbach , O. and Wendland , W. L. 1998 . The construction of some efficient preconditioners in the boundary element method . Adv. Comput. Math. , 9 : 191 – 216 .

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