SEARCH

SEARCH BY CITATION

References

  • Antoine, X., A. Bendali, and M. Darbas (2005), Analytic preconditioners for the boundary integral solution of the scattering of acoustic waves by open surfaces, J. Comput. Acoust., 13(3), 477498.
  • Atkinson, K., and I. Sloan (1991), The numerical solution of first-kind logarithmic-kernel integral equations on smooth open arcs, Math. Comp., 56(193), 119139.
  • Bleszynski, E., M. Bleszynski, and T. Jaroszewicz (1996), AIM: Adaptive integral method for solving large-scale electromagnetic scattering and radiation problems, Radio Sci., 31(5), 12251251.
  • Brown, A., P. R. Halmos, and A. L. Shields (1965), Cesàro operators, Acta Sci. Math. (Szeged), 26, 125137.
  • Bruno, O., and M. Haslam (2007), Regularity theory and superalgebraic solvers for wire antenna problems, SIAM J. Sci. Comput., 29(4), 13751402.
  • Bruno, O., and L. Kunyansky (2001), A fast, high-order algorithm for the solution of surface scattering problems: basic implementation, tests, and applications, J. Comput. Phys., 169(1), 80110.
  • Christiansen, S. H., and J.-C. Nédélec (2000), Preconditioners for the boundary element method in acoustics, in Mathematical and Numerical Aspects of Wave Propagation (Santiago de Compostela, 2000), pp. 776781, Soc. for Ind. and Appl. Math., Philadelphia, Pa.
  • Colton, D., and R. Kress (1983), Integral Equation Methods in Scattering Theory, John Wiley, New York.
  • Colton, D., and R. Kress (1997), Inverse Acoustic and Electromagnetic Scattering Theory, Springer, New York.
  • Costabel, M., M. Dauge, and R. Duduchava (2003), Asymptotics without logarithmic terms for crack problems, Commun. Partial Differential Equations, 28, 869926.
  • Erdélyi, A., W. Magnus, F. Oberhettinger, and F. Tricomi (1981), Higher Transcendental Functions, vol. II, 396 pp., Robert E. Krieger, Melbourne, Fla.
  • Hsiao, G. C., E. P. Stephan, and W. L. Wendland (1991), On the Dirichlet problem in elasticity for a domain exterior to an arc, J. Comput. Appl. Math., 34(1), 119.
  • Jiang, S., and V. Rokhlin (2004), Second kind integral equations for the classical potential theory on open surfaces. II, J. Comput. Phys., 195(1), 116.
  • Karam, M. A., and A. K. Fung (1983), Scattering from randomly oriented circular discs with application to vegetation, Radio Sci., 18(4), 557565, doi:10.1029/RS018i004p00557.
  • Keller, J. B. (1962), Geometrical theory of diffraction, J. Opt. Soc. Am., 52(2), 116130.
  • Kress, R. (1999), Linear Integral Equations, Appl. Math. Sci., vol. 82, 2nd ed., 365 pp., Springer-Verlag, New York.
  • Kussmaul, R. (1969), Ein numerisches Verfahren zur Lösung des Neumannschen Aussenraumproblems für die Helmholtzsche Schwingungsgleichung, Computing (Arch. Elektron. Rechnen), 4, 246273.
  • Lu, P., and M. Ando (2012), Difference of scattering geometrical optics components and line integrals of currents in modified edge representation, Radio Sci., 47, RS3007, doi:10.1029/2011RS004899.
  • Martensen, E. (1963), Über eine Methode zum räumlichen Neumannschen Problem mit einer Anwendung für torusartige Berandungen, Acta Math., 109, 75135.
  • Mason, J. C., and D. C. Handscomb (2003), Chebyshev Polynomials, 341 pp., Chapman and Hall, Boca Raton, Fla.
  • Maue, A.-W. (1949), Zur Formulierung eines allgemeinen Beugungsproblems durch eine Integralgleichung, Z. Phys., 126, 601618.
  • Meixner, J. (1949), Die Kantenbedingung in der Theorie der Beugung elektromagnetischer Wellen an vollkommen leitenden ebenen Schirmen, Ann. Phys., 6, 29.
  • Mittra, R., Y. Rahmat-Samii, D. Jamnejad, and W. Davis (1973), A new look at the thin-plate scattering problem, Radio Sci., 8(10), 869875.
  • Mönch, L. (1996), On the numerical solution of the direct scattering problem for an open sound-hard arc, J. Comput. Appl. Math., 71(2), 343356.
  • Nédélec, J. (2001), Acoustic and Electromagnetic Equations, Appl. Math. Sci., vol. 144, 316 pp., Springer-Verlag, New York.
  • Povzner, A. Y., and I. V. Suharevskiĭ (1960), Integral equations of the second kind in problems of diffraction by an infinitely thin screen, Sov. Phys. Dokl., 4, 798801.
  • Press, W. H., S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery (1992), Numerical Recipes in C, 2nd ed., Cambridge Univ. Press, Cambridge, U. K.
  • Rokhlin, V. (1993), Diagonal forms of translation operators for the Helmholtz equation in three dimensions, Appl. Comput. Harmon. Anal., 1(1), 8293.
  • Saad, Y., and M. H. Schultz (1986), GMRES: A generalized minimal residual algorithm for solving nonsymmetric linear systems, SIAM J. Sci. Stat. Comput., 7(3), 856869, doi:10.1137/0907058.
  • Saranen, J., and G. Vainikko (2002), Periodic Integral and Pseudodifferential Equations With Numerical Approximation, 452 pp., Springer-Verlag, Berlin.
  • Stephan, E. (1987), Boundary integral equations for screen problems in R3, Integral Equations Operator Theory, 10(2), 236257.
  • Stephan, E., and T. Tran (1998), Domain decomposition algorithms for indefininte hypersingular integral equations: The h and p versions, SIAM J. Sci. Comput., 19(4), 11391153.
  • Stephan, E., and W. Wendland (1984), An augmented Galerkin procedure for the boundary integral method applied to two-dimensional screen and crack problems, Appl. Anal., 18(3), 183219.
  • Wendland, W. L., and E. P. Stephan (1990), A hypersingular boundary integral method for two-dimensional screen and crack problems, Arch. Rational Mech. Anal., 112(4), 363390.
  • Yan, Y., and I. H. Sloan (1988), On integral equations of the first kind with logarithmic kernels, J. Integral Equations Appl., 1(4), 549579.