PIER | |

Progress In Electromagnetics Research | ISSN: 1070-4698, E-ISSN: 1559-8985 |

Home > Vol. 127 > pp. 211-257
## AN EFFICIENT METHOD FOR COMPUTING HIGHLY OSCILLATORY PHYSICAL OPTICS INTEGRALBy Y. Wu, L. J. Jiang, and W. C. Chew
Abstract:
In this work, we use the numerical steepest descent path (numerical SDP) method in complex analysis theory to calculate the highly oscillatory physical optics (PO) integral with quadratic phase and amplitude variations on the triangular patch. The Stokes' phenomenon will occur due to various asymptotic behaviors on different domains. The stationary phase point contributions are carefully studied by the numerical SDP method and complex analysis using contour deformation. Its result agrees very well with the leading terms of the traditional asymptotic expansion. Furthermore, the resonance points and vertex points contributions from the PO integral are also extracted. Compared with traditional approximate asymptotic expansion approach, our method has significantly improved the PO integral accuracy by one to two digits (10 ^{-1} to 10^{-2}) for evaluating the PO integral. Moreover, the computation effort for the highly oscillatory integral is frequency independent. Numerical results for PO integral on the triangular patch are given to verify the proposed numerical SDP theory.
2. Knott, E. F., J. F. Shaeffer, and M. T. Tuley, 3. Ufimtsev, P. Y., 4. Macdonald , H. M., "The effect produced by an obstacle on a train of electric waves," 5. Ludwig, A. C., "Computation of radiation patterns involving numerical double integration," 6. Gordon, W. B., "Far-field approximations to the Kirchhoff-Helmholtz representation of scattered fields," 7. Gordon, W. B., "High-frequency approximations to the physical optics scattering integral ," 8. Bolukbas, D. and A. A. Ergin, "A radon transform interpretation of the physical optics integral," 9. Serim, H. A. and A. A. Ergin, "Computation of the physical optics integral on NURBS surfaces using a radon transform interpretation," 10. Ulku, H. A. and A. A. Ergin, "Radon transform interpretation of the physical optics integral and application to near and far field acoustic scattering problems," 11. Infante, L. and M. Stefano, "Near-field line-integral representation of the Kirchhoff-type aperture radiation for parabolic reflector," 12. Burkholder, R. J. and T. H. Lee, "Adaptive sampling for fast physical optics numerical integration," 13. Conde, O. M., J. Perez, and M. F. Catedra, "Stationary phase method application for the analysis of radiation of complex 3-D conducting structures," 14. Catedra, M. F., C. Delgado, S. Luceri, O. G. Blanco, and F. S. Adana, "Physical optics analysis of multiple interactions in large scatters using current modes," 15. Delgado, C., J. M. Gomez, and M. F. Catedra, "Analytical field calculation involving current modes and quadratic phase expressions," 16. Catedra, M. F., C. Delgado, and I. G. Diego, "New physical optics approach for an efficient treatment of multiple bounces in curved bodies defined by an impedance boundary condition," 17. Vico, F., M. Ferrando, and A. Valero, "A new fast physical optics for smooth surfaces by means of a numerical theory of diffraction ," 18. Carluccio, G., M. Albani, and P. H. Pathak, "Uniform asymptotic evaluation of surface integrals with polygonal integration domains in terms of UTD transition functions ," 19. Albani, M., G. Carluccio, and P. H. Pathak, "Uniform ray description for the PO scattering by vertices in curved surface with curvilinear edges and relatively general boundary conditions," 20. Harrington, R., 21. Borovikov, V. A., 22. James, G. L., "Geometrical Theory of Diffraction for Electromagnetic Waves," 23. Langdon, S. and S. N. Chandler-Wilde, "A wavenumber independent boundary element method for an acoustic scattering problem," 24. Bruno, O. P., C. A. Geuzaine, J. A. Monro, Jr., and F. Reitich, "Prescribed error tolerances within fixed computational times for scattering problems of arbitrarily high frequency: The convex case," 25. Geuzaine, C., O. Bruno, and F. Reitich, "On the O(1) solution of multiple-scattering problems," 26. Bruno, O. P. and C. A. Geuzaine, "An O(1) integration scheme for three-dimensional surface scattering problems," 27. Engquist, B., E. Fatemi, and S. Osher, "Numerical solution of the high frequency asymptotic expansion for the scalar wave equation," 28. Engquist, B. and O. Runborg, "Multi-Phase computations in geometrical optics," 29. Engquist, B. and O. Runborg, "Computational high frequency wave propagation," 30. Iserles, A. and S. P. NΦsett, "Quadrature methods for multivariate highly oscillatory integrals using derivatives," 31. Iserles, A. and S. P. NΦsett, "On the computation of highly oscillatory multivariate integrals with critical points," 32. Iserles, A. and S. P. NΦsett, "From high oscillation to rapid approximation III: Multivariate expansions," 33. Iserles, A. and D. Levin, "Asymptotic expansion and quadrature of composite highly oscillatory integrals," 34. Huybrechs, D. and S. Vandewalle, "The construction of cubature rules for multivariate highly oscillatory integrals," 35. Huybrechs, D. and S. Vandewalle, "A sparse discretisation for integral equation formulations of high frequency scattering problems," 36. Asheim, A. and D. Huybrechs, "Asymptotic analysis of numerical steepest descent with path approximations," 37. Asheim, A., "Numerical methods for highly oscillatory problems,", Ph.D. Dissertation,-Norwegian University of Science and Technology, Department of Mathematical Sciences, 2010.
38. Wong, R., 39. Kouyoumjian, R. G. and P. H. Pathak, "A uniform geometrical theory of diffraction for an edge in a perfectly conducting surface," 40. Lee, S. W. and G. A. Deschamps, "A uniform asymptotic theory of electromagnetic diffraction by a curved wedge," 41. Ikuno, H. and M. Nishimoto, "Calculation of transfer functions of three-dimensional indented objects by the physical optics approximation combined with the method of stationary phase," 42. Jones, D. S. and M. Kline, "Asymptotic expansion of multiple integrals and the method of stationary phase," 43. Chako, N., "Asymptotic expansions of double and multiple integral," 44. Davis, C. P. and W. C. Chew, "Frequency-independent scattering fom a flat strip with TEz-polarized fields," 45. Sha, W. E. I. and W. C. Chew, "High frequency scattering by an impenetrable sphere," 46. Abramowitz, M. and I. A. Stegun, 47. Josef, S. and B. Roland, |

© Copyright 2014 EMW Publishing. All Rights Reserved