Abstract

This paper presents high-order integral equation methods for the evaluation of electromagnetic wave scattering by dielectric bumps and dielectric cavities on perfectly conducting or dielectric half-planes. In detail, the algorithms introduced in this paper apply to eight classical scattering problems, namely, scattering by a dielectric bump on a perfectly conducting or a dielectric half-plane, and scattering by a filled, overfilled, or void dielectric cavity on a perfectly conducting or a dielectric half-plane. In all cases field representations based on single-layer potentials for appropriately chosen Green functions are used. The numerical far fields and near fields exhibit excellent convergence as discretizations are refined—even at and around points where singular fields and infinite currents exist.

© 2014 Optical Society of America

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  1. R. Ruppin, “Electric field enhancement near a surface bump,” Solid State Commun. 39, 903–906 (1981).
    [CrossRef]
  2. P. Zhang, Y. Y. Lau, and R. M. Gilgenbach, “Analysis of radio-frequency absorption and electric and magnetic field enhancements due to surface roughness,” J. Appl. Phys. 105, 1–9 (2009).
  3. B. Alavikia and O. M. Ramahi, “Hybrid finite element-boundary integral algorithm to solve the problem of scattering from a finite array of cavities with multilayer stratified dielectric coating,” J. Opt. Soc. Am. A 28, 2192–2199 (2011).
    [CrossRef]
  4. Rayleigh, “On the light dispersed from fine lines ruled upon reflecting surfaces or transmitted by very narrow slits,” Philos. Mag. Series 14(81), 350–359 (1907).
  5. W. J. Byun, J. W. Yu, and N. H. Myung, “TM scattering from hollow and dielectric-filled semielliptic channels with arbitrary eccentricity in a perfectly conducting plane,” IEEE Trans. Microwave Theory Tech. 46, 1336–1339 (1998).
    [CrossRef]
  6. H. Eom and G. Hur, “Gaussian beam scattering from a semicircular boss above a conducting plane,” IEEE Trans. Antennas Propag. 41, 106–108 (1993).
    [CrossRef]
  7. S. J. Lee, D. J. Lee, W. S. Lee, and J. W. Yu, “Electromagnetic scattering from both finite semi-circular channels and bosses in a conducting plane: TM case,” J. Electromagn. Waves Appl. 26, 2398–2409 (2012).
  8. T. Park, H. Eom, and K. Yoshitomi, “Analysis of TM scattering from finite rectangular grooves in a conducting plane,” J. Opt. Soc. Am. A 10, 905–911 (1993).
    [CrossRef]
  9. T. J. Park, H. J. Eom, Y. Yamaguchi, and W.-M. Boerner, “TE-plane wave scattering from a trough in a conducting plane,” J. Electromagn. Waves Appl. 7, 235–245 (1993).
  10. A. Tyzhnenko, “Two-dimensional TE-plane wave scattering by a dielectric-loaded semicircular trough in a ground plane,” Electromagnetics 24, 357–368 (2004).
    [CrossRef]
  11. A. G. Tyzhnenko, “A unique solution to the 2-d H-scattering problem for a semicircular trough in a PEC ground plane,” Prog. Electromagn. Res. 54, 303–319 (2005).
    [CrossRef]
  12. J.-W. Yu, W. J. Byun, and N.-H. Myung, “Multiple scattering from two dielectric-filled semi-circular channels in a conducting plane: TM case,” IEEE Trans. Antennas Propag. 50, 1250–1253 (2002).
    [CrossRef]
  13. M. Basha, S. Chaudhuri, S. Safavi-Naeini, and H. Eom, “Rigorous formulation for electromagnetic plane-wave scattering from a general-shaped groove in a perfectly conducting plane,” J. Opt. Soc. Am. A 24, 1647–1655 (2007).
    [CrossRef]
  14. M. K. Hinders and A. D. Yaghjian, “Dual-series solution to scattering from a semicircular channel in a ground plane,” IEEE Microwave Guided Wave Lett. 1, 239–242 (1991).
  15. B. K. Sachdeva and R. A. Hurd, “Scattering by a dielectric loaded trough in a conducting plane,” J. Appl. Phys. 48, 1473–1476 (1977).
    [CrossRef]
  16. B. Alavikia and O. M. Ramahi, “Finite-element solution of the problem of scattering from cavities in metallic screens using the surface integral equation as a boundary constraint,” J. Opt. Soc. Am. A 26, 1915–1925 (2009).
    [CrossRef]
  17. G. Bao and W. Sun, “A fast algorithm for the electromagnetic scattering from a large cavity,” SIAM J. Sci. Comput. 27, 553–574 (2005).
    [CrossRef]
  18. K. Du, “Two transparent boundary conditions for the electromagnetic scattering from two-dimensional overfilled cavities,” J. Comput. Phys. 230, 5822–5835 (2011).
    [CrossRef]
  19. P. Li and A. Wood, “A two-dimensional Helmhotlz equation solution for the multiple cavity scattering problem,” J. Comput. Phys. 240, 100–120 (2013).
    [CrossRef]
  20. T. Van and A. Wood, “Finite element analysis of electromagnetic scattering from a cavity,” IEEE Trans. Antennas Propag. 51, 130–137 (2003).
    [CrossRef]
  21. Y. Wang, K. Du, and W. Sun, “A second-order method for the electromagnetic scattering from a large cavity,” Numer. Math. Theory Methods Appl. 1, 357–382 (2008).
  22. A. Wood, “Analysis of electromagnetic scattering from an overfilled cavity in the ground plane,” J. Comput. Phys. 215, 630–641 (2006).
    [CrossRef]
  23. E. Howe and A. Wood, “TE solutions of an integral equations method for electromagnetic scattering from a 2D cavity,” IEEE Antennas Wirel. Propag. Lett. 2, 93–96 (2003).
  24. C.-F. Wang and Y.-B. Gan, “2D cavity modeling using method of moments and iterative solvers,” Prog. Electromagn. Res. 43, 123–142 (2003).
    [CrossRef]
  25. W. D. Wood and A. W. Wood, “Development and numerical solution of integral equations for electromagnetic scattering from a trough in a ground plane,” IEEE Trans. Antennas Propag. 47, 1318–1322 (1999).
    [CrossRef]
  26. C. Pérez-Arancibia and O. P. Bruno, “High-order integral equation methods for problems of scattering by bumps and cavities on half-planes,” arXiv:1405.4336 (2014).
  27. D. Colton and R. Kress, Inverse Acoustic and Electromagnetic Scattering Theory, 3rd ed. (Springer, 2012), Vol. 93.
  28. O. P. Bruno, J. S. Ovall, and C. Turc, “A high-order integral algorithm for highly singular PDE solutions in Lipschitz domains,” Computing 84, 149–181 (2009).
  29. J. Meixner, “The behavior of electromagnetic fields at edges,” IEEE Trans. Antennas Propag. 20, 442–446 (1972).
    [CrossRef]
  30. J. Van Bladel, “Field singularities at metal-dielectric wedges,” IEEE Trans. Antennas Propag. 33, 450–455 (1985).
    [CrossRef]
  31. R. Kress, “A Nystrom method for boundary integral equations in domains with corners,” Numer. Math. 58, 145–161 (1990).
    [CrossRef]
  32. E. Akhmetgaliyev and O. P. Bruno are preparing a manuscript to be called “A boundary integral strategy for the Laplace Dirichlet/Neumann mixed eigenvalue problem.”
  33. D. L. Colton and R. Kress, Integral Equation Methods in Scattering Theory, 1st ed., Pure and Applied Mathematics (Wiley, 1983).
  34. M. Taylor, Partial Differential Equations II: Qualitative Studies of Linear Equations, Vol. 117 of Applied Mathematical Sciences (Springer, 1996).
  35. E. Isaacson and H. Keller, Analysis of Numerical Methods (Dover, 1994).

2013 (1)

P. Li and A. Wood, “A two-dimensional Helmhotlz equation solution for the multiple cavity scattering problem,” J. Comput. Phys. 240, 100–120 (2013).
[CrossRef]

2012 (1)

S. J. Lee, D. J. Lee, W. S. Lee, and J. W. Yu, “Electromagnetic scattering from both finite semi-circular channels and bosses in a conducting plane: TM case,” J. Electromagn. Waves Appl. 26, 2398–2409 (2012).

2011 (2)

2009 (3)

B. Alavikia and O. M. Ramahi, “Finite-element solution of the problem of scattering from cavities in metallic screens using the surface integral equation as a boundary constraint,” J. Opt. Soc. Am. A 26, 1915–1925 (2009).
[CrossRef]

O. P. Bruno, J. S. Ovall, and C. Turc, “A high-order integral algorithm for highly singular PDE solutions in Lipschitz domains,” Computing 84, 149–181 (2009).

P. Zhang, Y. Y. Lau, and R. M. Gilgenbach, “Analysis of radio-frequency absorption and electric and magnetic field enhancements due to surface roughness,” J. Appl. Phys. 105, 1–9 (2009).

2008 (1)

Y. Wang, K. Du, and W. Sun, “A second-order method for the electromagnetic scattering from a large cavity,” Numer. Math. Theory Methods Appl. 1, 357–382 (2008).

2007 (1)

2006 (1)

A. Wood, “Analysis of electromagnetic scattering from an overfilled cavity in the ground plane,” J. Comput. Phys. 215, 630–641 (2006).
[CrossRef]

2005 (2)

G. Bao and W. Sun, “A fast algorithm for the electromagnetic scattering from a large cavity,” SIAM J. Sci. Comput. 27, 553–574 (2005).
[CrossRef]

A. G. Tyzhnenko, “A unique solution to the 2-d H-scattering problem for a semicircular trough in a PEC ground plane,” Prog. Electromagn. Res. 54, 303–319 (2005).
[CrossRef]

2004 (1)

A. Tyzhnenko, “Two-dimensional TE-plane wave scattering by a dielectric-loaded semicircular trough in a ground plane,” Electromagnetics 24, 357–368 (2004).
[CrossRef]

2003 (3)

T. Van and A. Wood, “Finite element analysis of electromagnetic scattering from a cavity,” IEEE Trans. Antennas Propag. 51, 130–137 (2003).
[CrossRef]

E. Howe and A. Wood, “TE solutions of an integral equations method for electromagnetic scattering from a 2D cavity,” IEEE Antennas Wirel. Propag. Lett. 2, 93–96 (2003).

C.-F. Wang and Y.-B. Gan, “2D cavity modeling using method of moments and iterative solvers,” Prog. Electromagn. Res. 43, 123–142 (2003).
[CrossRef]

2002 (1)

J.-W. Yu, W. J. Byun, and N.-H. Myung, “Multiple scattering from two dielectric-filled semi-circular channels in a conducting plane: TM case,” IEEE Trans. Antennas Propag. 50, 1250–1253 (2002).
[CrossRef]

1999 (1)

W. D. Wood and A. W. Wood, “Development and numerical solution of integral equations for electromagnetic scattering from a trough in a ground plane,” IEEE Trans. Antennas Propag. 47, 1318–1322 (1999).
[CrossRef]

1998 (1)

W. J. Byun, J. W. Yu, and N. H. Myung, “TM scattering from hollow and dielectric-filled semielliptic channels with arbitrary eccentricity in a perfectly conducting plane,” IEEE Trans. Microwave Theory Tech. 46, 1336–1339 (1998).
[CrossRef]

1993 (3)

H. Eom and G. Hur, “Gaussian beam scattering from a semicircular boss above a conducting plane,” IEEE Trans. Antennas Propag. 41, 106–108 (1993).
[CrossRef]

T. J. Park, H. J. Eom, Y. Yamaguchi, and W.-M. Boerner, “TE-plane wave scattering from a trough in a conducting plane,” J. Electromagn. Waves Appl. 7, 235–245 (1993).

T. Park, H. Eom, and K. Yoshitomi, “Analysis of TM scattering from finite rectangular grooves in a conducting plane,” J. Opt. Soc. Am. A 10, 905–911 (1993).
[CrossRef]

1991 (1)

M. K. Hinders and A. D. Yaghjian, “Dual-series solution to scattering from a semicircular channel in a ground plane,” IEEE Microwave Guided Wave Lett. 1, 239–242 (1991).

1990 (1)

R. Kress, “A Nystrom method for boundary integral equations in domains with corners,” Numer. Math. 58, 145–161 (1990).
[CrossRef]

1985 (1)

J. Van Bladel, “Field singularities at metal-dielectric wedges,” IEEE Trans. Antennas Propag. 33, 450–455 (1985).
[CrossRef]

1981 (1)

R. Ruppin, “Electric field enhancement near a surface bump,” Solid State Commun. 39, 903–906 (1981).
[CrossRef]

1977 (1)

B. K. Sachdeva and R. A. Hurd, “Scattering by a dielectric loaded trough in a conducting plane,” J. Appl. Phys. 48, 1473–1476 (1977).
[CrossRef]

1972 (1)

J. Meixner, “The behavior of electromagnetic fields at edges,” IEEE Trans. Antennas Propag. 20, 442–446 (1972).
[CrossRef]

1907 (1)

Rayleigh, “On the light dispersed from fine lines ruled upon reflecting surfaces or transmitted by very narrow slits,” Philos. Mag. Series 14(81), 350–359 (1907).

Akhmetgaliyev, E.

E. Akhmetgaliyev and O. P. Bruno are preparing a manuscript to be called “A boundary integral strategy for the Laplace Dirichlet/Neumann mixed eigenvalue problem.”

Alavikia, B.

Bao, G.

G. Bao and W. Sun, “A fast algorithm for the electromagnetic scattering from a large cavity,” SIAM J. Sci. Comput. 27, 553–574 (2005).
[CrossRef]

Basha, M.

Boerner, W.-M.

T. J. Park, H. J. Eom, Y. Yamaguchi, and W.-M. Boerner, “TE-plane wave scattering from a trough in a conducting plane,” J. Electromagn. Waves Appl. 7, 235–245 (1993).

Bruno, O. P.

O. P. Bruno, J. S. Ovall, and C. Turc, “A high-order integral algorithm for highly singular PDE solutions in Lipschitz domains,” Computing 84, 149–181 (2009).

E. Akhmetgaliyev and O. P. Bruno are preparing a manuscript to be called “A boundary integral strategy for the Laplace Dirichlet/Neumann mixed eigenvalue problem.”

C. Pérez-Arancibia and O. P. Bruno, “High-order integral equation methods for problems of scattering by bumps and cavities on half-planes,” arXiv:1405.4336 (2014).

Byun, W. J.

J.-W. Yu, W. J. Byun, and N.-H. Myung, “Multiple scattering from two dielectric-filled semi-circular channels in a conducting plane: TM case,” IEEE Trans. Antennas Propag. 50, 1250–1253 (2002).
[CrossRef]

W. J. Byun, J. W. Yu, and N. H. Myung, “TM scattering from hollow and dielectric-filled semielliptic channels with arbitrary eccentricity in a perfectly conducting plane,” IEEE Trans. Microwave Theory Tech. 46, 1336–1339 (1998).
[CrossRef]

Chaudhuri, S.

Colton, D.

D. Colton and R. Kress, Inverse Acoustic and Electromagnetic Scattering Theory, 3rd ed. (Springer, 2012), Vol. 93.

Colton, D. L.

D. L. Colton and R. Kress, Integral Equation Methods in Scattering Theory, 1st ed., Pure and Applied Mathematics (Wiley, 1983).

Du, K.

K. Du, “Two transparent boundary conditions for the electromagnetic scattering from two-dimensional overfilled cavities,” J. Comput. Phys. 230, 5822–5835 (2011).
[CrossRef]

Y. Wang, K. Du, and W. Sun, “A second-order method for the electromagnetic scattering from a large cavity,” Numer. Math. Theory Methods Appl. 1, 357–382 (2008).

Eom, H.

Eom, H. J.

T. J. Park, H. J. Eom, Y. Yamaguchi, and W.-M. Boerner, “TE-plane wave scattering from a trough in a conducting plane,” J. Electromagn. Waves Appl. 7, 235–245 (1993).

Gan, Y.-B.

C.-F. Wang and Y.-B. Gan, “2D cavity modeling using method of moments and iterative solvers,” Prog. Electromagn. Res. 43, 123–142 (2003).
[CrossRef]

Gilgenbach, R. M.

P. Zhang, Y. Y. Lau, and R. M. Gilgenbach, “Analysis of radio-frequency absorption and electric and magnetic field enhancements due to surface roughness,” J. Appl. Phys. 105, 1–9 (2009).

Hinders, M. K.

M. K. Hinders and A. D. Yaghjian, “Dual-series solution to scattering from a semicircular channel in a ground plane,” IEEE Microwave Guided Wave Lett. 1, 239–242 (1991).

Howe, E.

E. Howe and A. Wood, “TE solutions of an integral equations method for electromagnetic scattering from a 2D cavity,” IEEE Antennas Wirel. Propag. Lett. 2, 93–96 (2003).

Hur, G.

H. Eom and G. Hur, “Gaussian beam scattering from a semicircular boss above a conducting plane,” IEEE Trans. Antennas Propag. 41, 106–108 (1993).
[CrossRef]

Hurd, R. A.

B. K. Sachdeva and R. A. Hurd, “Scattering by a dielectric loaded trough in a conducting plane,” J. Appl. Phys. 48, 1473–1476 (1977).
[CrossRef]

Isaacson, E.

E. Isaacson and H. Keller, Analysis of Numerical Methods (Dover, 1994).

Keller, H.

E. Isaacson and H. Keller, Analysis of Numerical Methods (Dover, 1994).

Kress, R.

R. Kress, “A Nystrom method for boundary integral equations in domains with corners,” Numer. Math. 58, 145–161 (1990).
[CrossRef]

D. L. Colton and R. Kress, Integral Equation Methods in Scattering Theory, 1st ed., Pure and Applied Mathematics (Wiley, 1983).

D. Colton and R. Kress, Inverse Acoustic and Electromagnetic Scattering Theory, 3rd ed. (Springer, 2012), Vol. 93.

Lau, Y. Y.

P. Zhang, Y. Y. Lau, and R. M. Gilgenbach, “Analysis of radio-frequency absorption and electric and magnetic field enhancements due to surface roughness,” J. Appl. Phys. 105, 1–9 (2009).

Lee, D. J.

S. J. Lee, D. J. Lee, W. S. Lee, and J. W. Yu, “Electromagnetic scattering from both finite semi-circular channels and bosses in a conducting plane: TM case,” J. Electromagn. Waves Appl. 26, 2398–2409 (2012).

Lee, S. J.

S. J. Lee, D. J. Lee, W. S. Lee, and J. W. Yu, “Electromagnetic scattering from both finite semi-circular channels and bosses in a conducting plane: TM case,” J. Electromagn. Waves Appl. 26, 2398–2409 (2012).

Lee, W. S.

S. J. Lee, D. J. Lee, W. S. Lee, and J. W. Yu, “Electromagnetic scattering from both finite semi-circular channels and bosses in a conducting plane: TM case,” J. Electromagn. Waves Appl. 26, 2398–2409 (2012).

Li, P.

P. Li and A. Wood, “A two-dimensional Helmhotlz equation solution for the multiple cavity scattering problem,” J. Comput. Phys. 240, 100–120 (2013).
[CrossRef]

Meixner, J.

J. Meixner, “The behavior of electromagnetic fields at edges,” IEEE Trans. Antennas Propag. 20, 442–446 (1972).
[CrossRef]

Myung, N. H.

W. J. Byun, J. W. Yu, and N. H. Myung, “TM scattering from hollow and dielectric-filled semielliptic channels with arbitrary eccentricity in a perfectly conducting plane,” IEEE Trans. Microwave Theory Tech. 46, 1336–1339 (1998).
[CrossRef]

Myung, N.-H.

J.-W. Yu, W. J. Byun, and N.-H. Myung, “Multiple scattering from two dielectric-filled semi-circular channels in a conducting plane: TM case,” IEEE Trans. Antennas Propag. 50, 1250–1253 (2002).
[CrossRef]

Ovall, J. S.

O. P. Bruno, J. S. Ovall, and C. Turc, “A high-order integral algorithm for highly singular PDE solutions in Lipschitz domains,” Computing 84, 149–181 (2009).

Park, T.

Park, T. J.

T. J. Park, H. J. Eom, Y. Yamaguchi, and W.-M. Boerner, “TE-plane wave scattering from a trough in a conducting plane,” J. Electromagn. Waves Appl. 7, 235–245 (1993).

Pérez-Arancibia, C.

C. Pérez-Arancibia and O. P. Bruno, “High-order integral equation methods for problems of scattering by bumps and cavities on half-planes,” arXiv:1405.4336 (2014).

Ramahi, O. M.

Rayleigh,

Rayleigh, “On the light dispersed from fine lines ruled upon reflecting surfaces or transmitted by very narrow slits,” Philos. Mag. Series 14(81), 350–359 (1907).

Ruppin, R.

R. Ruppin, “Electric field enhancement near a surface bump,” Solid State Commun. 39, 903–906 (1981).
[CrossRef]

Sachdeva, B. K.

B. K. Sachdeva and R. A. Hurd, “Scattering by a dielectric loaded trough in a conducting plane,” J. Appl. Phys. 48, 1473–1476 (1977).
[CrossRef]

Safavi-Naeini, S.

Sun, W.

Y. Wang, K. Du, and W. Sun, “A second-order method for the electromagnetic scattering from a large cavity,” Numer. Math. Theory Methods Appl. 1, 357–382 (2008).

G. Bao and W. Sun, “A fast algorithm for the electromagnetic scattering from a large cavity,” SIAM J. Sci. Comput. 27, 553–574 (2005).
[CrossRef]

Taylor, M.

M. Taylor, Partial Differential Equations II: Qualitative Studies of Linear Equations, Vol. 117 of Applied Mathematical Sciences (Springer, 1996).

Turc, C.

O. P. Bruno, J. S. Ovall, and C. Turc, “A high-order integral algorithm for highly singular PDE solutions in Lipschitz domains,” Computing 84, 149–181 (2009).

Tyzhnenko, A.

A. Tyzhnenko, “Two-dimensional TE-plane wave scattering by a dielectric-loaded semicircular trough in a ground plane,” Electromagnetics 24, 357–368 (2004).
[CrossRef]

Tyzhnenko, A. G.

A. G. Tyzhnenko, “A unique solution to the 2-d H-scattering problem for a semicircular trough in a PEC ground plane,” Prog. Electromagn. Res. 54, 303–319 (2005).
[CrossRef]

Van, T.

T. Van and A. Wood, “Finite element analysis of electromagnetic scattering from a cavity,” IEEE Trans. Antennas Propag. 51, 130–137 (2003).
[CrossRef]

Van Bladel, J.

J. Van Bladel, “Field singularities at metal-dielectric wedges,” IEEE Trans. Antennas Propag. 33, 450–455 (1985).
[CrossRef]

Wang, C.-F.

C.-F. Wang and Y.-B. Gan, “2D cavity modeling using method of moments and iterative solvers,” Prog. Electromagn. Res. 43, 123–142 (2003).
[CrossRef]

Wang, Y.

Y. Wang, K. Du, and W. Sun, “A second-order method for the electromagnetic scattering from a large cavity,” Numer. Math. Theory Methods Appl. 1, 357–382 (2008).

Wood, A.

P. Li and A. Wood, “A two-dimensional Helmhotlz equation solution for the multiple cavity scattering problem,” J. Comput. Phys. 240, 100–120 (2013).
[CrossRef]

A. Wood, “Analysis of electromagnetic scattering from an overfilled cavity in the ground plane,” J. Comput. Phys. 215, 630–641 (2006).
[CrossRef]

T. Van and A. Wood, “Finite element analysis of electromagnetic scattering from a cavity,” IEEE Trans. Antennas Propag. 51, 130–137 (2003).
[CrossRef]

E. Howe and A. Wood, “TE solutions of an integral equations method for electromagnetic scattering from a 2D cavity,” IEEE Antennas Wirel. Propag. Lett. 2, 93–96 (2003).

Wood, A. W.

W. D. Wood and A. W. Wood, “Development and numerical solution of integral equations for electromagnetic scattering from a trough in a ground plane,” IEEE Trans. Antennas Propag. 47, 1318–1322 (1999).
[CrossRef]

Wood, W. D.

W. D. Wood and A. W. Wood, “Development and numerical solution of integral equations for electromagnetic scattering from a trough in a ground plane,” IEEE Trans. Antennas Propag. 47, 1318–1322 (1999).
[CrossRef]

Yaghjian, A. D.

M. K. Hinders and A. D. Yaghjian, “Dual-series solution to scattering from a semicircular channel in a ground plane,” IEEE Microwave Guided Wave Lett. 1, 239–242 (1991).

Yamaguchi, Y.

T. J. Park, H. J. Eom, Y. Yamaguchi, and W.-M. Boerner, “TE-plane wave scattering from a trough in a conducting plane,” J. Electromagn. Waves Appl. 7, 235–245 (1993).

Yoshitomi, K.

Yu, J. W.

S. J. Lee, D. J. Lee, W. S. Lee, and J. W. Yu, “Electromagnetic scattering from both finite semi-circular channels and bosses in a conducting plane: TM case,” J. Electromagn. Waves Appl. 26, 2398–2409 (2012).

W. J. Byun, J. W. Yu, and N. H. Myung, “TM scattering from hollow and dielectric-filled semielliptic channels with arbitrary eccentricity in a perfectly conducting plane,” IEEE Trans. Microwave Theory Tech. 46, 1336–1339 (1998).
[CrossRef]

Yu, J.-W.

J.-W. Yu, W. J. Byun, and N.-H. Myung, “Multiple scattering from two dielectric-filled semi-circular channels in a conducting plane: TM case,” IEEE Trans. Antennas Propag. 50, 1250–1253 (2002).
[CrossRef]

Zhang, P.

P. Zhang, Y. Y. Lau, and R. M. Gilgenbach, “Analysis of radio-frequency absorption and electric and magnetic field enhancements due to surface roughness,” J. Appl. Phys. 105, 1–9 (2009).

Computing (1)

O. P. Bruno, J. S. Ovall, and C. Turc, “A high-order integral algorithm for highly singular PDE solutions in Lipschitz domains,” Computing 84, 149–181 (2009).

Electromagnetics (1)

A. Tyzhnenko, “Two-dimensional TE-plane wave scattering by a dielectric-loaded semicircular trough in a ground plane,” Electromagnetics 24, 357–368 (2004).
[CrossRef]

IEEE Antennas Wirel. Propag. Lett. (1)

E. Howe and A. Wood, “TE solutions of an integral equations method for electromagnetic scattering from a 2D cavity,” IEEE Antennas Wirel. Propag. Lett. 2, 93–96 (2003).

IEEE Microwave Guided Wave Lett. (1)

M. K. Hinders and A. D. Yaghjian, “Dual-series solution to scattering from a semicircular channel in a ground plane,” IEEE Microwave Guided Wave Lett. 1, 239–242 (1991).

IEEE Trans. Antennas Propag. (6)

J.-W. Yu, W. J. Byun, and N.-H. Myung, “Multiple scattering from two dielectric-filled semi-circular channels in a conducting plane: TM case,” IEEE Trans. Antennas Propag. 50, 1250–1253 (2002).
[CrossRef]

H. Eom and G. Hur, “Gaussian beam scattering from a semicircular boss above a conducting plane,” IEEE Trans. Antennas Propag. 41, 106–108 (1993).
[CrossRef]

W. D. Wood and A. W. Wood, “Development and numerical solution of integral equations for electromagnetic scattering from a trough in a ground plane,” IEEE Trans. Antennas Propag. 47, 1318–1322 (1999).
[CrossRef]

T. Van and A. Wood, “Finite element analysis of electromagnetic scattering from a cavity,” IEEE Trans. Antennas Propag. 51, 130–137 (2003).
[CrossRef]

J. Meixner, “The behavior of electromagnetic fields at edges,” IEEE Trans. Antennas Propag. 20, 442–446 (1972).
[CrossRef]

J. Van Bladel, “Field singularities at metal-dielectric wedges,” IEEE Trans. Antennas Propag. 33, 450–455 (1985).
[CrossRef]

IEEE Trans. Microwave Theory Tech. (1)

W. J. Byun, J. W. Yu, and N. H. Myung, “TM scattering from hollow and dielectric-filled semielliptic channels with arbitrary eccentricity in a perfectly conducting plane,” IEEE Trans. Microwave Theory Tech. 46, 1336–1339 (1998).
[CrossRef]

J. Appl. Phys. (2)

P. Zhang, Y. Y. Lau, and R. M. Gilgenbach, “Analysis of radio-frequency absorption and electric and magnetic field enhancements due to surface roughness,” J. Appl. Phys. 105, 1–9 (2009).

B. K. Sachdeva and R. A. Hurd, “Scattering by a dielectric loaded trough in a conducting plane,” J. Appl. Phys. 48, 1473–1476 (1977).
[CrossRef]

J. Comput. Phys. (3)

K. Du, “Two transparent boundary conditions for the electromagnetic scattering from two-dimensional overfilled cavities,” J. Comput. Phys. 230, 5822–5835 (2011).
[CrossRef]

P. Li and A. Wood, “A two-dimensional Helmhotlz equation solution for the multiple cavity scattering problem,” J. Comput. Phys. 240, 100–120 (2013).
[CrossRef]

A. Wood, “Analysis of electromagnetic scattering from an overfilled cavity in the ground plane,” J. Comput. Phys. 215, 630–641 (2006).
[CrossRef]

J. Electromagn. Waves Appl. (2)

S. J. Lee, D. J. Lee, W. S. Lee, and J. W. Yu, “Electromagnetic scattering from both finite semi-circular channels and bosses in a conducting plane: TM case,” J. Electromagn. Waves Appl. 26, 2398–2409 (2012).

T. J. Park, H. J. Eom, Y. Yamaguchi, and W.-M. Boerner, “TE-plane wave scattering from a trough in a conducting plane,” J. Electromagn. Waves Appl. 7, 235–245 (1993).

J. Opt. Soc. Am. A (4)

Numer. Math. (1)

R. Kress, “A Nystrom method for boundary integral equations in domains with corners,” Numer. Math. 58, 145–161 (1990).
[CrossRef]

Numer. Math. Theory Methods Appl. (1)

Y. Wang, K. Du, and W. Sun, “A second-order method for the electromagnetic scattering from a large cavity,” Numer. Math. Theory Methods Appl. 1, 357–382 (2008).

Philos. Mag. Series (1)

Rayleigh, “On the light dispersed from fine lines ruled upon reflecting surfaces or transmitted by very narrow slits,” Philos. Mag. Series 14(81), 350–359 (1907).

Prog. Electromagn. Res. (2)

A. G. Tyzhnenko, “A unique solution to the 2-d H-scattering problem for a semicircular trough in a PEC ground plane,” Prog. Electromagn. Res. 54, 303–319 (2005).
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C.-F. Wang and Y.-B. Gan, “2D cavity modeling using method of moments and iterative solvers,” Prog. Electromagn. Res. 43, 123–142 (2003).
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SIAM J. Sci. Comput. (1)

G. Bao and W. Sun, “A fast algorithm for the electromagnetic scattering from a large cavity,” SIAM J. Sci. Comput. 27, 553–574 (2005).
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Solid State Commun. (1)

R. Ruppin, “Electric field enhancement near a surface bump,” Solid State Commun. 39, 903–906 (1981).
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Other (6)

C. Pérez-Arancibia and O. P. Bruno, “High-order integral equation methods for problems of scattering by bumps and cavities on half-planes,” arXiv:1405.4336 (2014).

D. Colton and R. Kress, Inverse Acoustic and Electromagnetic Scattering Theory, 3rd ed. (Springer, 2012), Vol. 93.

E. Akhmetgaliyev and O. P. Bruno are preparing a manuscript to be called “A boundary integral strategy for the Laplace Dirichlet/Neumann mixed eigenvalue problem.”

D. L. Colton and R. Kress, Integral Equation Methods in Scattering Theory, 1st ed., Pure and Applied Mathematics (Wiley, 1983).

M. Taylor, Partial Differential Equations II: Qualitative Studies of Linear Equations, Vol. 117 of Applied Mathematical Sciences (Springer, 1996).

E. Isaacson and H. Keller, Analysis of Numerical Methods (Dover, 1994).

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Figures (5)

Fig. 1.
Fig. 1.

Schematics of the eight physical problems considered in this paper.

Fig. 2.
Fig. 2.

Compact mathematical description of the problems considered in this paper.

Fig. 3.
Fig. 3.

Minimum singular value of A as a function of κ=k3 for the problem of scattering by a semicircular bump on a PEC half-plane in TE polarization.

Fig. 4.
Fig. 4.

Error in the approximation of u˜κ* by Chebyshev interpolation/analytic continuation for various spurious resonant frequencies κ* as a function of the order 2m of the Chebyshev expansion.

Fig. 5.
Fig. 5.

Diffraction pattern resulting from the scattering of a plane wave by (a), (b) dielectric-filled cavity on a dielectric half-plane, (c), (d) dielectric-filled cavity on a PEC half-plane, and (e), (f) dielectric bump on a PEC half-plane.

Tables (1)

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Table 1. Convergence Test for the Numerical Solution of Problem Type I (k1=5, k2=15 or 15+5i, k3=5, and k4=7), II (k1=5, k2=15, or 15+5i, and k3=5), and III (k1=15 or 15+5i, and k3=5)

Equations (37)

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Δu+kj2u=0inΩj,
u={u1inΩ1,u2inΩ2,u3+finΩ3,u4+finΩ4,
uiuj=g,1βiuin1βjujn=1βjgn,
uj=0andujn=0,j=2,3
u={Sint[ψint]inΩ1Ω2,Sext[ψext]+finΩ3Ω4,
Sint[ψ](x)=Γ13Γ24Gk2k1(x,y)ψ(y)dsy,
Sext[ψ](x)=Γ13Γ24Gk4k3(x,y)ψ(y)dsy.
SintΓ13[ψint]SextΓ13[ψext]=f,β3β1{ψint2+KintΓ13[ψint]}+ψext2KextΓ13[ψext]=fn,SintΓ24[ψint]SextΓ24[ψext]=f,β4β2{ψint2+KintΓ24[ψint]}+ψext2KextΓ24[ψext]=fn
SintΓij[ψ](x)=Γ13Γ24Gk2k1(x,y)ψ(y)dsy,xΓij,SextΓij[ψ](x)=Γ13Γ24Gk4k3(x,y)ψ(y)dsy,xΓij,KintΓij[ψ](x)=Γ13Γ24Gk2k1nx(x,y)ψ(y)dsy,xΓij,KextΓij[ψ](x)=Γ13Γ24Gk4k3nx(x,y)ψ(y)dsy,xΓij.
u={Sint[ψint]inΩ1Ω2,Sext[ψext]+finΩ3,0inΩ4,
Sint[ψ](x)=Γ13Γ24Gk2k1(x,y)ψ(y)dsy,
Sext[ψ](x)=Γ13Gk3(x,y)ψ(y)dsy.
SintΓ13[ψint]SextΓ13[ψext]=f,β3β1{ψint2+KintΓ13[ψint]}+ψext2KextΓ13[ψext]=fn,
ψint2+KintΓ24[ψint]=0(TE polarization),
SintΓ24[ψint]=0(TM polarization)
SintΓij[ψ](x)=Γ13Γ24Gk2k1(x,y)ψ(y)dsy,xΓij,SextΓij[ψ](x)=Γ13Gk3(x,y)ψ(y)dsy,xΓij,KintΓij[ψ](x)=Γ13Γ24Gk2k1nx(x,y)ψ(y)dsy,xΓij,KextΓij[ψ](x)=Γ13Gk3nx(x,y)ψ(y)dsy,xΓij.
u={Sint[ψint]inΩ1,Sext[ψext]+finΩ3,0inΩ2Ω4,
Sint[ψ](x)=Γ13Gk1(x,y)ψ(y)dsy,
Sext[ψ](x)=Γ13Gk3(x,y)ψ(y)dsy.
SintΓ13[ψint]SextΓ13[ψext]=f,β3β1{ψint2+KintΓ13[ψint]}+ψext2KextΓ13[ψext]=fn,
SintΓ13[ψ](x)=Γ13Gk1(x,y)ψ(y)dsy,xΓ13,SextΓ13[ψ](x)=Γ13Gk3(x,y)ψ(y)dsy,xΓ13,KintΓ13[ψ](x)=Γ13Gk1nx(x,y)ψ(y)dsy,xΓ13,KextΓ13[ψ](x)=Γ13Gk3nx(x,y)ψ(y)dsy,xΓ13.
02πL(t,τ)ϕ(τ)dτand02πM(t,τ)ϕ(τ)dτ,
L(t,τ)=G(x(t),y(τ))|y(τ)|,M(t,τ)=x[G](x(t),y(τ))·n(t)|y(τ)|,
L(t,τ)=L1(t,τ)logr2(t,τ)+L2(t,τ),
M(t,τ)=M1(t,τ)logr2(t,τ)+M2(t,τ),
L1(t,τ)=14πJ0(kr(t,τ))|y(τ)|,L2(t,τ)=L(t,τ)L1(t,τ)logr2(t,τ),M1(t,τ)=k4πJ1(kr(t,τ))n(t)·r(t,τ)r|y(τ)|,M2(t,τ)=M(t,τ)M1(t,τ)logr2(t,τ).
w(s)=2π[v(s)]p[v(s)]p+[v(2πs)]p,0s2π,
v(s)=(1p12)(πsπ)3+1psππ+12,
K(t,τ)=K(w(s),w(σ))=K1(w(s),w(σ))log(4sin2sσ2)+K˜2(s,σ),
K˜2(s,σ)=K1(w(s),w(σ))log(r2(w(s),w(σ))4sin2sσ2)+K2(w(s),w(σ)),
02πf(σ)dσπnj=02n1f(σj)
02πf(σ)log(4sin2sσ2)dσj=02n1Rj(n)(s)f(σj),
Rj(s)=2πnm=1n11mcosm(sσj)πn2cosn(sσj).
Rk=2πnm=1n11mcosmkπn(1)kπn2.
02πK(ti,τ)ϕ(τ)dτj=12n1{K1(ti,τj)Wij+K2(ti,τj)πn}ϕjw(σj)
Wij=R|ij|+πnlog(r2(ti,tj)4sin2(sisj)/2).
Ej=maxxΠ1|u˜j(x)u˜5(x)|maxxΠ1|u˜5(x)|,1j4.

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