Abstract

A multilevel Green's function interpolation method based on two kinds of multilevel partitioning schemes--the quasi-2D and the hybrid partitioning scheme--is proposed for analyzing electromagnetic scattering from objects comprising both conducting and dielectric parts. The problem is formulated using the surface integral equation for homogeneous dielectric and conducting bodies. A quasi-2D multilevel partitioning scheme is devised to improve the efficiency of the Green's function interpolation. In contrast to previous multilevel partitioning schemes, noncubic groups are introduced to discretize the whole EM structure in this quasi-2D multilevel partitioning scheme. Based on the detailed analysis of the dimension of the group in this partitioning scheme, a hybrid quasi-2D/3D multilevel partitioning scheme is proposed to effectively handle objects with fine local structures. Selection criteria for some key parameters relating to the interpolation technique are given. The proposed algorithm is ideal for the solution of problems involving objects such as missiles, microstrip antenna arrays, photonic bandgap structures, etc. Numerical examples are presented to show that CPU time is between O(N) and O(NlogN) while the computer memory requirement is O(N).

© 2008 Optical Society of America

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  1. R. F. Harrington, Field Computation by Moment Methods (IEEE, 1993).
  2. J. M. Jin, The Finite Element Method in Electromagnetics, 2nd ed. (Wiley, 1993).
  3. A. Taflove and S. C. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method, 3rd ed. (Artech House, 2005).
  4. X. Q. Sheng, J. M. Jin, J. M. Song, W. C. Chew, and C. C. Lu, “Solution of combined-field integral equation using multilevel fast multipole algorithm for scattering by homogeneous bodies,” IEEE Trans. Antennas Propag. 46, 1718-1726 (1998).
    [CrossRef]
  5. B. M. Kolundzija, “Electromagnetic modeling of composite metallic and dielectric structures,” IEEE Trans. Microwave Theory Tech. 47, 1021-1032 (1999).
    [CrossRef]
  6. K. C. Donepudi, J. M. Jin, and W. C. Chew, “A higher order multilevel fast multipole algorithm for scattering from mixed conducting/dielectric bodies,” IEEE Trans. Antennas Propag. 51, 2814-2821 (2003).
    [CrossRef]
  7. P. Y. Oijala, M. Taskinen, and J. Sarvas, “Surface integral equation method for general composite metallic and dielectric structures with junctions,” Prog. Electromagn. Res. PIER 52, 81-108 (2005).
  8. B. M. Kolundzija and A. R. Djordjevic, Electromagnetic Modeling of Composite Metallic and Dielectric Structure (Artech House, 2002).
  9. V. Rokhlin, “Rapid solution of integral equations of classic potential theory,” J. Comput. Phys. 60, 187-207 (1985).
    [CrossRef]
  10. L. Greengard and V. Rokhlin, “A fast algorithm for particle simulations,” J. Comput. Phys. 73, 325-348 (1987).
    [CrossRef]
  11. E. Darve, “The fast multipole method: numerical implementation,” J. Comput. Phys. 160, 195-240 (2000).
    [CrossRef]
  12. C. C. Lu and W. C. Chew, “A multilevel algorithm for solving a boundary integral equation of wave scattering,” Microwave Opt. Technol. Lett. 7, 456-461 (1994).
  13. J. M. Song, C. C. Lu, and W. C. Chew, “Multilevel fast multipole algorithm for electromagnetic scattering by large complex objects,” IEEE Trans. Antennas Propag. 45, 1488-1493 (1997).
    [CrossRef]
  14. W. C. Chew, J. M. Jin, E. Michielssen, and J. M. Song, Fast and Efficient Algorithms in Computational Electromagnetics (Artech House, 2001).
  15. N. Yarvin and V. Rokhlin, “A generalized one-dimensional fast multipole method with application to filtering of spherical harmonics,” J. Comput. Phys. 147, 594-609 (1998).
    [CrossRef]
  16. E. Bleszynski, M. Bleszynski, and T. Jaroszewicz, “AIM: adaptive integral method for solving large-scale electromagnetic scattering and radiation problems,” Radio Sci. 31, 1225-1251 (1996).
    [CrossRef]
  17. F. Ling, C. F. Wang, and J. M. Jin, “An efficient algorithm for analyzing large-scale microstrip structures using adaptive integral method combined with discrete complex image method,” IEEE Trans. Microwave Theory Tech. 48, 832-837 (2000).
  18. C. H. Chan, C. M. Lin, L. Tsang, and Y. F. Leung, “A sparse-matrix/canonical grid method for analyzing microstrip structures,” IEICE Trans. Electron. E80-C, 1354-1359 (1997).
  19. S. Q. Li, Y. X. Yu, C. H. Chan, K. F. Chan, and L. Tsang, “A sparse-matrix/canonical grid method for analyzing densely packed interconnects,” IEEE Trans. Microwave Theory Tech. 49, 1221-1228 (2001).
  20. J. R. Phillips and J. K. White, “A precorrected-FFT method for electrostatic analysis of complicated 3-D structures,” IEEE Trans. Comput.-Aided Des. 16, 1059-1072 (1997).
    [CrossRef]
  21. X. C. Nie, N. Yuan, L. W. Li, Y. B. Gan, and T. S. Yeo, “A fast volume-surface integral equation solver for scattering from composite conducting-dielectric objects,” IEEE Trans. Antennas Propag. 52, 818-824 (2005).
  22. H. G. Wang, C. H. Chan, and L. Tsang, “A new multilevel Green's function interpolation method for large-scale low-frequency EM simulations,” IEEE Trans. Comput.-Aided Des. 24, 1427-1443 (2005).
    [CrossRef]
  23. H. G. Wang and C. H. Chan, “The implementation of multilevel Green's function interpolation method for full-wave electromagnetic problems,” IEEE Trans. Antennas Propag. 55, 1348-1358 (2007).
    [CrossRef]
  24. A. Brandt, “Multilevel computations of integral transforms and particle interactions with oscillatory kernels,” Comput. Phys. Commun. 65, 24-38 (1991).
    [CrossRef]
  25. L. Li, H. G. Wang, and C. H. Chan, “A novel interpolation scheme for full-wave electromagnetic simulations,” presented at the International Symposium on Antennas and Propagation (ISAP), Singapore, 2006.
  26. L. Li, H. G. Wang, and C. H. Chan, “An improved multilevel Green's function interpolation method with adaptive phase compensation for large-scale full-wave EM simulation,” IEEE Trans. Antennas Propag. 56, 1381-1393 (2008).
  27. R. D. Graglia, D. R. Wilton, and A. F. Peterson, “Higher order interpolatory vector bases for computational electromagnetics,” IEEE Trans. Antennas Propag. 45, 329-342 (1997).
    [CrossRef]
  28. Y. Saad and M. Schultz, “GMRES: A generalized minimal residual algorithm for solving non symmetric linear systems,” SIAM (Soc. Ind. Appl. Math.) J. Sci. Stat. Comput. 7, 856-869 (1986).
    [CrossRef]
  29. R. A. Horn and C. R. Johnson, Topics in Matrix Analysis (Cambridge U. Press, 1991).
  30. Y. A. Liu and W. C. Chew, “Stability of surface integral equation for left-handed materials,” IET Proc. Microwaves, Antennas Propag. 1, 84-89 (2007).
  31. D. L. Smith, L. N. M. Mitschang, and D. W. Forester, “Surface integral equation formulations for left-handed materials,” Prog. Electromagn. Res. PIER 51, 27-48 (2005).
  32. K. M. Ho, C. T. Chan, C. M. Soukoulis, R. Biswas, and M. Sigalas, “Photonic band gaps in three dimensions: new layer-by-layer periodic structures,” Solid State Commun. 89, 413-416 (1994).
    [CrossRef]
  33. E. Ozbay, A. Abeyta, G. Tuttle, M. C. Tringides, R. Biswas, M. Sigalas, C. M. Soukoulis, C. T. Chan, and K. M. Ho, “Measurement of a three-dimensional photonic band gap in a crystal structure made of dielectric rods,” Phys. Rev. B 50, 1945-1948 (1994).
    [CrossRef]

2008 (1)

L. Li, H. G. Wang, and C. H. Chan, “An improved multilevel Green's function interpolation method with adaptive phase compensation for large-scale full-wave EM simulation,” IEEE Trans. Antennas Propag. 56, 1381-1393 (2008).

2007 (2)

H. G. Wang and C. H. Chan, “The implementation of multilevel Green's function interpolation method for full-wave electromagnetic problems,” IEEE Trans. Antennas Propag. 55, 1348-1358 (2007).
[CrossRef]

Y. A. Liu and W. C. Chew, “Stability of surface integral equation for left-handed materials,” IET Proc. Microwaves, Antennas Propag. 1, 84-89 (2007).

2005 (4)

D. L. Smith, L. N. M. Mitschang, and D. W. Forester, “Surface integral equation formulations for left-handed materials,” Prog. Electromagn. Res. PIER 51, 27-48 (2005).

P. Y. Oijala, M. Taskinen, and J. Sarvas, “Surface integral equation method for general composite metallic and dielectric structures with junctions,” Prog. Electromagn. Res. PIER 52, 81-108 (2005).

X. C. Nie, N. Yuan, L. W. Li, Y. B. Gan, and T. S. Yeo, “A fast volume-surface integral equation solver for scattering from composite conducting-dielectric objects,” IEEE Trans. Antennas Propag. 52, 818-824 (2005).

H. G. Wang, C. H. Chan, and L. Tsang, “A new multilevel Green's function interpolation method for large-scale low-frequency EM simulations,” IEEE Trans. Comput.-Aided Des. 24, 1427-1443 (2005).
[CrossRef]

2003 (1)

K. C. Donepudi, J. M. Jin, and W. C. Chew, “A higher order multilevel fast multipole algorithm for scattering from mixed conducting/dielectric bodies,” IEEE Trans. Antennas Propag. 51, 2814-2821 (2003).
[CrossRef]

2001 (1)

S. Q. Li, Y. X. Yu, C. H. Chan, K. F. Chan, and L. Tsang, “A sparse-matrix/canonical grid method for analyzing densely packed interconnects,” IEEE Trans. Microwave Theory Tech. 49, 1221-1228 (2001).

2000 (2)

F. Ling, C. F. Wang, and J. M. Jin, “An efficient algorithm for analyzing large-scale microstrip structures using adaptive integral method combined with discrete complex image method,” IEEE Trans. Microwave Theory Tech. 48, 832-837 (2000).

E. Darve, “The fast multipole method: numerical implementation,” J. Comput. Phys. 160, 195-240 (2000).
[CrossRef]

1999 (1)

B. M. Kolundzija, “Electromagnetic modeling of composite metallic and dielectric structures,” IEEE Trans. Microwave Theory Tech. 47, 1021-1032 (1999).
[CrossRef]

1998 (2)

X. Q. Sheng, J. M. Jin, J. M. Song, W. C. Chew, and C. C. Lu, “Solution of combined-field integral equation using multilevel fast multipole algorithm for scattering by homogeneous bodies,” IEEE Trans. Antennas Propag. 46, 1718-1726 (1998).
[CrossRef]

N. Yarvin and V. Rokhlin, “A generalized one-dimensional fast multipole method with application to filtering of spherical harmonics,” J. Comput. Phys. 147, 594-609 (1998).
[CrossRef]

1997 (4)

C. H. Chan, C. M. Lin, L. Tsang, and Y. F. Leung, “A sparse-matrix/canonical grid method for analyzing microstrip structures,” IEICE Trans. Electron. E80-C, 1354-1359 (1997).

J. R. Phillips and J. K. White, “A precorrected-FFT method for electrostatic analysis of complicated 3-D structures,” IEEE Trans. Comput.-Aided Des. 16, 1059-1072 (1997).
[CrossRef]

R. D. Graglia, D. R. Wilton, and A. F. Peterson, “Higher order interpolatory vector bases for computational electromagnetics,” IEEE Trans. Antennas Propag. 45, 329-342 (1997).
[CrossRef]

J. M. Song, C. C. Lu, and W. C. Chew, “Multilevel fast multipole algorithm for electromagnetic scattering by large complex objects,” IEEE Trans. Antennas Propag. 45, 1488-1493 (1997).
[CrossRef]

1996 (1)

E. Bleszynski, M. Bleszynski, and T. Jaroszewicz, “AIM: adaptive integral method for solving large-scale electromagnetic scattering and radiation problems,” Radio Sci. 31, 1225-1251 (1996).
[CrossRef]

1994 (3)

C. C. Lu and W. C. Chew, “A multilevel algorithm for solving a boundary integral equation of wave scattering,” Microwave Opt. Technol. Lett. 7, 456-461 (1994).

K. M. Ho, C. T. Chan, C. M. Soukoulis, R. Biswas, and M. Sigalas, “Photonic band gaps in three dimensions: new layer-by-layer periodic structures,” Solid State Commun. 89, 413-416 (1994).
[CrossRef]

E. Ozbay, A. Abeyta, G. Tuttle, M. C. Tringides, R. Biswas, M. Sigalas, C. M. Soukoulis, C. T. Chan, and K. M. Ho, “Measurement of a three-dimensional photonic band gap in a crystal structure made of dielectric rods,” Phys. Rev. B 50, 1945-1948 (1994).
[CrossRef]

1991 (1)

A. Brandt, “Multilevel computations of integral transforms and particle interactions with oscillatory kernels,” Comput. Phys. Commun. 65, 24-38 (1991).
[CrossRef]

1987 (1)

L. Greengard and V. Rokhlin, “A fast algorithm for particle simulations,” J. Comput. Phys. 73, 325-348 (1987).
[CrossRef]

1986 (1)

Y. Saad and M. Schultz, “GMRES: A generalized minimal residual algorithm for solving non symmetric linear systems,” SIAM (Soc. Ind. Appl. Math.) J. Sci. Stat. Comput. 7, 856-869 (1986).
[CrossRef]

1985 (1)

V. Rokhlin, “Rapid solution of integral equations of classic potential theory,” J. Comput. Phys. 60, 187-207 (1985).
[CrossRef]

Abeyta, A.

E. Ozbay, A. Abeyta, G. Tuttle, M. C. Tringides, R. Biswas, M. Sigalas, C. M. Soukoulis, C. T. Chan, and K. M. Ho, “Measurement of a three-dimensional photonic band gap in a crystal structure made of dielectric rods,” Phys. Rev. B 50, 1945-1948 (1994).
[CrossRef]

Biswas, R.

E. Ozbay, A. Abeyta, G. Tuttle, M. C. Tringides, R. Biswas, M. Sigalas, C. M. Soukoulis, C. T. Chan, and K. M. Ho, “Measurement of a three-dimensional photonic band gap in a crystal structure made of dielectric rods,” Phys. Rev. B 50, 1945-1948 (1994).
[CrossRef]

K. M. Ho, C. T. Chan, C. M. Soukoulis, R. Biswas, and M. Sigalas, “Photonic band gaps in three dimensions: new layer-by-layer periodic structures,” Solid State Commun. 89, 413-416 (1994).
[CrossRef]

Bleszynski, E.

E. Bleszynski, M. Bleszynski, and T. Jaroszewicz, “AIM: adaptive integral method for solving large-scale electromagnetic scattering and radiation problems,” Radio Sci. 31, 1225-1251 (1996).
[CrossRef]

Bleszynski, M.

E. Bleszynski, M. Bleszynski, and T. Jaroszewicz, “AIM: adaptive integral method for solving large-scale electromagnetic scattering and radiation problems,” Radio Sci. 31, 1225-1251 (1996).
[CrossRef]

Brandt, A.

A. Brandt, “Multilevel computations of integral transforms and particle interactions with oscillatory kernels,” Comput. Phys. Commun. 65, 24-38 (1991).
[CrossRef]

Chan, C. H.

L. Li, H. G. Wang, and C. H. Chan, “An improved multilevel Green's function interpolation method with adaptive phase compensation for large-scale full-wave EM simulation,” IEEE Trans. Antennas Propag. 56, 1381-1393 (2008).

H. G. Wang and C. H. Chan, “The implementation of multilevel Green's function interpolation method for full-wave electromagnetic problems,” IEEE Trans. Antennas Propag. 55, 1348-1358 (2007).
[CrossRef]

H. G. Wang, C. H. Chan, and L. Tsang, “A new multilevel Green's function interpolation method for large-scale low-frequency EM simulations,” IEEE Trans. Comput.-Aided Des. 24, 1427-1443 (2005).
[CrossRef]

S. Q. Li, Y. X. Yu, C. H. Chan, K. F. Chan, and L. Tsang, “A sparse-matrix/canonical grid method for analyzing densely packed interconnects,” IEEE Trans. Microwave Theory Tech. 49, 1221-1228 (2001).

C. H. Chan, C. M. Lin, L. Tsang, and Y. F. Leung, “A sparse-matrix/canonical grid method for analyzing microstrip structures,” IEICE Trans. Electron. E80-C, 1354-1359 (1997).

L. Li, H. G. Wang, and C. H. Chan, “A novel interpolation scheme for full-wave electromagnetic simulations,” presented at the International Symposium on Antennas and Propagation (ISAP), Singapore, 2006.

Chan, C. T.

K. M. Ho, C. T. Chan, C. M. Soukoulis, R. Biswas, and M. Sigalas, “Photonic band gaps in three dimensions: new layer-by-layer periodic structures,” Solid State Commun. 89, 413-416 (1994).
[CrossRef]

E. Ozbay, A. Abeyta, G. Tuttle, M. C. Tringides, R. Biswas, M. Sigalas, C. M. Soukoulis, C. T. Chan, and K. M. Ho, “Measurement of a three-dimensional photonic band gap in a crystal structure made of dielectric rods,” Phys. Rev. B 50, 1945-1948 (1994).
[CrossRef]

Chan, K. F.

S. Q. Li, Y. X. Yu, C. H. Chan, K. F. Chan, and L. Tsang, “A sparse-matrix/canonical grid method for analyzing densely packed interconnects,” IEEE Trans. Microwave Theory Tech. 49, 1221-1228 (2001).

Chew, W. C.

Y. A. Liu and W. C. Chew, “Stability of surface integral equation for left-handed materials,” IET Proc. Microwaves, Antennas Propag. 1, 84-89 (2007).

K. C. Donepudi, J. M. Jin, and W. C. Chew, “A higher order multilevel fast multipole algorithm for scattering from mixed conducting/dielectric bodies,” IEEE Trans. Antennas Propag. 51, 2814-2821 (2003).
[CrossRef]

X. Q. Sheng, J. M. Jin, J. M. Song, W. C. Chew, and C. C. Lu, “Solution of combined-field integral equation using multilevel fast multipole algorithm for scattering by homogeneous bodies,” IEEE Trans. Antennas Propag. 46, 1718-1726 (1998).
[CrossRef]

J. M. Song, C. C. Lu, and W. C. Chew, “Multilevel fast multipole algorithm for electromagnetic scattering by large complex objects,” IEEE Trans. Antennas Propag. 45, 1488-1493 (1997).
[CrossRef]

C. C. Lu and W. C. Chew, “A multilevel algorithm for solving a boundary integral equation of wave scattering,” Microwave Opt. Technol. Lett. 7, 456-461 (1994).

W. C. Chew, J. M. Jin, E. Michielssen, and J. M. Song, Fast and Efficient Algorithms in Computational Electromagnetics (Artech House, 2001).

Darve, E.

E. Darve, “The fast multipole method: numerical implementation,” J. Comput. Phys. 160, 195-240 (2000).
[CrossRef]

Djordjevic, A. R.

B. M. Kolundzija and A. R. Djordjevic, Electromagnetic Modeling of Composite Metallic and Dielectric Structure (Artech House, 2002).

Donepudi, K. C.

K. C. Donepudi, J. M. Jin, and W. C. Chew, “A higher order multilevel fast multipole algorithm for scattering from mixed conducting/dielectric bodies,” IEEE Trans. Antennas Propag. 51, 2814-2821 (2003).
[CrossRef]

Forester, D. W.

D. L. Smith, L. N. M. Mitschang, and D. W. Forester, “Surface integral equation formulations for left-handed materials,” Prog. Electromagn. Res. PIER 51, 27-48 (2005).

Gan, Y. B.

X. C. Nie, N. Yuan, L. W. Li, Y. B. Gan, and T. S. Yeo, “A fast volume-surface integral equation solver for scattering from composite conducting-dielectric objects,” IEEE Trans. Antennas Propag. 52, 818-824 (2005).

Graglia, R. D.

R. D. Graglia, D. R. Wilton, and A. F. Peterson, “Higher order interpolatory vector bases for computational electromagnetics,” IEEE Trans. Antennas Propag. 45, 329-342 (1997).
[CrossRef]

Greengard, L.

L. Greengard and V. Rokhlin, “A fast algorithm for particle simulations,” J. Comput. Phys. 73, 325-348 (1987).
[CrossRef]

Hagness, S. C.

A. Taflove and S. C. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method, 3rd ed. (Artech House, 2005).

Harrington, R. F.

R. F. Harrington, Field Computation by Moment Methods (IEEE, 1993).

Ho, K. M.

E. Ozbay, A. Abeyta, G. Tuttle, M. C. Tringides, R. Biswas, M. Sigalas, C. M. Soukoulis, C. T. Chan, and K. M. Ho, “Measurement of a three-dimensional photonic band gap in a crystal structure made of dielectric rods,” Phys. Rev. B 50, 1945-1948 (1994).
[CrossRef]

K. M. Ho, C. T. Chan, C. M. Soukoulis, R. Biswas, and M. Sigalas, “Photonic band gaps in three dimensions: new layer-by-layer periodic structures,” Solid State Commun. 89, 413-416 (1994).
[CrossRef]

Horn, R. A.

R. A. Horn and C. R. Johnson, Topics in Matrix Analysis (Cambridge U. Press, 1991).

Jaroszewicz, T.

E. Bleszynski, M. Bleszynski, and T. Jaroszewicz, “AIM: adaptive integral method for solving large-scale electromagnetic scattering and radiation problems,” Radio Sci. 31, 1225-1251 (1996).
[CrossRef]

Jin, J. M.

K. C. Donepudi, J. M. Jin, and W. C. Chew, “A higher order multilevel fast multipole algorithm for scattering from mixed conducting/dielectric bodies,” IEEE Trans. Antennas Propag. 51, 2814-2821 (2003).
[CrossRef]

F. Ling, C. F. Wang, and J. M. Jin, “An efficient algorithm for analyzing large-scale microstrip structures using adaptive integral method combined with discrete complex image method,” IEEE Trans. Microwave Theory Tech. 48, 832-837 (2000).

X. Q. Sheng, J. M. Jin, J. M. Song, W. C. Chew, and C. C. Lu, “Solution of combined-field integral equation using multilevel fast multipole algorithm for scattering by homogeneous bodies,” IEEE Trans. Antennas Propag. 46, 1718-1726 (1998).
[CrossRef]

J. M. Jin, The Finite Element Method in Electromagnetics, 2nd ed. (Wiley, 1993).

W. C. Chew, J. M. Jin, E. Michielssen, and J. M. Song, Fast and Efficient Algorithms in Computational Electromagnetics (Artech House, 2001).

Johnson, C. R.

R. A. Horn and C. R. Johnson, Topics in Matrix Analysis (Cambridge U. Press, 1991).

Kolundzija, B. M.

B. M. Kolundzija, “Electromagnetic modeling of composite metallic and dielectric structures,” IEEE Trans. Microwave Theory Tech. 47, 1021-1032 (1999).
[CrossRef]

B. M. Kolundzija and A. R. Djordjevic, Electromagnetic Modeling of Composite Metallic and Dielectric Structure (Artech House, 2002).

Leung, Y. F.

C. H. Chan, C. M. Lin, L. Tsang, and Y. F. Leung, “A sparse-matrix/canonical grid method for analyzing microstrip structures,” IEICE Trans. Electron. E80-C, 1354-1359 (1997).

Li, L.

L. Li, H. G. Wang, and C. H. Chan, “An improved multilevel Green's function interpolation method with adaptive phase compensation for large-scale full-wave EM simulation,” IEEE Trans. Antennas Propag. 56, 1381-1393 (2008).

L. Li, H. G. Wang, and C. H. Chan, “A novel interpolation scheme for full-wave electromagnetic simulations,” presented at the International Symposium on Antennas and Propagation (ISAP), Singapore, 2006.

Li, L. W.

X. C. Nie, N. Yuan, L. W. Li, Y. B. Gan, and T. S. Yeo, “A fast volume-surface integral equation solver for scattering from composite conducting-dielectric objects,” IEEE Trans. Antennas Propag. 52, 818-824 (2005).

Li, S. Q.

S. Q. Li, Y. X. Yu, C. H. Chan, K. F. Chan, and L. Tsang, “A sparse-matrix/canonical grid method for analyzing densely packed interconnects,” IEEE Trans. Microwave Theory Tech. 49, 1221-1228 (2001).

Lin, C. M.

C. H. Chan, C. M. Lin, L. Tsang, and Y. F. Leung, “A sparse-matrix/canonical grid method for analyzing microstrip structures,” IEICE Trans. Electron. E80-C, 1354-1359 (1997).

Ling, F.

F. Ling, C. F. Wang, and J. M. Jin, “An efficient algorithm for analyzing large-scale microstrip structures using adaptive integral method combined with discrete complex image method,” IEEE Trans. Microwave Theory Tech. 48, 832-837 (2000).

Liu, Y. A.

Y. A. Liu and W. C. Chew, “Stability of surface integral equation for left-handed materials,” IET Proc. Microwaves, Antennas Propag. 1, 84-89 (2007).

Lu, C. C.

X. Q. Sheng, J. M. Jin, J. M. Song, W. C. Chew, and C. C. Lu, “Solution of combined-field integral equation using multilevel fast multipole algorithm for scattering by homogeneous bodies,” IEEE Trans. Antennas Propag. 46, 1718-1726 (1998).
[CrossRef]

J. M. Song, C. C. Lu, and W. C. Chew, “Multilevel fast multipole algorithm for electromagnetic scattering by large complex objects,” IEEE Trans. Antennas Propag. 45, 1488-1493 (1997).
[CrossRef]

C. C. Lu and W. C. Chew, “A multilevel algorithm for solving a boundary integral equation of wave scattering,” Microwave Opt. Technol. Lett. 7, 456-461 (1994).

Michielssen, E.

W. C. Chew, J. M. Jin, E. Michielssen, and J. M. Song, Fast and Efficient Algorithms in Computational Electromagnetics (Artech House, 2001).

Mitschang, L. N. M.

D. L. Smith, L. N. M. Mitschang, and D. W. Forester, “Surface integral equation formulations for left-handed materials,” Prog. Electromagn. Res. PIER 51, 27-48 (2005).

Nie, X. C.

X. C. Nie, N. Yuan, L. W. Li, Y. B. Gan, and T. S. Yeo, “A fast volume-surface integral equation solver for scattering from composite conducting-dielectric objects,” IEEE Trans. Antennas Propag. 52, 818-824 (2005).

Oijala, P. Y.

P. Y. Oijala, M. Taskinen, and J. Sarvas, “Surface integral equation method for general composite metallic and dielectric structures with junctions,” Prog. Electromagn. Res. PIER 52, 81-108 (2005).

Ozbay, E.

E. Ozbay, A. Abeyta, G. Tuttle, M. C. Tringides, R. Biswas, M. Sigalas, C. M. Soukoulis, C. T. Chan, and K. M. Ho, “Measurement of a three-dimensional photonic band gap in a crystal structure made of dielectric rods,” Phys. Rev. B 50, 1945-1948 (1994).
[CrossRef]

Peterson, A. F.

R. D. Graglia, D. R. Wilton, and A. F. Peterson, “Higher order interpolatory vector bases for computational electromagnetics,” IEEE Trans. Antennas Propag. 45, 329-342 (1997).
[CrossRef]

Phillips, J. R.

J. R. Phillips and J. K. White, “A precorrected-FFT method for electrostatic analysis of complicated 3-D structures,” IEEE Trans. Comput.-Aided Des. 16, 1059-1072 (1997).
[CrossRef]

Rokhlin, V.

N. Yarvin and V. Rokhlin, “A generalized one-dimensional fast multipole method with application to filtering of spherical harmonics,” J. Comput. Phys. 147, 594-609 (1998).
[CrossRef]

L. Greengard and V. Rokhlin, “A fast algorithm for particle simulations,” J. Comput. Phys. 73, 325-348 (1987).
[CrossRef]

V. Rokhlin, “Rapid solution of integral equations of classic potential theory,” J. Comput. Phys. 60, 187-207 (1985).
[CrossRef]

Saad, Y.

Y. Saad and M. Schultz, “GMRES: A generalized minimal residual algorithm for solving non symmetric linear systems,” SIAM (Soc. Ind. Appl. Math.) J. Sci. Stat. Comput. 7, 856-869 (1986).
[CrossRef]

Sarvas, J.

P. Y. Oijala, M. Taskinen, and J. Sarvas, “Surface integral equation method for general composite metallic and dielectric structures with junctions,” Prog. Electromagn. Res. PIER 52, 81-108 (2005).

Schultz, M.

Y. Saad and M. Schultz, “GMRES: A generalized minimal residual algorithm for solving non symmetric linear systems,” SIAM (Soc. Ind. Appl. Math.) J. Sci. Stat. Comput. 7, 856-869 (1986).
[CrossRef]

Sheng, X. Q.

X. Q. Sheng, J. M. Jin, J. M. Song, W. C. Chew, and C. C. Lu, “Solution of combined-field integral equation using multilevel fast multipole algorithm for scattering by homogeneous bodies,” IEEE Trans. Antennas Propag. 46, 1718-1726 (1998).
[CrossRef]

Sigalas, M.

K. M. Ho, C. T. Chan, C. M. Soukoulis, R. Biswas, and M. Sigalas, “Photonic band gaps in three dimensions: new layer-by-layer periodic structures,” Solid State Commun. 89, 413-416 (1994).
[CrossRef]

E. Ozbay, A. Abeyta, G. Tuttle, M. C. Tringides, R. Biswas, M. Sigalas, C. M. Soukoulis, C. T. Chan, and K. M. Ho, “Measurement of a three-dimensional photonic band gap in a crystal structure made of dielectric rods,” Phys. Rev. B 50, 1945-1948 (1994).
[CrossRef]

Smith, D. L.

D. L. Smith, L. N. M. Mitschang, and D. W. Forester, “Surface integral equation formulations for left-handed materials,” Prog. Electromagn. Res. PIER 51, 27-48 (2005).

Song, J. M.

X. Q. Sheng, J. M. Jin, J. M. Song, W. C. Chew, and C. C. Lu, “Solution of combined-field integral equation using multilevel fast multipole algorithm for scattering by homogeneous bodies,” IEEE Trans. Antennas Propag. 46, 1718-1726 (1998).
[CrossRef]

J. M. Song, C. C. Lu, and W. C. Chew, “Multilevel fast multipole algorithm for electromagnetic scattering by large complex objects,” IEEE Trans. Antennas Propag. 45, 1488-1493 (1997).
[CrossRef]

W. C. Chew, J. M. Jin, E. Michielssen, and J. M. Song, Fast and Efficient Algorithms in Computational Electromagnetics (Artech House, 2001).

Soukoulis, C. M.

K. M. Ho, C. T. Chan, C. M. Soukoulis, R. Biswas, and M. Sigalas, “Photonic band gaps in three dimensions: new layer-by-layer periodic structures,” Solid State Commun. 89, 413-416 (1994).
[CrossRef]

E. Ozbay, A. Abeyta, G. Tuttle, M. C. Tringides, R. Biswas, M. Sigalas, C. M. Soukoulis, C. T. Chan, and K. M. Ho, “Measurement of a three-dimensional photonic band gap in a crystal structure made of dielectric rods,” Phys. Rev. B 50, 1945-1948 (1994).
[CrossRef]

Taflove, A.

A. Taflove and S. C. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method, 3rd ed. (Artech House, 2005).

Taskinen, M.

P. Y. Oijala, M. Taskinen, and J. Sarvas, “Surface integral equation method for general composite metallic and dielectric structures with junctions,” Prog. Electromagn. Res. PIER 52, 81-108 (2005).

Tringides, M. C.

E. Ozbay, A. Abeyta, G. Tuttle, M. C. Tringides, R. Biswas, M. Sigalas, C. M. Soukoulis, C. T. Chan, and K. M. Ho, “Measurement of a three-dimensional photonic band gap in a crystal structure made of dielectric rods,” Phys. Rev. B 50, 1945-1948 (1994).
[CrossRef]

Tsang, L.

H. G. Wang, C. H. Chan, and L. Tsang, “A new multilevel Green's function interpolation method for large-scale low-frequency EM simulations,” IEEE Trans. Comput.-Aided Des. 24, 1427-1443 (2005).
[CrossRef]

S. Q. Li, Y. X. Yu, C. H. Chan, K. F. Chan, and L. Tsang, “A sparse-matrix/canonical grid method for analyzing densely packed interconnects,” IEEE Trans. Microwave Theory Tech. 49, 1221-1228 (2001).

C. H. Chan, C. M. Lin, L. Tsang, and Y. F. Leung, “A sparse-matrix/canonical grid method for analyzing microstrip structures,” IEICE Trans. Electron. E80-C, 1354-1359 (1997).

Tuttle, G.

E. Ozbay, A. Abeyta, G. Tuttle, M. C. Tringides, R. Biswas, M. Sigalas, C. M. Soukoulis, C. T. Chan, and K. M. Ho, “Measurement of a three-dimensional photonic band gap in a crystal structure made of dielectric rods,” Phys. Rev. B 50, 1945-1948 (1994).
[CrossRef]

Wang, C. F.

F. Ling, C. F. Wang, and J. M. Jin, “An efficient algorithm for analyzing large-scale microstrip structures using adaptive integral method combined with discrete complex image method,” IEEE Trans. Microwave Theory Tech. 48, 832-837 (2000).

Wang, H. G.

L. Li, H. G. Wang, and C. H. Chan, “An improved multilevel Green's function interpolation method with adaptive phase compensation for large-scale full-wave EM simulation,” IEEE Trans. Antennas Propag. 56, 1381-1393 (2008).

H. G. Wang and C. H. Chan, “The implementation of multilevel Green's function interpolation method for full-wave electromagnetic problems,” IEEE Trans. Antennas Propag. 55, 1348-1358 (2007).
[CrossRef]

H. G. Wang, C. H. Chan, and L. Tsang, “A new multilevel Green's function interpolation method for large-scale low-frequency EM simulations,” IEEE Trans. Comput.-Aided Des. 24, 1427-1443 (2005).
[CrossRef]

L. Li, H. G. Wang, and C. H. Chan, “A novel interpolation scheme for full-wave electromagnetic simulations,” presented at the International Symposium on Antennas and Propagation (ISAP), Singapore, 2006.

White, J. K.

J. R. Phillips and J. K. White, “A precorrected-FFT method for electrostatic analysis of complicated 3-D structures,” IEEE Trans. Comput.-Aided Des. 16, 1059-1072 (1997).
[CrossRef]

Wilton, D. R.

R. D. Graglia, D. R. Wilton, and A. F. Peterson, “Higher order interpolatory vector bases for computational electromagnetics,” IEEE Trans. Antennas Propag. 45, 329-342 (1997).
[CrossRef]

Yarvin, N.

N. Yarvin and V. Rokhlin, “A generalized one-dimensional fast multipole method with application to filtering of spherical harmonics,” J. Comput. Phys. 147, 594-609 (1998).
[CrossRef]

Yeo, T. S.

X. C. Nie, N. Yuan, L. W. Li, Y. B. Gan, and T. S. Yeo, “A fast volume-surface integral equation solver for scattering from composite conducting-dielectric objects,” IEEE Trans. Antennas Propag. 52, 818-824 (2005).

Yu, Y. X.

S. Q. Li, Y. X. Yu, C. H. Chan, K. F. Chan, and L. Tsang, “A sparse-matrix/canonical grid method for analyzing densely packed interconnects,” IEEE Trans. Microwave Theory Tech. 49, 1221-1228 (2001).

Yuan, N.

X. C. Nie, N. Yuan, L. W. Li, Y. B. Gan, and T. S. Yeo, “A fast volume-surface integral equation solver for scattering from composite conducting-dielectric objects,” IEEE Trans. Antennas Propag. 52, 818-824 (2005).

Comput. Phys. Commun. (1)

A. Brandt, “Multilevel computations of integral transforms and particle interactions with oscillatory kernels,” Comput. Phys. Commun. 65, 24-38 (1991).
[CrossRef]

IEEE Trans. Antennas Propag. (7)

H. G. Wang and C. H. Chan, “The implementation of multilevel Green's function interpolation method for full-wave electromagnetic problems,” IEEE Trans. Antennas Propag. 55, 1348-1358 (2007).
[CrossRef]

X. C. Nie, N. Yuan, L. W. Li, Y. B. Gan, and T. S. Yeo, “A fast volume-surface integral equation solver for scattering from composite conducting-dielectric objects,” IEEE Trans. Antennas Propag. 52, 818-824 (2005).

L. Li, H. G. Wang, and C. H. Chan, “An improved multilevel Green's function interpolation method with adaptive phase compensation for large-scale full-wave EM simulation,” IEEE Trans. Antennas Propag. 56, 1381-1393 (2008).

R. D. Graglia, D. R. Wilton, and A. F. Peterson, “Higher order interpolatory vector bases for computational electromagnetics,” IEEE Trans. Antennas Propag. 45, 329-342 (1997).
[CrossRef]

X. Q. Sheng, J. M. Jin, J. M. Song, W. C. Chew, and C. C. Lu, “Solution of combined-field integral equation using multilevel fast multipole algorithm for scattering by homogeneous bodies,” IEEE Trans. Antennas Propag. 46, 1718-1726 (1998).
[CrossRef]

K. C. Donepudi, J. M. Jin, and W. C. Chew, “A higher order multilevel fast multipole algorithm for scattering from mixed conducting/dielectric bodies,” IEEE Trans. Antennas Propag. 51, 2814-2821 (2003).
[CrossRef]

J. M. Song, C. C. Lu, and W. C. Chew, “Multilevel fast multipole algorithm for electromagnetic scattering by large complex objects,” IEEE Trans. Antennas Propag. 45, 1488-1493 (1997).
[CrossRef]

IEEE Trans. Comput.-Aided Des. (2)

H. G. Wang, C. H. Chan, and L. Tsang, “A new multilevel Green's function interpolation method for large-scale low-frequency EM simulations,” IEEE Trans. Comput.-Aided Des. 24, 1427-1443 (2005).
[CrossRef]

J. R. Phillips and J. K. White, “A precorrected-FFT method for electrostatic analysis of complicated 3-D structures,” IEEE Trans. Comput.-Aided Des. 16, 1059-1072 (1997).
[CrossRef]

IEEE Trans. Microwave Theory Tech. (3)

S. Q. Li, Y. X. Yu, C. H. Chan, K. F. Chan, and L. Tsang, “A sparse-matrix/canonical grid method for analyzing densely packed interconnects,” IEEE Trans. Microwave Theory Tech. 49, 1221-1228 (2001).

F. Ling, C. F. Wang, and J. M. Jin, “An efficient algorithm for analyzing large-scale microstrip structures using adaptive integral method combined with discrete complex image method,” IEEE Trans. Microwave Theory Tech. 48, 832-837 (2000).

B. M. Kolundzija, “Electromagnetic modeling of composite metallic and dielectric structures,” IEEE Trans. Microwave Theory Tech. 47, 1021-1032 (1999).
[CrossRef]

IEICE Trans. Electron. (1)

C. H. Chan, C. M. Lin, L. Tsang, and Y. F. Leung, “A sparse-matrix/canonical grid method for analyzing microstrip structures,” IEICE Trans. Electron. E80-C, 1354-1359 (1997).

IET Proc. Microwaves, Antennas Propag. (1)

Y. A. Liu and W. C. Chew, “Stability of surface integral equation for left-handed materials,” IET Proc. Microwaves, Antennas Propag. 1, 84-89 (2007).

J. Comput. Phys. (4)

N. Yarvin and V. Rokhlin, “A generalized one-dimensional fast multipole method with application to filtering of spherical harmonics,” J. Comput. Phys. 147, 594-609 (1998).
[CrossRef]

V. Rokhlin, “Rapid solution of integral equations of classic potential theory,” J. Comput. Phys. 60, 187-207 (1985).
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L. Greengard and V. Rokhlin, “A fast algorithm for particle simulations,” J. Comput. Phys. 73, 325-348 (1987).
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E. Darve, “The fast multipole method: numerical implementation,” J. Comput. Phys. 160, 195-240 (2000).
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C. C. Lu and W. C. Chew, “A multilevel algorithm for solving a boundary integral equation of wave scattering,” Microwave Opt. Technol. Lett. 7, 456-461 (1994).

Phys. Rev. B (1)

E. Ozbay, A. Abeyta, G. Tuttle, M. C. Tringides, R. Biswas, M. Sigalas, C. M. Soukoulis, C. T. Chan, and K. M. Ho, “Measurement of a three-dimensional photonic band gap in a crystal structure made of dielectric rods,” Phys. Rev. B 50, 1945-1948 (1994).
[CrossRef]

Prog. Electromagn. Res. (2)

D. L. Smith, L. N. M. Mitschang, and D. W. Forester, “Surface integral equation formulations for left-handed materials,” Prog. Electromagn. Res. PIER 51, 27-48 (2005).

P. Y. Oijala, M. Taskinen, and J. Sarvas, “Surface integral equation method for general composite metallic and dielectric structures with junctions,” Prog. Electromagn. Res. PIER 52, 81-108 (2005).

Radio Sci. (1)

E. Bleszynski, M. Bleszynski, and T. Jaroszewicz, “AIM: adaptive integral method for solving large-scale electromagnetic scattering and radiation problems,” Radio Sci. 31, 1225-1251 (1996).
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SIAM (Soc. Ind. Appl. Math.) J. Sci. Stat. Comput. (1)

Y. Saad and M. Schultz, “GMRES: A generalized minimal residual algorithm for solving non symmetric linear systems,” SIAM (Soc. Ind. Appl. Math.) J. Sci. Stat. Comput. 7, 856-869 (1986).
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Solid State Commun. (1)

K. M. Ho, C. T. Chan, C. M. Soukoulis, R. Biswas, and M. Sigalas, “Photonic band gaps in three dimensions: new layer-by-layer periodic structures,” Solid State Commun. 89, 413-416 (1994).
[CrossRef]

Other (7)

L. Li, H. G. Wang, and C. H. Chan, “A novel interpolation scheme for full-wave electromagnetic simulations,” presented at the International Symposium on Antennas and Propagation (ISAP), Singapore, 2006.

R. A. Horn and C. R. Johnson, Topics in Matrix Analysis (Cambridge U. Press, 1991).

B. M. Kolundzija and A. R. Djordjevic, Electromagnetic Modeling of Composite Metallic and Dielectric Structure (Artech House, 2002).

W. C. Chew, J. M. Jin, E. Michielssen, and J. M. Song, Fast and Efficient Algorithms in Computational Electromagnetics (Artech House, 2001).

R. F. Harrington, Field Computation by Moment Methods (IEEE, 1993).

J. M. Jin, The Finite Element Method in Electromagnetics, 2nd ed. (Wiley, 1993).

A. Taflove and S. C. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method, 3rd ed. (Artech House, 2005).

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