Abstract

Fast and accurate solutions of large-scale electromagnetics problems involving homogeneous dielectric objects are considered. Problems are formulated with the electric and magnetic current combined-field integral equation and discretized with the Rao–Wilton–Glisson functions. Solutions are performed iteratively by using the multilevel fast multipole algorithm (MLFMA). For the solution of large-scale problems discretized with millions of unknowns, MLFMA is parallelized on distributed-memory architectures using a rigorous technique, namely, the hierarchical partitioning strategy. Efficiency and accuracy of the developed implementation are demonstrated on very large problems involving as many as 100 million unknowns.

© 2011 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. Ö. Ergül, A. Arslan-Ergül, and L. Gürel, “Computational study of scattering from healthy and diseased red blood cells using surface integral equations and the multilevel fast multipole algorithm,” J. Biomed. Opt. 15, 045004 (2010).
    [PubMed]
  2. Ö. Ergül, T. Malas, and L. Gürel, “Analysis of dielectric photonic-crystal problems with MLFMA and Schur-complement preconditioners,” J. Lightwave Technol. 29, 888–897 (2011).
    [Crossref]
  3. J. 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]
  4. X.-Q. Sheng, J.-M. Jin, J. 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. W. C. Chew, J.-M. Jin, E. Michielssen, and J. Song, Fast and Efficient Algorithms in Computational Electromagnetics(Artech House, 2001).
  6. S. Velamparambil, W. C. Chew, and J. Song, “10 million unknowns: Is it that big?” IEEE Trans. Antennas Propag. 45, 43–58 (2003).
  7. L. Gürel and Ö. Ergül, “Fast and accurate solutions of integral-equation formulations discretised with tens of millions of unknowns,” Electron. Lett. 43, 499–500 (2007).
    [Crossref]
  8. Ö. Ergül and L. Gürel, “Hierarchical parallelisation strategy for multilevel fast multipole algorithm in computational electromagnetics,” Electron. Lett. 44, 3–5 (2008).
    [Crossref]
  9. X.-M. Pan and X.-Q. Sheng, “A sophisticated parallel MLFMA for scattering by extremely large targets,” IEEE Trans. Antennas Propag. 50, 129–138 (2008).
  10. Ö. Ergül and L. Gürel, “Efficient parallelization of the multilevel fast multipole algorithm for the solution of large-scale scattering problems,” IEEE Trans. Antennas Propag. 56, 2335–2345 (2008).
    [Crossref]
  11. J. Fostier and F. Olyslager, “An asynchronous parallel MLFMA for scattering at multiple dielectric objects,” IEEE Trans. Antennas Propag. 56, 2346–2355 (2008).
    [Crossref]
  12. J. Fostier and F. Olyslager, “Full-wave electromagnetic scattering at extremely large 2-D objects,” Electron. Lett. 45, 245–246 (2009).
    [Crossref]
  13. Ö. Ergül and L. Gürel, “A hierarchical partitioning strategy for an efficient parallelization of the multilevel fast multipole algorithm,” IEEE Trans. Antennas Propag. 57, 1740–1750(2009).
    [Crossref]
  14. J. M. Taboada, L. Landesa, F. Obelleiro, J. L. Rodriguez, J. M. Bertolo, M. G. Araujo, J. C. Mourino, and A. Gomez, “High scalability FMM-FFT electromagnetic solver for supercomputer systems,” IEEE Trans. Antennas Propag. 51, 21–28(2009).
  15. J. M. Taboada, M. G. Araujo, J. M. Bertolo, L. Landesa, F. Obelleiro, and J. L. Rodriguez, “MLFMA-FFT parallel algorithm for the solution of large-scale problems in electromagnetics,” Prog. Electromagn. Res. 105, 15–30 (2010).
    [Crossref]
  16. Ö. Ergül and L. Gürel, “Rigorous solutions of electromagnetics problems involving hundreds of millions of unknowns,” IEEE Trans. Antennas Propag. 53, 18–26 (2011).
  17. P. Ylä-Oijala and M. Taskinen, “Application of combined field integral equation for electromagnetic scattering by dielectric and composite objects,” IEEE Trans. Antennas Propag. 53, 1168–1173 (2005).
    [Crossref]
  18. P. Ylä-Oijala, “Numerical analysis of combined field integral equation formulations for electromagnetic scattering by dielectric and composite objects,” Prog. Electromagn. Res. C 3, 19–43 (2008).
    [Crossref]
  19. Ö. Ergül and L. Gürel, “Comparison of integral-equation formulations for the fast and accurate solution of scattering problems involving dielectric objects with the multilevel fast multipole algorithm,” IEEE Trans. Antennas Propag. 57, 176–187 (2009).
    [Crossref]
  20. Ö. Ergül and L. Gürel, “Efficient solution of the electric and magnetic current combined-field integral equation with the multilevel fast multipole algorithm and block-diagonal preconditioning,” Radio Sci. 44 (2009).
    [Crossref]
  21. S. M. Rao, D. R. Wilton, and A. W. Glisson, “Electromagnetic scattering by surfaces of arbitrary shape,” IEEE Trans. Antennas Propag. 30, 409–418 (1982).
    [Crossref]
  22. Ö. Ergül and L. Gürel, “An efficient parallel implementation of the multilevel fast multipole algorithm for rigorous solutions of large-scale scattering problems,” in International Symposium on Electromagnetic Theory (IEEE, 2010), pp. 616–619.
    [Crossref]
  23. Ö. Ergül and L. Gürel, “Advanced partitioning and communication strategies for the efficient parallelization of the multilevel fast multipole algorithm,” in IEEE Antennas and Propagation Society International Symposium (APSURSI) (IEEE, 2010), pp. 1–4.
  24. Ö. Ergül, “Accurate and efficient solutions of electromagnetics problems with the multilevel fast multipole algorithm,” Ph.D thesis (Bilkent University, , 2009).
  25. H. A. van der Vorst, “Bi-CGSTAB: A fast and smoothly converging variant of Bi-CG for the solution of nonsymmetric linear systems,” SIAM J. Sci. Stat. Comput. 13, 631–644 (1992).
    [Crossref]

2011 (2)

Ö. Ergül, T. Malas, and L. Gürel, “Analysis of dielectric photonic-crystal problems with MLFMA and Schur-complement preconditioners,” J. Lightwave Technol. 29, 888–897 (2011).
[Crossref]

Ö. Ergül and L. Gürel, “Rigorous solutions of electromagnetics problems involving hundreds of millions of unknowns,” IEEE Trans. Antennas Propag. 53, 18–26 (2011).

2010 (4)

J. M. Taboada, M. G. Araujo, J. M. Bertolo, L. Landesa, F. Obelleiro, and J. L. Rodriguez, “MLFMA-FFT parallel algorithm for the solution of large-scale problems in electromagnetics,” Prog. Electromagn. Res. 105, 15–30 (2010).
[Crossref]

Ö. Ergül, A. Arslan-Ergül, and L. Gürel, “Computational study of scattering from healthy and diseased red blood cells using surface integral equations and the multilevel fast multipole algorithm,” J. Biomed. Opt. 15, 045004 (2010).
[PubMed]

Ö. Ergül and L. Gürel, “An efficient parallel implementation of the multilevel fast multipole algorithm for rigorous solutions of large-scale scattering problems,” in International Symposium on Electromagnetic Theory (IEEE, 2010), pp. 616–619.
[Crossref]

Ö. Ergül and L. Gürel, “Advanced partitioning and communication strategies for the efficient parallelization of the multilevel fast multipole algorithm,” in IEEE Antennas and Propagation Society International Symposium (APSURSI) (IEEE, 2010), pp. 1–4.

2009 (6)

Ö. Ergül, “Accurate and efficient solutions of electromagnetics problems with the multilevel fast multipole algorithm,” Ph.D thesis (Bilkent University, , 2009).

Ö. Ergül and L. Gürel, “Comparison of integral-equation formulations for the fast and accurate solution of scattering problems involving dielectric objects with the multilevel fast multipole algorithm,” IEEE Trans. Antennas Propag. 57, 176–187 (2009).
[Crossref]

Ö. Ergül and L. Gürel, “Efficient solution of the electric and magnetic current combined-field integral equation with the multilevel fast multipole algorithm and block-diagonal preconditioning,” Radio Sci. 44 (2009).
[Crossref]

J. Fostier and F. Olyslager, “Full-wave electromagnetic scattering at extremely large 2-D objects,” Electron. Lett. 45, 245–246 (2009).
[Crossref]

Ö. Ergül and L. Gürel, “A hierarchical partitioning strategy for an efficient parallelization of the multilevel fast multipole algorithm,” IEEE Trans. Antennas Propag. 57, 1740–1750(2009).
[Crossref]

J. M. Taboada, L. Landesa, F. Obelleiro, J. L. Rodriguez, J. M. Bertolo, M. G. Araujo, J. C. Mourino, and A. Gomez, “High scalability FMM-FFT electromagnetic solver for supercomputer systems,” IEEE Trans. Antennas Propag. 51, 21–28(2009).

2008 (5)

Ö. Ergül and L. Gürel, “Hierarchical parallelisation strategy for multilevel fast multipole algorithm in computational electromagnetics,” Electron. Lett. 44, 3–5 (2008).
[Crossref]

X.-M. Pan and X.-Q. Sheng, “A sophisticated parallel MLFMA for scattering by extremely large targets,” IEEE Trans. Antennas Propag. 50, 129–138 (2008).

Ö. Ergül and L. Gürel, “Efficient parallelization of the multilevel fast multipole algorithm for the solution of large-scale scattering problems,” IEEE Trans. Antennas Propag. 56, 2335–2345 (2008).
[Crossref]

J. Fostier and F. Olyslager, “An asynchronous parallel MLFMA for scattering at multiple dielectric objects,” IEEE Trans. Antennas Propag. 56, 2346–2355 (2008).
[Crossref]

P. Ylä-Oijala, “Numerical analysis of combined field integral equation formulations for electromagnetic scattering by dielectric and composite objects,” Prog. Electromagn. Res. C 3, 19–43 (2008).
[Crossref]

2007 (1)

L. Gürel and Ö. Ergül, “Fast and accurate solutions of integral-equation formulations discretised with tens of millions of unknowns,” Electron. Lett. 43, 499–500 (2007).
[Crossref]

2005 (1)

P. Ylä-Oijala and M. Taskinen, “Application of combined field integral equation for electromagnetic scattering by dielectric and composite objects,” IEEE Trans. Antennas Propag. 53, 1168–1173 (2005).
[Crossref]

2003 (1)

S. Velamparambil, W. C. Chew, and J. Song, “10 million unknowns: Is it that big?” IEEE Trans. Antennas Propag. 45, 43–58 (2003).

2001 (1)

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

1998 (1)

X.-Q. Sheng, J.-M. Jin, J. 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]

1997 (1)

J. 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]

1992 (1)

H. A. van der Vorst, “Bi-CGSTAB: A fast and smoothly converging variant of Bi-CG for the solution of nonsymmetric linear systems,” SIAM J. Sci. Stat. Comput. 13, 631–644 (1992).
[Crossref]

1982 (1)

S. M. Rao, D. R. Wilton, and A. W. Glisson, “Electromagnetic scattering by surfaces of arbitrary shape,” IEEE Trans. Antennas Propag. 30, 409–418 (1982).
[Crossref]

Araujo, M. G.

J. M. Taboada, M. G. Araujo, J. M. Bertolo, L. Landesa, F. Obelleiro, and J. L. Rodriguez, “MLFMA-FFT parallel algorithm for the solution of large-scale problems in electromagnetics,” Prog. Electromagn. Res. 105, 15–30 (2010).
[Crossref]

J. M. Taboada, L. Landesa, F. Obelleiro, J. L. Rodriguez, J. M. Bertolo, M. G. Araujo, J. C. Mourino, and A. Gomez, “High scalability FMM-FFT electromagnetic solver for supercomputer systems,” IEEE Trans. Antennas Propag. 51, 21–28(2009).

Arslan-Ergül, A.

Ö. Ergül, A. Arslan-Ergül, and L. Gürel, “Computational study of scattering from healthy and diseased red blood cells using surface integral equations and the multilevel fast multipole algorithm,” J. Biomed. Opt. 15, 045004 (2010).
[PubMed]

Bertolo, J. M.

J. M. Taboada, M. G. Araujo, J. M. Bertolo, L. Landesa, F. Obelleiro, and J. L. Rodriguez, “MLFMA-FFT parallel algorithm for the solution of large-scale problems in electromagnetics,” Prog. Electromagn. Res. 105, 15–30 (2010).
[Crossref]

J. M. Taboada, L. Landesa, F. Obelleiro, J. L. Rodriguez, J. M. Bertolo, M. G. Araujo, J. C. Mourino, and A. Gomez, “High scalability FMM-FFT electromagnetic solver for supercomputer systems,” IEEE Trans. Antennas Propag. 51, 21–28(2009).

Chew, W. C.

S. Velamparambil, W. C. Chew, and J. Song, “10 million unknowns: Is it that big?” IEEE Trans. Antennas Propag. 45, 43–58 (2003).

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

X.-Q. Sheng, J.-M. Jin, J. 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. 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]

Ergül, Ö.

Ö. Ergül, T. Malas, and L. Gürel, “Analysis of dielectric photonic-crystal problems with MLFMA and Schur-complement preconditioners,” J. Lightwave Technol. 29, 888–897 (2011).
[Crossref]

Ö. Ergül and L. Gürel, “Rigorous solutions of electromagnetics problems involving hundreds of millions of unknowns,” IEEE Trans. Antennas Propag. 53, 18–26 (2011).

Ö. Ergül, A. Arslan-Ergül, and L. Gürel, “Computational study of scattering from healthy and diseased red blood cells using surface integral equations and the multilevel fast multipole algorithm,” J. Biomed. Opt. 15, 045004 (2010).
[PubMed]

Ö. Ergül and L. Gürel, “An efficient parallel implementation of the multilevel fast multipole algorithm for rigorous solutions of large-scale scattering problems,” in International Symposium on Electromagnetic Theory (IEEE, 2010), pp. 616–619.
[Crossref]

Ö. Ergül and L. Gürel, “Advanced partitioning and communication strategies for the efficient parallelization of the multilevel fast multipole algorithm,” in IEEE Antennas and Propagation Society International Symposium (APSURSI) (IEEE, 2010), pp. 1–4.

Ö. Ergül, “Accurate and efficient solutions of electromagnetics problems with the multilevel fast multipole algorithm,” Ph.D thesis (Bilkent University, , 2009).

Ö. Ergül and L. Gürel, “Comparison of integral-equation formulations for the fast and accurate solution of scattering problems involving dielectric objects with the multilevel fast multipole algorithm,” IEEE Trans. Antennas Propag. 57, 176–187 (2009).
[Crossref]

Ö. Ergül and L. Gürel, “Efficient solution of the electric and magnetic current combined-field integral equation with the multilevel fast multipole algorithm and block-diagonal preconditioning,” Radio Sci. 44 (2009).
[Crossref]

Ö. Ergül and L. Gürel, “A hierarchical partitioning strategy for an efficient parallelization of the multilevel fast multipole algorithm,” IEEE Trans. Antennas Propag. 57, 1740–1750(2009).
[Crossref]

Ö. Ergül and L. Gürel, “Hierarchical parallelisation strategy for multilevel fast multipole algorithm in computational electromagnetics,” Electron. Lett. 44, 3–5 (2008).
[Crossref]

Ö. Ergül and L. Gürel, “Efficient parallelization of the multilevel fast multipole algorithm for the solution of large-scale scattering problems,” IEEE Trans. Antennas Propag. 56, 2335–2345 (2008).
[Crossref]

L. Gürel and Ö. Ergül, “Fast and accurate solutions of integral-equation formulations discretised with tens of millions of unknowns,” Electron. Lett. 43, 499–500 (2007).
[Crossref]

Fostier, J.

J. Fostier and F. Olyslager, “Full-wave electromagnetic scattering at extremely large 2-D objects,” Electron. Lett. 45, 245–246 (2009).
[Crossref]

J. Fostier and F. Olyslager, “An asynchronous parallel MLFMA for scattering at multiple dielectric objects,” IEEE Trans. Antennas Propag. 56, 2346–2355 (2008).
[Crossref]

Glisson, A. W.

S. M. Rao, D. R. Wilton, and A. W. Glisson, “Electromagnetic scattering by surfaces of arbitrary shape,” IEEE Trans. Antennas Propag. 30, 409–418 (1982).
[Crossref]

Gomez, A.

J. M. Taboada, L. Landesa, F. Obelleiro, J. L. Rodriguez, J. M. Bertolo, M. G. Araujo, J. C. Mourino, and A. Gomez, “High scalability FMM-FFT electromagnetic solver for supercomputer systems,” IEEE Trans. Antennas Propag. 51, 21–28(2009).

Gürel, L.

Ö. Ergül and L. Gürel, “Rigorous solutions of electromagnetics problems involving hundreds of millions of unknowns,” IEEE Trans. Antennas Propag. 53, 18–26 (2011).

Ö. Ergül, T. Malas, and L. Gürel, “Analysis of dielectric photonic-crystal problems with MLFMA and Schur-complement preconditioners,” J. Lightwave Technol. 29, 888–897 (2011).
[Crossref]

Ö. Ergül, A. Arslan-Ergül, and L. Gürel, “Computational study of scattering from healthy and diseased red blood cells using surface integral equations and the multilevel fast multipole algorithm,” J. Biomed. Opt. 15, 045004 (2010).
[PubMed]

Ö. Ergül and L. Gürel, “An efficient parallel implementation of the multilevel fast multipole algorithm for rigorous solutions of large-scale scattering problems,” in International Symposium on Electromagnetic Theory (IEEE, 2010), pp. 616–619.
[Crossref]

Ö. Ergül and L. Gürel, “Advanced partitioning and communication strategies for the efficient parallelization of the multilevel fast multipole algorithm,” in IEEE Antennas and Propagation Society International Symposium (APSURSI) (IEEE, 2010), pp. 1–4.

Ö. Ergül and L. Gürel, “Efficient solution of the electric and magnetic current combined-field integral equation with the multilevel fast multipole algorithm and block-diagonal preconditioning,” Radio Sci. 44 (2009).
[Crossref]

Ö. Ergül and L. Gürel, “Comparison of integral-equation formulations for the fast and accurate solution of scattering problems involving dielectric objects with the multilevel fast multipole algorithm,” IEEE Trans. Antennas Propag. 57, 176–187 (2009).
[Crossref]

Ö. Ergül and L. Gürel, “A hierarchical partitioning strategy for an efficient parallelization of the multilevel fast multipole algorithm,” IEEE Trans. Antennas Propag. 57, 1740–1750(2009).
[Crossref]

Ö. Ergül and L. Gürel, “Efficient parallelization of the multilevel fast multipole algorithm for the solution of large-scale scattering problems,” IEEE Trans. Antennas Propag. 56, 2335–2345 (2008).
[Crossref]

Ö. Ergül and L. Gürel, “Hierarchical parallelisation strategy for multilevel fast multipole algorithm in computational electromagnetics,” Electron. Lett. 44, 3–5 (2008).
[Crossref]

L. Gürel and Ö. Ergül, “Fast and accurate solutions of integral-equation formulations discretised with tens of millions of unknowns,” Electron. Lett. 43, 499–500 (2007).
[Crossref]

Jin, J.-M.

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

X.-Q. Sheng, J.-M. Jin, J. 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]

Landesa, L.

J. M. Taboada, M. G. Araujo, J. M. Bertolo, L. Landesa, F. Obelleiro, and J. L. Rodriguez, “MLFMA-FFT parallel algorithm for the solution of large-scale problems in electromagnetics,” Prog. Electromagn. Res. 105, 15–30 (2010).
[Crossref]

J. M. Taboada, L. Landesa, F. Obelleiro, J. L. Rodriguez, J. M. Bertolo, M. G. Araujo, J. C. Mourino, and A. Gomez, “High scalability FMM-FFT electromagnetic solver for supercomputer systems,” IEEE Trans. Antennas Propag. 51, 21–28(2009).

Lu, C.-C.

X.-Q. Sheng, J.-M. Jin, J. 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. 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]

Malas, T.

Michielssen, E.

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

Mourino, J. C.

J. M. Taboada, L. Landesa, F. Obelleiro, J. L. Rodriguez, J. M. Bertolo, M. G. Araujo, J. C. Mourino, and A. Gomez, “High scalability FMM-FFT electromagnetic solver for supercomputer systems,” IEEE Trans. Antennas Propag. 51, 21–28(2009).

Obelleiro, F.

J. M. Taboada, M. G. Araujo, J. M. Bertolo, L. Landesa, F. Obelleiro, and J. L. Rodriguez, “MLFMA-FFT parallel algorithm for the solution of large-scale problems in electromagnetics,” Prog. Electromagn. Res. 105, 15–30 (2010).
[Crossref]

J. M. Taboada, L. Landesa, F. Obelleiro, J. L. Rodriguez, J. M. Bertolo, M. G. Araujo, J. C. Mourino, and A. Gomez, “High scalability FMM-FFT electromagnetic solver for supercomputer systems,” IEEE Trans. Antennas Propag. 51, 21–28(2009).

Olyslager, F.

J. Fostier and F. Olyslager, “Full-wave electromagnetic scattering at extremely large 2-D objects,” Electron. Lett. 45, 245–246 (2009).
[Crossref]

J. Fostier and F. Olyslager, “An asynchronous parallel MLFMA for scattering at multiple dielectric objects,” IEEE Trans. Antennas Propag. 56, 2346–2355 (2008).
[Crossref]

Pan, X.-M.

X.-M. Pan and X.-Q. Sheng, “A sophisticated parallel MLFMA for scattering by extremely large targets,” IEEE Trans. Antennas Propag. 50, 129–138 (2008).

Rao, S. M.

S. M. Rao, D. R. Wilton, and A. W. Glisson, “Electromagnetic scattering by surfaces of arbitrary shape,” IEEE Trans. Antennas Propag. 30, 409–418 (1982).
[Crossref]

Rodriguez, J. L.

J. M. Taboada, M. G. Araujo, J. M. Bertolo, L. Landesa, F. Obelleiro, and J. L. Rodriguez, “MLFMA-FFT parallel algorithm for the solution of large-scale problems in electromagnetics,” Prog. Electromagn. Res. 105, 15–30 (2010).
[Crossref]

J. M. Taboada, L. Landesa, F. Obelleiro, J. L. Rodriguez, J. M. Bertolo, M. G. Araujo, J. C. Mourino, and A. Gomez, “High scalability FMM-FFT electromagnetic solver for supercomputer systems,” IEEE Trans. Antennas Propag. 51, 21–28(2009).

Sheng, X.-Q.

X.-M. Pan and X.-Q. Sheng, “A sophisticated parallel MLFMA for scattering by extremely large targets,” IEEE Trans. Antennas Propag. 50, 129–138 (2008).

X.-Q. Sheng, J.-M. Jin, J. 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]

Song, J.

S. Velamparambil, W. C. Chew, and J. Song, “10 million unknowns: Is it that big?” IEEE Trans. Antennas Propag. 45, 43–58 (2003).

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

X.-Q. Sheng, J.-M. Jin, J. 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. 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]

Taboada, J. M.

J. M. Taboada, M. G. Araujo, J. M. Bertolo, L. Landesa, F. Obelleiro, and J. L. Rodriguez, “MLFMA-FFT parallel algorithm for the solution of large-scale problems in electromagnetics,” Prog. Electromagn. Res. 105, 15–30 (2010).
[Crossref]

J. M. Taboada, L. Landesa, F. Obelleiro, J. L. Rodriguez, J. M. Bertolo, M. G. Araujo, J. C. Mourino, and A. Gomez, “High scalability FMM-FFT electromagnetic solver for supercomputer systems,” IEEE Trans. Antennas Propag. 51, 21–28(2009).

Taskinen, M.

P. Ylä-Oijala and M. Taskinen, “Application of combined field integral equation for electromagnetic scattering by dielectric and composite objects,” IEEE Trans. Antennas Propag. 53, 1168–1173 (2005).
[Crossref]

van der Vorst, H. A.

H. A. van der Vorst, “Bi-CGSTAB: A fast and smoothly converging variant of Bi-CG for the solution of nonsymmetric linear systems,” SIAM J. Sci. Stat. Comput. 13, 631–644 (1992).
[Crossref]

Velamparambil, S.

S. Velamparambil, W. C. Chew, and J. Song, “10 million unknowns: Is it that big?” IEEE Trans. Antennas Propag. 45, 43–58 (2003).

Wilton, D. R.

S. M. Rao, D. R. Wilton, and A. W. Glisson, “Electromagnetic scattering by surfaces of arbitrary shape,” IEEE Trans. Antennas Propag. 30, 409–418 (1982).
[Crossref]

Ylä-Oijala, P.

P. Ylä-Oijala, “Numerical analysis of combined field integral equation formulations for electromagnetic scattering by dielectric and composite objects,” Prog. Electromagn. Res. C 3, 19–43 (2008).
[Crossref]

P. Ylä-Oijala and M. Taskinen, “Application of combined field integral equation for electromagnetic scattering by dielectric and composite objects,” IEEE Trans. Antennas Propag. 53, 1168–1173 (2005).
[Crossref]

Electron. Lett. (3)

L. Gürel and Ö. Ergül, “Fast and accurate solutions of integral-equation formulations discretised with tens of millions of unknowns,” Electron. Lett. 43, 499–500 (2007).
[Crossref]

Ö. Ergül and L. Gürel, “Hierarchical parallelisation strategy for multilevel fast multipole algorithm in computational electromagnetics,” Electron. Lett. 44, 3–5 (2008).
[Crossref]

J. Fostier and F. Olyslager, “Full-wave electromagnetic scattering at extremely large 2-D objects,” Electron. Lett. 45, 245–246 (2009).
[Crossref]

IEEE Trans. Antennas Propag. (12)

Ö. Ergül and L. Gürel, “A hierarchical partitioning strategy for an efficient parallelization of the multilevel fast multipole algorithm,” IEEE Trans. Antennas Propag. 57, 1740–1750(2009).
[Crossref]

J. M. Taboada, L. Landesa, F. Obelleiro, J. L. Rodriguez, J. M. Bertolo, M. G. Araujo, J. C. Mourino, and A. Gomez, “High scalability FMM-FFT electromagnetic solver for supercomputer systems,” IEEE Trans. Antennas Propag. 51, 21–28(2009).

X.-M. Pan and X.-Q. Sheng, “A sophisticated parallel MLFMA for scattering by extremely large targets,” IEEE Trans. Antennas Propag. 50, 129–138 (2008).

Ö. Ergül and L. Gürel, “Efficient parallelization of the multilevel fast multipole algorithm for the solution of large-scale scattering problems,” IEEE Trans. Antennas Propag. 56, 2335–2345 (2008).
[Crossref]

J. Fostier and F. Olyslager, “An asynchronous parallel MLFMA for scattering at multiple dielectric objects,” IEEE Trans. Antennas Propag. 56, 2346–2355 (2008).
[Crossref]

J. 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]

X.-Q. Sheng, J.-M. Jin, J. 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]

Ö. Ergül and L. Gürel, “Rigorous solutions of electromagnetics problems involving hundreds of millions of unknowns,” IEEE Trans. Antennas Propag. 53, 18–26 (2011).

P. Ylä-Oijala and M. Taskinen, “Application of combined field integral equation for electromagnetic scattering by dielectric and composite objects,” IEEE Trans. Antennas Propag. 53, 1168–1173 (2005).
[Crossref]

S. M. Rao, D. R. Wilton, and A. W. Glisson, “Electromagnetic scattering by surfaces of arbitrary shape,” IEEE Trans. Antennas Propag. 30, 409–418 (1982).
[Crossref]

Ö. Ergül and L. Gürel, “Comparison of integral-equation formulations for the fast and accurate solution of scattering problems involving dielectric objects with the multilevel fast multipole algorithm,” IEEE Trans. Antennas Propag. 57, 176–187 (2009).
[Crossref]

S. Velamparambil, W. C. Chew, and J. Song, “10 million unknowns: Is it that big?” IEEE Trans. Antennas Propag. 45, 43–58 (2003).

J. Biomed. Opt. (1)

Ö. Ergül, A. Arslan-Ergül, and L. Gürel, “Computational study of scattering from healthy and diseased red blood cells using surface integral equations and the multilevel fast multipole algorithm,” J. Biomed. Opt. 15, 045004 (2010).
[PubMed]

J. Lightwave Technol. (1)

Prog. Electromagn. Res. (1)

J. M. Taboada, M. G. Araujo, J. M. Bertolo, L. Landesa, F. Obelleiro, and J. L. Rodriguez, “MLFMA-FFT parallel algorithm for the solution of large-scale problems in electromagnetics,” Prog. Electromagn. Res. 105, 15–30 (2010).
[Crossref]

Prog. Electromagn. Res. C (1)

P. Ylä-Oijala, “Numerical analysis of combined field integral equation formulations for electromagnetic scattering by dielectric and composite objects,” Prog. Electromagn. Res. C 3, 19–43 (2008).
[Crossref]

Radio Sci. (1)

Ö. Ergül and L. Gürel, “Efficient solution of the electric and magnetic current combined-field integral equation with the multilevel fast multipole algorithm and block-diagonal preconditioning,” Radio Sci. 44 (2009).
[Crossref]

SIAM J. Sci. Stat. Comput. (1)

H. A. van der Vorst, “Bi-CGSTAB: A fast and smoothly converging variant of Bi-CG for the solution of nonsymmetric linear systems,” SIAM J. Sci. Stat. Comput. 13, 631–644 (1992).
[Crossref]

Other (4)

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

Ö. Ergül and L. Gürel, “An efficient parallel implementation of the multilevel fast multipole algorithm for rigorous solutions of large-scale scattering problems,” in International Symposium on Electromagnetic Theory (IEEE, 2010), pp. 616–619.
[Crossref]

Ö. Ergül and L. Gürel, “Advanced partitioning and communication strategies for the efficient parallelization of the multilevel fast multipole algorithm,” in IEEE Antennas and Propagation Society International Symposium (APSURSI) (IEEE, 2010), pp. 1–4.

Ö. Ergül, “Accurate and efficient solutions of electromagnetics problems with the multilevel fast multipole algorithm,” Ph.D thesis (Bilkent University, , 2009).

Cited By

OSA participates in Crossref's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (8)

Fig. 1
Fig. 1

Solutions of a scattering problem involving a dielectric sphere with a radius of 0.3 m at 20 GHz discretized with 2,925,708 unknowns. The total computing time is plotted as a function of the number of processes from 1 to 128.

Fig. 2
Fig. 2

Solution of a scattering problem involving a dielectric sphere with a radius of 0.3 m at 100 GHz discretized with 67,582,464 unknowns. SCS (in dBms) is plotted as a function of the bistatic angle from 0 ° to 180 ° , where 0 ° and 180 ° correspond to the backscattering and forward-scattering directions, respectively. Computational values provided by the parallel MLFMA implementation agree well with the analytical Mie-series solution.

Fig. 3
Fig. 3

Electromagnetics problems involving a dielectric hemisphere lens with a radius of 25 mm and a periodic structure involving 2 × 2 × 0.41 cm slabs (a simple photonic crystal). Both objects are illuminated by plane waves.

Fig. 4
Fig. 4

Solution of an electromagnetics problem involving a dielectric hemisphere lens with a radius of 25 mm at 120 GHz . The lens has a relative permittivity of 4.8 and the problem is discretized with 615,456 unknowns. The total electric field in the vicinity of the lens is plotted for the inner and outer problems, in addition to the complete plot obtained via their superposition.

Fig. 5
Fig. 5

Solution of an electromagnetics problem involving a dielectric hemisphere lens with a radius of 25 mm at 1.08 THz . The lens has a relative permittivity of 4.8 and the problem is discretized with 49,851,936 unknowns. The total electric field on the axis of rotation of the lens is plotted from z = 40 mm to 40 mm .

Fig. 6
Fig. 6

Solution of an electromagnetics problem involving five 2 × 2 × 0.41 cm dielectric slabs at 120 GHz . The structure has a relative permittivity of 1.6 and the problem is discretized with 619,200 unknowns. The total electric field in the vicinity of the structure is plotted for the inner and outer problems, in addition to the complete plot obtained via their superposition.

Fig. 7
Fig. 7

Solution of an electromagnetics problem involving five 2 × 2 × 0.41 cm dielectric slabs at 1.62 THz . The structure has a relative permittivity of 1.6 and the problem is discretized with 112,849,200 unknowns. The total electric field on the axis of symmetry is plotted from z = 5 cm to 5 cm for the inner and outer problems.

Fig. 8
Fig. 8

Solution of a scattering problem involving an array of 81 × 81 = 6561 lossy dielectric cubes. (a) Cubes with edges of 1 μm are periodically arranged on the x - y plane with 2 μm periodicity in both directions. The relative permittivity and conductivity of the cubes are 8.0 and 0.01 S / m , respectively. (b) SCS is plotted on the z - x plane, when the array is illuminated by a plane wave propagating in the z direction with the electric field polarized in the x direction at 300 THz .

Equations (18)

Equations on this page are rendered with MathJax. Learn more.

[ Z ¯ ( 11 ) Z ¯ ( 12 ) Z ¯ ( 21 ) Z ¯ ( 22 ) ] · [ x y ] = [ v w ] ,
Z m n ( 11 ) = α S m d r t m ( r ) · ( T o + T i ) { b n } ( r ) + ( 1 α ) S m d r t m ( r ) · n ^ × ( K o K i ) { b n } ( r ) ( 1 α ) S m d r t m ( r ) · b n ( r ) ,
Z m n ( 12 ) = ( 1 α ) S m d r t m ( r ) · n ^ × ( η o 1 T o η i 1 T i ) { b n } ( r ) α S m d r t m ( r ) · ( η o 1 K o + η i 1 K i ) { b n } ( r ) 1 2 α ( η o 1 η i 1 ) S m d r t m ( r ) · n ^ × b n ( r ) ,
Z m n ( 21 ) = ( 1 α ) S m d r t m ( r ) · n ^ × ( η o T o η i T i ) { b n } ( r ) + α S m d r t m ( r ) · ( η o K o + η i K i ) { b n } ( r ) + 1 2 α ( η o η i ) S m d r t m ( r ) · n ^ × b n ( r ) ,
T u { b n } ( r ) = i k u S n d r b n ( r ) g u ( r , r ) + i k u S n d r · b n ( r ) g u ( r , r ) ,
K u { b n } ( r ) = PV , S n d r b n ( r ) × g u ( r , r ) ,
g u ( r , r ) = exp ( i k u | r r | ) 4 π | r r |
v m = ( 1 α ) S m d r t m ( r ) · n ^ × H inc ( r ) α η o 1 S m d r t m ( r ) · E inc ( r ) ,
w m = ( 1 α ) S m d r t m ( r ) · n ^ × E inc ( r ) α η o S m d r t m ( r ) · H inc ( r ) ,
R n ( u ) ( r C , k u ) = γ n ( I ¯ k ^ k ^ ) · S n ( r C , k u ) ,
S n ( r C , k u ) = S n d r exp [ i k u · ( r r C ) ] b n ( r ) .
R m ( 11 , u ) ( r C , k u ) = R m ( 22 , u ) ( r C , k u ) = α γ m ( I ¯ k ^ k ^ ) · S m + ( r C , k u ) ( 1 α ) k ^ × S m × n ( r C , k u ) ,
R m ( 12 , u ) ( r C , k u ) = ( 1 α ) η u 1 ( I ¯ k ^ k ^ ) · S m × n ( r C , k u ) + α γ m η u 1 k ^ × S m + ( r C , k u ) ,
R m ( 21 , u ) ( r C , k u ) = ( 1 α ) η u ( I ¯ k ^ k ^ ) · S m × n ( r C , k u ) α γ m η u k ^ × S m + ( r C , k u ) ,
S m + ( r C , k u ) = S m d r exp [ i k u · ( r r C ) ] t m ( r ) ,
S m × n ( r C , k u ) = S m d r exp [ i k u · ( r r C ) ] t m ( r ) × n ^ .
S m + ( r C , k u ) = { S m ( r C , k u ) } * ,
N l S l 4 ( 1 l ) N 1 4 ( l 1 ) S 1 = N 1 S 1 = O ( N ) ,

Metrics