Fast and accurate finite element analysis of large-scale three-dimensional photonic devices with a robust domain decomposition method |
Optics Express, Vol. 22, Issue 4, pp. 4437-4452 (2014)
http://dx.doi.org/10.1364/OE.22.004437
Acrobat PDF (1614 KB)
Abstract
A fast and accurate full-wave technique based on the dual-primal finite element tearing and interconnecting method and the second-order transmission condition is presented for large-scale three-dimensional photonic device simulations. The technique decomposes a general three-dimensional electromagnetic problem into smaller subdomain problems so that parallel computing can be performed on distributed-memory computer clusters to reduce the simulation time significantly. With the electric fields computed everywhere, photonic device parameters such as transmission and reflection coefficients are extracted. Several photonic devices, with simulation volumes up to
© 2014 Optical Society of America
1. Introduction
1. Y. Kawabe, C. Spiegelberg, A. Schülzgen, M. F. Nabor, B. Kippelen, E. A. Mash, P. M. Allemand, M. Kuwata-Gonokami, K. Takeda, and N. Peyghambarian, “Whispering-gallery-mode microring laser using a conjugated polymer,” Appl. Phys. Lett. 72(2), 141–143 (1998). [CrossRef]
2. V. R. Almeida, C. A. Barrios, R. R. Panepucci, and M. Lipson, “All-optical control of light on a silicon chip,” Nature 431(7012), 1081–1084 (2004). [CrossRef] [PubMed]
6. T. Barwicz, M. A. Popović, P. T. Rakich, M. R. Watts, H. A. Haus, E. P. Ippen, and H. I. Smith, “Microring-resonator-based add-drop filters in SiN: fabrication and analysis,” Opt. Express 12(7), 1437–1442 (2004). [CrossRef] [PubMed]
7. B. E. Little, S. T. Chu, H. A. Haus, J. Foresi, and J. Laine, “Microring resonator channel dropping filters,” J. Lightwave Technol. 15(6), 998–1005 (1997). [CrossRef]
13. Y. M. Kang, M. F. Xue, A. Arbabi, J. M. Jin, and L. L. Goddard, “Modal expansion approach for accurately computing resonant modes in a high-Q optical resonator,” Microw. Opt. Technol. Lett. 56(2), 278–284 (2014). [CrossRef]
14. C.-Y. Chao and L. J. Guo, “Biochemical sensors based on polymer microrings with sharp asymmetrical resonance,” Appl. Phys. Lett. 83(8), 1527–1529 (2003). [CrossRef]
15. A. Arbabi and L. Goddard, “Integrated Optical Resonators: Progress in 2011,” IEEE Photonics J. 4(2), 574–577 (2012). [CrossRef]
10. A. Arbabi, Y. M. Kang, C.-Y. Lu, E. Chow, and L. Goddard, “Realization of a narrowband single wavelength microring mirror,” Appl. Phys. Lett. 99(9), 091105 (2011). [CrossRef]
11. Y. M. Kang, A. Arbabi, and L. L. Goddard, “A microring resonator with an integrated Bragg grating: a compact replacement for a sampled grating distributed Bragg reflector,” Opt. Quantum Electron. 41(9), 689–697 (2009). [CrossRef]
16. S. J. McKeown and L. L. Goddard, “Hydrogen detection using polarization diversity via a subwavelength fiber aperture,” IEEE Photonics J. 4(5), 1752–1761 (2012). [CrossRef]
17. X. Shi and L. Hesselink, “Design of a C aperture to achieve λ/10 resolution and resonant transmission,” J. Opt. Soc. Am. B 21(7), 1305–1317 (2004). [CrossRef]
16. S. J. McKeown and L. L. Goddard, “Hydrogen detection using polarization diversity via a subwavelength fiber aperture,” IEEE Photonics J. 4(5), 1752–1761 (2012). [CrossRef]
17. X. Shi and L. Hesselink, “Design of a C aperture to achieve λ/10 resolution and resonant transmission,” J. Opt. Soc. Am. B 21(7), 1305–1317 (2004). [CrossRef]
18. J. S. Ayubi-Moak, S. M. Goodnick, D. Stanzione, G. Speyer, and P. Sotirelis, “Improved parallel 3D FDTD simulator for photonic crystals,” in Proceedings of DoD HPCMP Users Group Conference, 319–326 (2008). [CrossRef]
19. B. Radjenović and M. Radmilović-Radjenović, “Computer-aided design and simulation of optical microring resonators”, Int. J. Numer. Model., Electron. Netw., Devices Fields, available online: http://onlinelibrary.wiley.com/doi/10.1002/jnm.1920/abstract. [CrossRef]
23. B. Radjenović and M. Radmilovic-Radjenović, “Excitation of confined modes in silicon slotted waveguides and microring resonators for sensing purposes,” IEEE Sens. J., doi:. [CrossRef]
24. A. Arbabi, Y. M. Kang, and L. Goddard, “Cylindrical coordinates coupled mode theory,” IEEE J. Quantum Electron. 46(12), 1769–1774 (2010). [CrossRef]
2. Formulation
2.1 FETI-DP formulation with the SOTC-TE
35. C. T. Wolfe, U. Navsariwala, and S. D. Gedney, “A parallel finite-element tearing and interconnecting algorithm for solution of the vector wave equation with PML absorbing medium,” IEEE Trans. Antenn. Propag. 48(2), 278–284 (2000). [CrossRef]
35. C. T. Wolfe, U. Navsariwala, and S. D. Gedney, “A parallel finite-element tearing and interconnecting algorithm for solution of the vector wave equation with PML absorbing medium,” IEEE Trans. Antenn. Propag. 48(2), 278–284 (2000). [CrossRef]
25. Y. J. Li and J. M. Jin, “A new dual-primal domain decomposition approach for finite element simulation of 3D large-scale electromagnetic problems,” IEEE Trans. Antenn. Propag. 55(10), 2803–2810 (2007). [CrossRef]
27. M. F. Xue and J. M. Jin, “A hybrid nonconformal FETI/conformal FETI-DP method for arbitrary nonoverlapping domain decomposition modeling,” in Proceedings of IEEE AP-S Int. Symp. (2013). [CrossRef]
32. Z. Peng, V. Rawat, and J.-F. Lee, “One way domain decomposition method with second order transmission conditions for solving electromagnetic wave problems,” J. Comput. Phys. 229(4), 1181–1197 (2010). [CrossRef]
2.2 Calculation of device parameters using the current sheet excitation
2.3 Consideration for parallel implementation
34. Y. J. Li and J. M. Jin, “Parallel implementation of the FETI-DPEM algorithm for general 3D EM simulations,” J. Comput. Phys. 228(9), 3255–3267 (2009). [CrossRef]
37. MUMPS, A parallel sparse direct solver, available online: http://graal.ens-lyon.fr/MUMPS/.
34. Y. J. Li and J. M. Jin, “Parallel implementation of the FETI-DPEM algorithm for general 3D EM simulations,” J. Comput. Phys. 228(9), 3255–3267 (2009). [CrossRef]
3. Numerical results
38. CUBIT, available online: https://cubit.sandia.gov/.
39. METIS, Serial graph partitioning and fill-reducing matrix ordering, available online: http://glaros.dtc.umn.edu/gkhome/metis/metis/overview.
3.1 Medium-scale 2D MRR simulation
12. Y. M. Kang, A. Arbabi, and L. L. Goddard, “Engineering the spectral reflectance of microring resonators with integrated reflective elements,” Opt. Express 18(16), 16813–16825 (2010). [CrossRef] [PubMed]
40. COMSOL Multiphysics ver. 4.2, available online: http://www.comsol.com/.
3.2 Full-scale evanescently coupled double-microring resonator simulation
41. A. Arbabi and L. L. Goddard, “Measurements of the refractive indices and thermo-optic coefficients of Si_{3}N_{4} and SiO_{x} using microring resonances,” Opt. Lett. 38(19), 3878–3881 (2013). [CrossRef] [PubMed]
3.3 Optical fiber sensor with C-shaped aperture
16. S. J. McKeown and L. L. Goddard, “Hydrogen detection using polarization diversity via a subwavelength fiber aperture,” IEEE Photonics J. 4(5), 1752–1761 (2012). [CrossRef]
16. S. J. McKeown and L. L. Goddard, “Hydrogen detection using polarization diversity via a subwavelength fiber aperture,” IEEE Photonics J. 4(5), 1752–1761 (2012). [CrossRef]
4. Conclusion
19. B. Radjenović and M. Radmilović-Radjenović, “Computer-aided design and simulation of optical microring resonators”, Int. J. Numer. Model., Electron. Netw., Devices Fields, available online: http://onlinelibrary.wiley.com/doi/10.1002/jnm.1920/abstract. [CrossRef]
Acknowledgments
References and links
1. | Y. Kawabe, C. Spiegelberg, A. Schülzgen, M. F. Nabor, B. Kippelen, E. A. Mash, P. M. Allemand, M. Kuwata-Gonokami, K. Takeda, and N. Peyghambarian, “Whispering-gallery-mode microring laser using a conjugated polymer,” Appl. Phys. Lett. 72(2), 141–143 (1998). [CrossRef] |
2. | V. R. Almeida, C. A. Barrios, R. R. Panepucci, and M. Lipson, “All-optical control of light on a silicon chip,” Nature 431(7012), 1081–1084 (2004). [CrossRef] [PubMed] |
3. | Q. Xu, B. Schmidt, S. Pradhan, and M. Lipson, “Micrometre-scale silicon electro-optic modulator,” Nature 435(7040), 325–327 (2005). [CrossRef] [PubMed] |
4. | T. A. Ibrahim, R. Grover, L.-C. Kuo, S. Kanakaraju, L. C. Calhoun, and P.-T. Ho, “All-optical AND/NAND logic gates using semiconductor microresonators,” IEEE Photon. Technol. Lett. 15(10), 1422–1424 (2003). [CrossRef] |
5. | M. T. Hill, H. J. S. Dorren, T. De Vries, X. J. M. Leijtens, J. H. Den Besten, B. Smalbrugge, Y.-S. Oei, H. Binsma, G.-D. Khoe, and M. K. Smit, “A fast low-power optical memory based on coupled micro-ring lasers,” Nature 432(7014), 206–209 (2004). [CrossRef] [PubMed] |
6. | T. Barwicz, M. A. Popović, P. T. Rakich, M. R. Watts, H. A. Haus, E. P. Ippen, and H. I. Smith, “Microring-resonator-based add-drop filters in SiN: fabrication and analysis,” Opt. Express 12(7), 1437–1442 (2004). [CrossRef] [PubMed] |
7. | B. E. Little, S. T. Chu, H. A. Haus, J. Foresi, and J. Laine, “Microring resonator channel dropping filters,” J. Lightwave Technol. 15(6), 998–1005 (1997). [CrossRef] |
8. | Y. Ding, M. Pu, L. Liu, J. Xu, C. Peucheret, X. Zhang, D. Huang, and H. Ou, “Bandwidth and wavelength-tunable optical bandpass filter based on silicon microring-MZI structure,” Opt. Express 19(7), 6462–6470 (2011). [CrossRef] [PubMed] |
9. | J. K. S. Poon, J. Scheuer, and A. Yariv, “Wavelength-selective reflector based on a circular array of coupled microring resonators,” IEEE Photon. Technol. Lett. 16(5), 1331–1333 (2004). [CrossRef] |
10. | A. Arbabi, Y. M. Kang, C.-Y. Lu, E. Chow, and L. Goddard, “Realization of a narrowband single wavelength microring mirror,” Appl. Phys. Lett. 99(9), 091105 (2011). [CrossRef] |
11. | Y. M. Kang, A. Arbabi, and L. L. Goddard, “A microring resonator with an integrated Bragg grating: a compact replacement for a sampled grating distributed Bragg reflector,” Opt. Quantum Electron. 41(9), 689–697 (2009). [CrossRef] |
12. | Y. M. Kang, A. Arbabi, and L. L. Goddard, “Engineering the spectral reflectance of microring resonators with integrated reflective elements,” Opt. Express 18(16), 16813–16825 (2010). [CrossRef] [PubMed] |
13. | Y. M. Kang, M. F. Xue, A. Arbabi, J. M. Jin, and L. L. Goddard, “Modal expansion approach for accurately computing resonant modes in a high-Q optical resonator,” Microw. Opt. Technol. Lett. 56(2), 278–284 (2014). [CrossRef] |
14. | C.-Y. Chao and L. J. Guo, “Biochemical sensors based on polymer microrings with sharp asymmetrical resonance,” Appl. Phys. Lett. 83(8), 1527–1529 (2003). [CrossRef] |
15. | A. Arbabi and L. Goddard, “Integrated Optical Resonators: Progress in 2011,” IEEE Photonics J. 4(2), 574–577 (2012). [CrossRef] |
16. | S. J. McKeown and L. L. Goddard, “Hydrogen detection using polarization diversity via a subwavelength fiber aperture,” IEEE Photonics J. 4(5), 1752–1761 (2012). [CrossRef] |
17. | X. Shi and L. Hesselink, “Design of a C aperture to achieve λ/10 resolution and resonant transmission,” J. Opt. Soc. Am. B 21(7), 1305–1317 (2004). [CrossRef] |
18. | J. S. Ayubi-Moak, S. M. Goodnick, D. Stanzione, G. Speyer, and P. Sotirelis, “Improved parallel 3D FDTD simulator for photonic crystals,” in Proceedings of DoD HPCMP Users Group Conference, 319–326 (2008). [CrossRef] |
19. | B. Radjenović and M. Radmilović-Radjenović, “Computer-aided design and simulation of optical microring resonators”, Int. J. Numer. Model., Electron. Netw., Devices Fields, available online: http://onlinelibrary.wiley.com/doi/10.1002/jnm.1920/abstract. [CrossRef] |
20. | M. M. El Gowini and W. A. Moussa, “A finite element model of a MEMS-based surface acoustic wave hydrogen sensor,” Sensors (Basel) 10(2), 1232–1250 (2010). [CrossRef] [PubMed] |
21. | A. Einat and U. Levy, “Analysis of the optical force in the micro ring resonator,” Opt. Express 19(21), 20405–20419 (2011). [CrossRef] [PubMed] |
22. | B. Milanović, B. Radjenović, and M. Radmilović-Radjenović, “Three-dimensional finite-element modeling of optical microring resonators,” Phys. Scr. T 149, 014026 (2012). [CrossRef] |
23. | B. Radjenović and M. Radmilovic-Radjenović, “Excitation of confined modes in silicon slotted waveguides and microring resonators for sensing purposes,” IEEE Sens. J., doi:. [CrossRef] |
24. | A. Arbabi, Y. M. Kang, and L. Goddard, “Cylindrical coordinates coupled mode theory,” IEEE J. Quantum Electron. 46(12), 1769–1774 (2010). [CrossRef] |
25. | Y. J. Li and J. M. Jin, “A new dual-primal domain decomposition approach for finite element simulation of 3D large-scale electromagnetic problems,” IEEE Trans. Antenn. Propag. 55(10), 2803–2810 (2007). [CrossRef] |
26. | M. F. Xue and J. M. Jin, “Nonconformal FETI-DP methods for large-scale electromagnetic simulation,” IEEE Trans. Antenn. Propag. 60(9), 4291–4305 (2012). [CrossRef] |
27. | M. F. Xue and J. M. Jin, “A hybrid nonconformal FETI/conformal FETI-DP method for arbitrary nonoverlapping domain decomposition modeling,” in Proceedings of IEEE AP-S Int. Symp. (2013). [CrossRef] |
28. | Y. J. Li and J. M. Jin, “Fast full-wave analysis of large-scale three-dimensional photonic crystal devices,” J. Opt. Soc. Am. B 24(9), 2406–2415 (2007). [CrossRef] |
29. | W. Yao, J. M. Jin, and P. T. Krein, “A dual-primal finite-element tearing and interconnecting method combined with tree-cotree splitting for modeling electromechanical devices,” Int. J. Numer. Model., Electron. Netw., Devices Fields 26, 151–163 (2012). |
30. | W. Yao, J. M. Jin, and P. T. Krein, “A highly efficient domain decomposition method applied to 3-D finite-element analysis of electromechanical and electric machine problems,” IEEE Trans. Energ. Convers. 27(4), 1078–1086 (2012). [CrossRef] |
31. | A. Alonso-Rodriguez and L. Gerardo-Giorda, “New nonoverlapping domain decomposition methods for the harmonic Maxwell system,” SIAM J. Sci. Comput. 28(1), 102–122 (2006). [CrossRef] |
32. | Z. Peng, V. Rawat, and J.-F. Lee, “One way domain decomposition method with second order transmission conditions for solving electromagnetic wave problems,” J. Comput. Phys. 229(4), 1181–1197 (2010). [CrossRef] |
33. | Z. Peng and J.-F. Lee, “Non-conformal domain decomposition method with second-order transmission conditions for time-harmonic electromagnetics,” J. Comput. Phys. 229(16), 5615–5629 (2010). [CrossRef] |
34. | Y. J. Li and J. M. Jin, “Parallel implementation of the FETI-DPEM algorithm for general 3D EM simulations,” J. Comput. Phys. 228(9), 3255–3267 (2009). [CrossRef] |
35. | C. T. Wolfe, U. Navsariwala, and S. D. Gedney, “A parallel finite-element tearing and interconnecting algorithm for solution of the vector wave equation with PML absorbing medium,” IEEE Trans. Antenn. Propag. 48(2), 278–284 (2000). [CrossRef] |
36. | J. M. Jin, The Finite Element Method in Electromagnetics, 2nd ed. (Wiley, 2002). |
37. | MUMPS, A parallel sparse direct solver, available online: http://graal.ens-lyon.fr/MUMPS/. |
38. | CUBIT, available online: https://cubit.sandia.gov/. |
39. | METIS, Serial graph partitioning and fill-reducing matrix ordering, available online: http://glaros.dtc.umn.edu/gkhome/metis/metis/overview. |
40. | COMSOL Multiphysics ver. 4.2, available online: http://www.comsol.com/. |
41. | A. Arbabi and L. L. Goddard, “Measurements of the refractive indices and thermo-optic coefficients of Si_{3}N_{4} and SiO_{x} using microring resonances,” Opt. Lett. 38(19), 3878–3881 (2013). [CrossRef] [PubMed] |
OCIS Codes
(000.4430) General : Numerical approximation and analysis
(060.2370) Fiber optics and optical communications : Fiber optics sensors
(130.3120) Integrated optics : Integrated optics devices
(260.2110) Physical optics : Electromagnetic optics
(050.1755) Diffraction and gratings : Computational electromagnetic methods
(050.6624) Diffraction and gratings : Subwavelength structures
ToC Category:
Integrated Optics
History
Original Manuscript: December 20, 2013
Revised Manuscript: February 7, 2014
Manuscript Accepted: February 10, 2014
Published: February 19, 2014
Citation
Ming-Feng Xue, Young Mo Kang, Amir Arbabi, Steven J. McKeown, Lynford L. Goddard, and Jian-Ming Jin, "Fast and accurate finite element analysis of large-scale three-dimensional photonic devices with a robust domain decomposition method," Opt. Express 22, 4437-4452 (2014)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-22-4-4437
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References
- Y. Kawabe, C. Spiegelberg, A. Schülzgen, M. F. Nabor, B. Kippelen, E. A. Mash, P. M. Allemand, M. Kuwata-Gonokami, K. Takeda, N. Peyghambarian, “Whispering-gallery-mode microring laser using a conjugated polymer,” Appl. Phys. Lett. 72(2), 141–143 (1998). [CrossRef]
- V. R. Almeida, C. A. Barrios, R. R. Panepucci, M. Lipson, “All-optical control of light on a silicon chip,” Nature 431(7012), 1081–1084 (2004). [CrossRef] [PubMed]
- Q. Xu, B. Schmidt, S. Pradhan, M. Lipson, “Micrometre-scale silicon electro-optic modulator,” Nature 435(7040), 325–327 (2005). [CrossRef] [PubMed]
- T. A. Ibrahim, R. Grover, L.-C. Kuo, S. Kanakaraju, L. C. Calhoun, P.-T. Ho, “All-optical AND/NAND logic gates using semiconductor microresonators,” IEEE Photon. Technol. Lett. 15(10), 1422–1424 (2003). [CrossRef]
- M. T. Hill, H. J. S. Dorren, T. De Vries, X. J. M. Leijtens, J. H. Den Besten, B. Smalbrugge, Y.-S. Oei, H. Binsma, G.-D. Khoe, M. K. Smit, “A fast low-power optical memory based on coupled micro-ring lasers,” Nature 432(7014), 206–209 (2004). [CrossRef] [PubMed]
- T. Barwicz, M. A. Popović, P. T. Rakich, M. R. Watts, H. A. Haus, E. P. Ippen, H. I. Smith, “Microring-resonator-based add-drop filters in SiN: fabrication and analysis,” Opt. Express 12(7), 1437–1442 (2004). [CrossRef] [PubMed]
- B. E. Little, S. T. Chu, H. A. Haus, J. Foresi, J. Laine, “Microring resonator channel dropping filters,” J. Lightwave Technol. 15(6), 998–1005 (1997). [CrossRef]
- Y. Ding, M. Pu, L. Liu, J. Xu, C. Peucheret, X. Zhang, D. Huang, H. Ou, “Bandwidth and wavelength-tunable optical bandpass filter based on silicon microring-MZI structure,” Opt. Express 19(7), 6462–6470 (2011). [CrossRef] [PubMed]
- J. K. S. Poon, J. Scheuer, A. Yariv, “Wavelength-selective reflector based on a circular array of coupled microring resonators,” IEEE Photon. Technol. Lett. 16(5), 1331–1333 (2004). [CrossRef]
- A. Arbabi, Y. M. Kang, C.-Y. Lu, E. Chow, L. Goddard, “Realization of a narrowband single wavelength microring mirror,” Appl. Phys. Lett. 99(9), 091105 (2011). [CrossRef]
- Y. M. Kang, A. Arbabi, L. L. Goddard, “A microring resonator with an integrated Bragg grating: a compact replacement for a sampled grating distributed Bragg reflector,” Opt. Quantum Electron. 41(9), 689–697 (2009). [CrossRef]
- Y. M. Kang, A. Arbabi, L. L. Goddard, “Engineering the spectral reflectance of microring resonators with integrated reflective elements,” Opt. Express 18(16), 16813–16825 (2010). [CrossRef] [PubMed]
- Y. M. Kang, M. F. Xue, A. Arbabi, J. M. Jin, L. L. Goddard, “Modal expansion approach for accurately computing resonant modes in a high-Q optical resonator,” Microw. Opt. Technol. Lett. 56(2), 278–284 (2014). [CrossRef]
- C.-Y. Chao, L. J. Guo, “Biochemical sensors based on polymer microrings with sharp asymmetrical resonance,” Appl. Phys. Lett. 83(8), 1527–1529 (2003). [CrossRef]
- A. Arbabi, L. Goddard, “Integrated Optical Resonators: Progress in 2011,” IEEE Photonics J. 4(2), 574–577 (2012). [CrossRef]
- S. J. McKeown, L. L. Goddard, “Hydrogen detection using polarization diversity via a subwavelength fiber aperture,” IEEE Photonics J. 4(5), 1752–1761 (2012). [CrossRef]
- X. Shi, L. Hesselink, “Design of a C aperture to achieve λ/10 resolution and resonant transmission,” J. Opt. Soc. Am. B 21(7), 1305–1317 (2004). [CrossRef]
- J. S. Ayubi-Moak, S. M. Goodnick, D. Stanzione, G. Speyer, P. Sotirelis, “Improved parallel 3D FDTD simulator for photonic crystals,” in Proceedings of DoD HPCMP Users Group Conference, 319–326 (2008). [CrossRef]
- B. Radjenović and M. Radmilović-Radjenović, “Computer-aided design and simulation of optical microring resonators”, Int. J. Numer. Model., Electron. Netw., Devices Fields, available online: http://onlinelibrary.wiley.com/doi/10.1002/jnm.1920/abstract . [CrossRef]
- M. M. El Gowini, W. A. Moussa, “A finite element model of a MEMS-based surface acoustic wave hydrogen sensor,” Sensors (Basel) 10(2), 1232–1250 (2010). [CrossRef] [PubMed]
- A. Einat, U. Levy, “Analysis of the optical force in the micro ring resonator,” Opt. Express 19(21), 20405–20419 (2011). [CrossRef] [PubMed]
- B. Milanović, B. Radjenović, M. Radmilović-Radjenović, “Three-dimensional finite-element modeling of optical microring resonators,” Phys. Scr. T 149, 014026 (2012). [CrossRef]
- B. Radjenović, M. Radmilovic-Radjenović, “Excitation of confined modes in silicon slotted waveguides and microring resonators for sensing purposes,” IEEE Sens. J., doi:. [CrossRef]
- A. Arbabi, Y. M. Kang, L. Goddard, “Cylindrical coordinates coupled mode theory,” IEEE J. Quantum Electron. 46(12), 1769–1774 (2010). [CrossRef]
- Y. J. Li, J. M. Jin, “A new dual-primal domain decomposition approach for finite element simulation of 3D large-scale electromagnetic problems,” IEEE Trans. Antenn. Propag. 55(10), 2803–2810 (2007). [CrossRef]
- M. F. Xue, J. M. Jin, “Nonconformal FETI-DP methods for large-scale electromagnetic simulation,” IEEE Trans. Antenn. Propag. 60(9), 4291–4305 (2012). [CrossRef]
- M. F. Xue, J. M. Jin, “A hybrid nonconformal FETI/conformal FETI-DP method for arbitrary nonoverlapping domain decomposition modeling,” in Proceedings of IEEE AP-S Int. Symp. (2013). [CrossRef]
- Y. J. Li, J. M. Jin, “Fast full-wave analysis of large-scale three-dimensional photonic crystal devices,” J. Opt. Soc. Am. B 24(9), 2406–2415 (2007). [CrossRef]
- W. Yao, J. M. Jin, P. T. Krein, “A dual-primal finite-element tearing and interconnecting method combined with tree-cotree splitting for modeling electromechanical devices,” Int. J. Numer. Model., Electron. Netw., Devices Fields 26, 151–163 (2012).
- W. Yao, J. M. Jin, P. T. Krein, “A highly efficient domain decomposition method applied to 3-D finite-element analysis of electromechanical and electric machine problems,” IEEE Trans. Energ. Convers. 27(4), 1078–1086 (2012). [CrossRef]
- A. Alonso-Rodriguez, L. Gerardo-Giorda, “New nonoverlapping domain decomposition methods for the harmonic Maxwell system,” SIAM J. Sci. Comput. 28(1), 102–122 (2006). [CrossRef]
- Z. Peng, V. Rawat, J.-F. Lee, “One way domain decomposition method with second order transmission conditions for solving electromagnetic wave problems,” J. Comput. Phys. 229(4), 1181–1197 (2010). [CrossRef]
- Z. Peng, J.-F. Lee, “Non-conformal domain decomposition method with second-order transmission conditions for time-harmonic electromagnetics,” J. Comput. Phys. 229(16), 5615–5629 (2010). [CrossRef]
- Y. J. Li, J. M. Jin, “Parallel implementation of the FETI-DPEM algorithm for general 3D EM simulations,” J. Comput. Phys. 228(9), 3255–3267 (2009). [CrossRef]
- C. T. Wolfe, U. Navsariwala, S. D. Gedney, “A parallel finite-element tearing and interconnecting algorithm for solution of the vector wave equation with PML absorbing medium,” IEEE Trans. Antenn. Propag. 48(2), 278–284 (2000). [CrossRef]
- J. M. Jin, The Finite Element Method in Electromagnetics, 2nd ed. (Wiley, 2002).
- MUMPS, A parallel sparse direct solver, available online: http://graal.ens-lyon.fr/MUMPS/ .
- CUBIT, available online: https://cubit.sandia.gov/ .
- METIS, Serial graph partitioning and fill-reducing matrix ordering, available online: http://glaros.dtc.umn.edu/gkhome/metis/metis/overview .
- COMSOL Multiphysics ver. 4.2, available online: http://www.comsol.com/ .
- A. Arbabi, L. L. Goddard, “Measurements of the refractive indices and thermo-optic coefficients of Si3N4 and SiOx using microring resonances,” Opt. Lett. 38(19), 3878–3881 (2013). [CrossRef] [PubMed]
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