volume | PIER Journals

Abstract

In this paper, a novel second-order transmission condition is developed in the framework of non-conformal finite element domain decomposition method to meet the challenges brought by complex and large-scale electromagnetic modeling. First, it is implemented efficiently on the non-conformal interface via a Gauss integral scheme. Then, the eigenvalue analysis of the DDM system show a more clustered eigenvalue distribution of this transmission condition compared with several existing transmission conditions. After that, it is applied to large-scale complex problems such as S-type waveguides in the high frequency band and dielectric well-logging applications in the low frequency band. The final numerical results demonstrate that this transmission condition has high efficiency and huge capability for modeling large-scale problems with multi-resolution in any frequency band.

1. Piacentini, , A. and N. Rosa, "An improved domain decomposition method for the 3D Helniholtz equation," Comput. Methods Appl. Mech. Engrg.,, Vol. 162, 113-124, Oct. 1997.
doi:10.1016/S0045-7825(97)00336-8 Google Scholar

2. Stupfel, , B., "A fast-domain decomposition method for the solution of electromagnetic scattering by large objects," IEEE Transactions on Antennas and Propagation, Vol. 44, No. 10, 1375-1385, Oct. 1995.
doi:10.1109/8.537332 Google Scholar

3. Benamou, , J. D. and B. Despres, "A domain decomposition method for the Helmholtz equation and related optimal control problems," J. Comput. Phys., Vol. 136, 68-82, 1997.
doi:10.1006/jcph.1997.5742 Google Scholar

4. Stupfel, , B., M. Mognot, and , "A domain decomposition method for the vector wave equation," IEEE Transactions on Antennas and Propagation , Vol. 48, No. 5, 653-660, May 2000.
doi:10.1109/8.855483 Google Scholar

5. Vouvakis, , M. N., Z. Cendes, and J.-F. Lee, "A FEM domain decomposition method for photonic and electromagnetic band gap structures," IEEE Transactions on Antennas and Propagation, Vol. 54, No. 2, 721-733, Feb. 2006.
doi:10.1109/TAP.2005.863095 Google Scholar

6. Lee, , S.-C., M. N. Vouvakis, and J.-F. Lee, "A non-overlapping domain decomposition method with non-matching grids for modeling large finite antenna arrays," J. Comput. Phys.,, Vol. 203, 1-21, Feb. 2005. Google Scholar

7. Alonso-Rodriguez, , A. and L. Gerardo-Giorda, "New non-overlapping domain decomposition methods for the harmonic Maxwell system," SIAM J. Sci. Comput., Vol. 28, No. 1, 102-122, 2006.
doi:10.1137/040608696 Google Scholar

8. Li, , Y. and J.-M. Jin, "A vector dual-primal finite element tearing and interconnecting method for solving 3-D large-scale electromagnetic problems," IEEE Transactions on Antennas and Propagation, Vol. 54, No. 10, 3000-3009, Oct. 2006.
doi:10.1109/TAP.2006.882191 Google Scholar

9. Zhao, , K., V. Rawat, S.-C. Lee, and J.-F. Lee, "A domain decomposition method with nonconformal meshes for finite periodic and semi-periodic structures," IEEE Transactions on Antennas and Propagation,, Vol. 55, No. 9, 2559-2570, Sep. 2007.
doi:10.1109/TAP.2007.904107 Google Scholar

10. Vouvakis, M. N., K. Zhao, S. M. Seo, and J.-F. Lee, "A domain decomposition approach for nonconformal couplings between finite and boundary elements for unbounded electromagnetic problems in R3," J. Comput. Phys., Vol. 225, No. 1, 975-994, Jul. 2007.
doi:10.1016/j.jcp.2007.01.014 Google Scholar

11. Li, , Y.-J. and J.-M. Jin, "A new dual-primal domain decomposition approach for ¯nite element simulation of 3-D large-scale electromagnetic problems," IEEE Transactions on Antennas and Propagation , Vol. 55, No. 10, 2803-2810, 2007.
doi:10.1109/TAP.2007.905954 Google Scholar

12. Zhao, K., V. Rawat, S.-C. Lee, and J.-F. Lee, "A domain decomposition method with nonconformal meshes for finite periodic and semi-periodic structures," IEEE Transactions on Antennas and Propagation, Vol. 55, No. 9, 2559-2570, 2007.
doi:10.1109/TAP.2007.904107 Google Scholar

13. Peng, , Z., V. Rawat, and J. F. Lee, "One way domain decomposition method with second-order transmission conditions for solving electromagnetic wave problems," J. Comput. Phys., Vol. 229, No. 4, 1181-1197, 2010.
doi:10.1016/j.jcp.2009.10.024 Google Scholar

14. Peng, , Z., J. F. Lee, and , "Nonconformal domain decomposition method with second-order transmission conditions for time-harmonic electromagnetic," J. Comput. Phys.,, Vol. 229, 5615-5629, 2010.
doi:10.1016/j.jcp.2010.03.049 Google Scholar

15. Fernandez-Recio, , R., L. E. Garcia-Castillo, S. Llorente-Romano, and I. Gomez-Revuelto, "Convergence study of a non-standard schwarz domain decomposition method for finite element mesh truncation in electro-magnetics," Progress In Electromagnetics Research, Vol. 120, 439-457, 2011. Google Scholar

16. Fotyga, , G., K. Nyka, and M. Mrozowski, "Effcient model order reduction for FEM analysis of waveguide structures and resonators," Progress In Electromagnetics Research, Vol. 127, 277-295, 2012.
doi:10.2528/PIER12021609 Google Scholar

17. Guillod, , T., F. Kehl, and C. V. Hafner, "FEM-based method for the simulation of dielectric waveguide grating biosensors," Progress In Electromagnetics Research, Vol. 137, 565-583, 2013. Google Scholar

18. Hizem, , M., H. Budan, B. Deville, O. Faivre, L. Mosse, and M. Simon, "Dielectric dispersion: A new wireline petrophysical measurement," Society of Petroleum Engineers, 116130, 2008. Google Scholar

19. Jin, , J. M., "The Finite Element Method in Electromagnetics," Wiley, , 2002. Google Scholar

20. Jin, , J. M. and D. J. Riley, Finite Element Analysis of Antennas and Arrays, Wiley, 2009.

Dr. Jin Ma

Professor Zai-Ping Nie