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PIER PIER B PIER C PIER M PIER Letters
2012-04-04
A Comparison Between PML, Infinite Elements and an Iterative BEM as Mesh Truncation Methods for Hp Self-Adaptive Procedures in Electromagnetics
By
Ignacio Gomez-Revuelto,

    Dr. Ignacio Gomez-Revuelto

    Department de Ingenieria Audiovisual y Comunicaciones

    Universidad Politecnica de Madrid

    Spain

    Homepage

Luis E. Garcia-Castillo,

    Dr. Luis E. Garcia-Castillo

    Univ Carlos III Madrid

    Spain

    Homepage

Leszek F Demkowicz

    Prof. Leszek F Demkowicz

    The University of Texas at Austin

    USA

    Homepage

Progress In Electromagnetics Research, Vol. 126, 499-519, 2012
doi:10.2528/PIER12020201
Abstract
Finite element hp-adaptivity is a technology that allows for very accurate numerical solutions. When applied to open region problems such as radar cross section prediction or antenna analysis, a mesh truncation method needs to be used. This paper compares the following mesh truncation methods in the context of hp-adaptive methods: Infinite Elements, Perfectly Matched Layers and an iterative boundary element based methodology. These methods have been selected because they are exact at the continuous level (a desirable feature required by the extreme accuracy delivered by the hp-adaptive strategy) and they are easy to integrate with the logic of hp-adaptivity. The comparison is mainly based on the number of degrees of freedom needed for each method to achieve a given level of accuracy. Computational times are also included. Two-dimensional examples are used, but the conclusions directly extrapolated to the three dimensional case.
Citation
Ignacio Gomez-Revuelto, Luis E. Garcia-Castillo, and Leszek F Demkowicz, "A Comparison Between PML, Infinite Elements and an Iterative BEM as Mesh Truncation Methods for Hp Self-Adaptive Procedures in Electromagnetics," Progress In Electromagnetics Research, Vol. 126, 499-519, 2012.
doi:10.2528/PIER12020201
References

1. Rheinboldt, W. C. and I. Babuska, "Error estimates for adaptive finite element computations," SIAM Journal of Numerical Analysis, Vol. 15, 736-754, Aug. 1978.
doi:10.1137/0715001

2. Jin, J. M., The Finite Element Method in Electromagnetics, 2nd Ed., John Wiley & Sons, Inc., 2002.

3. Salazar-Palma, M., T. K. Sarkar, L. E. García-Castillo, T. Roy, and A. R. Djordjevic, Iterative and Self-Adaptive Finite-Elements in Electromagnetic Modeling, Artech House Publishers, Inc., Norwood, MA, 1998.

4. Ping, X. W. and T. J. Cui, "Factorized sparse approximate inverse preconditioned conjugate gradient algorithm for finite element analysis of scattering problems," Progress In Electromagnetics Progress In Electromagnetics, Vol. 98, 15-31, 2009.
doi:10.2528/PIER09071703

5. Tian, J., Z. Q. Lv, X. W. Shi, L. Xu, and F. Wei, "An efficient approach for multifrontal algorithm to solve non-positive-definite finite element equations in electromagnetic problems," Progress In Electromagnetics Research, Vol. 95, 121-133, 2009.
doi:10.2528/PIER09070207

6. Klopf, E. M., S. B. Manic, M. M. Ilc, and B. M. Notaros, "Efficient time-domain analysis of waveguide discontinuities using higher order FEM in frequency domain ," Progress In Electromagnetics Research, Vol. 120, 215-234, 2011.

7. Trujillo-Romero, C. J., L. Leija, and A. Vera, "FEM modeling for performance evaluation of an electromagnetic oncology deep hyperthermia applicator when using monopole, inverted T, and plate antennas," Progress In Electromagnetics Research, Vol. 120, 99-125, 2011.

8. Andersen, L. S. and J. L. Volakis, "Hierarchical tangential vector finite elements for tetrahedra," IEEE Microwave and Guided Wave Letters, Vol. 8, 127-129, Mar. 1998.
doi:10.1109/75.661137

9. Webb, J. P., "Hierarchical vector basis functions of arbitrary order for triangular and tetrahedral finite elements," IEEE Transactions on Antennas and Propagation, Vol. 47, 1244-1253, Aug. 1999.
doi:10.1109/8.791939

10. Sun, D. K., J. F. Lee, and Z. Csendes, "Construction of nearly orthogonal Nedelec bases for rapid convergence with multilevel preconditioned solvers," SIAM Journal of Scientific Computing, Vol. 23, No. 4, 1053-1076, 2003.
doi:10.1137/S1064827500367531

11. Zhu, Y. and A. C. Cangellaris, "Finite element basis functions spaces for tetrahedra elements," Applied Computational Electromagnetics Society (ACES) Meeting, Monterey, CA, USA, Mar. 2001.

12. Ilíc, M. M., A. Z. Ilíc, and B. M. Notaroš, "Efficient large-domain 2-D FEM solution of arbitrary waveguides using p-refinement on generalized quadrilaterals," IEEE Transactions on Microwave Theory and Techniques, Vol. 53, 1377-1383, Apr. 2005.
doi:10.1109/TMTT.2005.845761

13. Demkowicz, L., Computing with hp Finite Elements. I. One- and Two-Dimensional Elliptic and Maxwell Problems, Chapman & Hall/CRC Press, Taylor and Francis, 2007.

14. Demkowicz, L., L., J. Kurtz, D. Pardo, M. Paszynski, W. Rachowicz, and A. Zdunek, Computing with hp Finite Elements. II Frontiers: Three Dimensional Elliptic and Maxwell Problems with Applications, Chapman & Hall/CRC Press, Taylor and Francis, 2008.

15. García-Castillo, L. E., D. Pardo, and L. F. Demkowicz, "Energy norm based and goal-oriented automatic hp adaptivity for electromagnetics. Application to the analysis of H-plane and E-plane rectangular waveguide discontinuities," IEEE Transactions on Microwave Theory and Techniques, Vol. 56, 3039-3049, Dec. 2008, doi: 10.1109/TMTT.2008.2007096.
doi:10.1109/TMTT.2008.2007096

16. Gómez-Revuelto, I., L. E. García-Castillo, D. Pardo, and L. F. Demkowicz, "A two-dimensional self-adaptive hp finite element method for the analysis of open region problems in electromagnetics," IEEE Transactions on Magnetics, Vol. 43, 1337-1340, Apr. 2007, doi: 10.1109/TMAG.2007.892413.
doi:10.1109/TMAG.2007.892413

17. Shi, Y., X. Luan, J. Qin, C. Lv, and C. H. Liang, "Multilevel Green's function interpolation method solution of volume/surface integral equation for mixed conducting/bi-isotropic objects," Progress In Electromagnetics Research, Vol. 107-252, 2010.

18. Lancellotti, V., B. P. de Hon, and A. G. Tijhuis, "Scattering from large 3-D piecewise homogeneous bodies through linear embedding via Green's operators and Arnoldi basis functions ," Progress In Electromagnetics Research, Vol. 103, 305-322, 2010.
doi:10.2528/PIER10032915

19. Bettess, P., "Infinite elements," International Journal for Numerical Methods in Engineering, Vol. 11, 54-64, 1977.

20. Silvester, P. P. and M. S. Hsieh, "Finite-element solution of 2-dimensional exterior-field problems," IEE Proceedings-H (Microw. Antennas Propag.), Vol. 118, 1743-1747, Dec. 1971.

21. Mur, G., "Absorbing boundary conditions for the finite-di®erence approximation of the time-domain electromagnetic-field equations," IEEE Transactions on Electromagnetic Compatibility, Vol. 23, 377-382, Nov. 1981.
doi:10.1109/TEMC.1981.303970

22. Engquist, B. and A. Majda, "Absorbing boundary conditions for the numerical simulation of waves," Mathematics of Computation, Vol. 31, 629-651, Jul. 1977.

23. Bayliss, A. and E. Turkel, "Radiation boundary conditions for wave-like equations," Communications on Pure and Applied Mathematics, Vol. 33, 707-725, 1980.
doi:10.1002/cpa.3160330603

24. D'Angelo, J. and I. D. Mayergoyz, "Finite element methods for the solution of RF radiation and scattering problems," Electromagnetics, Vol. 10, 177-199, 1990.
doi:10.1080/02726349008908235

25. Mittra, R. and O. Ramahi, "Absorbing boundary conditions for the direct solution of partial differential equations arising in electromagnetic scattering problems," Progress In Electromagnetics Research, Vol. 2, 133-173, 1990.

26. Gordon, R., R. Mittra, A. Glisson, and E. Michielssen, "Finite element analysis of electromagnetic scattering by complex bodies using an efficient numerical boundary condition for mesh truncation ," Electronic Letters, Vol. 29, 1102-1103, 1993.
doi:10.1049/el:19930735

27. Mei, K. K., R. Pous, Z. Chen, and Y. W. Liu, "The measured equation of invariance: A new concept in field computations," IEEE Antennas and Propagation Society International Symposium Digest, Vol. 4, 2047-2048, Institute of Electrical and Electronics Engineer (IEEE), Chicago, Illinois, USA, Jul. 1992.

28. Alfonzetti, S., G. Borzi, and N. Salerno, "Iteratively-improved Robin boundary conditions for the finite element solution of scattering problems in unbounded domains," International Journal for Numerical Methods in Engineering, Vol. 42, 601-629, 1998.
doi:10.1002/(SICI)1097-0207(19980630)42:4<601::AID-NME373>3.0.CO;2-O

29. Liu, J. and J. M. Jin, "A novel hybridization of higher order finite element and boundary integral methods for electromagnetic scattering ," IEEE Transactions on Antennas and Propagation, Vol. 49, 1794-1806, Dec. 2001.

30. Gómez-Revuelto, I., L. E. García-Castillo, M. Salazar-Palma, and T. K. Sarkar, "Fully coupled hybrid method FEM/high-frequency technique for the analysis of radiation and scattering problems," Microwave and Optical Technology Letters, Vol. 47, 104-107, Oct. 2005.

31. Fernández-Recio, R., L. E. García-Castillo, I. Gómez-Revuelto, and M. Salazar-Palma, "Fully coupled hybrid FEM-UTD method using NURBS for the analysis of radiation problems," IEEE Transactions on Antennas and Propagation, Vol. 56, 774-783, Mar. 2008.
doi:10.1109/TAP.2008.916878

32. Berenger, J. P., "A perfectly matched layer for the absorption of electromagnetic waves," Journal of Computational Physics, Vol. 114, 185-200, Oct. 1994.

33. Chew, W. C. and W. H. Weedon, "A 3-D perfectly matched medium from modified Maxwell's equations with stretched coordinates," Microwave and Optical Technology Letters, 599-604, 1994.
doi:10.1002/mop.4650071304

34. Sacks, Z. S., D. M. Kingsland, R. Lee, and J. F. Lee, "A perfectly matched anisotropic absorber for use as an absorbing boundary condition ," IEEE Transactions on Antennas and Propagation, Vol. 43, 1460-1463, Dec. 1995.
doi:10.1109/8.477075

35. Stupfel, B., "A study of the condition number of various finite element matrices involved in the numerical solution of Maxwell's equations," IEEE Transactions on Antennas and Propagation, Vol. 52, 3048-3059, Nov. 2004.

36. Michler, C., L. Demkowicz, J. Kurtz, and D. Pardo, "Improving the performance of perfectly matched layers by means of hp-adaptivity ," Numerical Methods for Partial Differential Equations, Vol. 23, 832-858, Jul. 2007.
doi:10.1002/num.20252

37. Pardo, D., L. Demkowicz, C. Torres-Verdin, and C. Michler, "PML enhanced with a self-adaptive goal-oriented hp-finite element method: Simulation of through-casing borehole resistivity measurements ," SIAM Journal of Scientific Computing, Vol. 30, No. 6, 2948-2964, 2008.
doi:10.1137/070689796

38. García-Castillo, L. E., I. Gómez-Revuelto, F. Sáez de Adana, and M. Salazar-Palma, "A finite element method for the analysis of radiation and scattering of electromagnetic waves on complex environments," Computer Methods in Applied Mechanics and Engineering, Vol. 194, No. 2-5, 637-655, Feb. 2005.
doi:10.1016/j.cma.2004.05.025

39. Chew, W. C., J. M. Jin, and E. Michielssen, "Complex coordinate stretching as a generalized absorbing boundary condition," Microwave and Optical Technology Letters, Vol. 15, 363-369, Sept. 1997.
doi:10.1002/(SICI)1098-2760(19970820)15:6<363::AID-MOP8>3.0.CO;2-C

40. Ubeda, E., J. M. Tamayo, and J. M. Rius, "Taylor-orthogonal basis functions for the discretization in method of moments of second kind integral equations in the scattering analysis of perfectly conducting or dielectric objects," Progress In Electromagnetics Research, Vol. 119, 85-105, 2011.
doi:10.2528/PIER11051715

41. Bahadori, H., H. Alaeian, and R. Faraji-Dana, "Computation of periodic Green's functions in layered media using complex images technique," Progress In Electromagnetics Research, Vol. 112, 225-240, 2011.

42. Gómez-Revuelto, I., L. E. García-Castillo, and M. Salazar-Palma, "Goal-oriented self-adaptive hp-strategies for scattering and radiation problems," Progress In Electromagnetics Research, Vol. 125, 459-482, 2012.
doi:10.2528/PIER11121606

43. Babuška, I. and B. Guo, "Approximation properties of the hp-version of the finite element method," Computer Methods in Applied Mechanics and Engineering, Vol. 133, 319-346, 1996.

44. Coifman, R., V. Rokhlin, and S. Wandzura, "The fast multipole method for the wave equation: A pedestrian prescription," IEEE Antennas and Propagation Magazine, Vol. 35, 7-12, Jun. 1993.
doi:10.1109/74.250128

45. Eibert, T. F., Ismatullah, E. Kaliyaperumal, and C. H. Schmidt, "Inverse equivalent surface current method with hierarchical higher order basis functions, full probe correction and multi-level fast multipole acceleration," Progress In Electromagnetics Research, Vol. 106, 377-394, 2010.
doi:10.2528/PIER10061604

46. Pan, X.-M., W.-C. Pi, and X.-Q. Sheng, "On OpenMP parallelization of the multilevel fast multipole algorithm," Progress In Electromagnetics Research, Vol. 112, 199-213, 2011.

47. Bebendorf, M., "Approximation of boundary element matrices," Numerische Mathematik, Vol. 86, No. 4, 565-589, 2000.
doi:10.1007/PL00005410

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