volume | PIER Journals

Abstract

This paper presents a multilevel Model Order Reduction technique for a 3-D electromagnetic Finite Element Method analysis. The reduction process is carried out in a hierarchical way and involves several steps which are repeated at each level. This approach brings about versatility and allows one to efficiently analyze complex electromagnetic structures. In the proposed multilevel reduction the entire computational domain is covered with macro-elements which are subsequently nested, in such a way that size of the problem which has to be reduced at each level is relatively small. In order to increase the speed of the reduction at each level, the electric field at the macro-elements' boundaries is projected onto the subspace spanned by Legendre polynomials and trigonometric functions. The results of the numerical experiments confirm the validity and efficiency of the presented approach.

1. Dziekonski, A., A. Lamecki, and M. Mrozowski, "Tuning a hybrid GPU-CPU V-cycle multilevel preconditioner for solving large real and complex systems of FEM equations," IEEE Antennas and Wireless Propagation Letters, Vol. 10, 619-622, 2011.
doi:10.1109/LAWP.2011.2159769

2. Dziekonski, A., A. Lamecki, and M. Mrozowski, "A memory efficient and fast sparse matrix vector product on a GPU," Progress In Electromagnetics Research, Vol. 116, 49-63, 2011.

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

4. Zhu, Y. and A. C. Cangellaris, "Macro-elements for efficient FEM simulation of small geometric features in waveguide components," IEEE Trans. Microwave Theory Tech., Vol. 48, 2254-2260, Dec. 2000.
doi:10.1109/22.898972

5. De la Rubia, V. and J. Zapata, "Microwave circuit design by means of direct decomposition in the finite-element method," IEEE Trans. Microwave Theory Tech., Vol. 55, No. 7, 1520-1530, Jul. 2007.
doi:10.1109/TMTT.2007.900307

6. Wu, H. and A. C. Cangellaris, "A finite-element domain-decomposition methodology for electromagnetic modeling of multilayer high-speed interconnects," IEEE Transactions on Advanced Packaging, Vol. 31, No. 2, 339-350, May 2010.

7. Lee, S.-H. and J.-M. Jin, "Adaptive solution space projection for fast and robust wideband finite-element simulation of microwave components," IEEE Microwave and Wireless Components Letters, Vol. 17, No. 7, 474-476, Jul. 2007.
doi:10.1109/LMWC.2007.899290

8. Fotyga, G., K. Nyka, and L. Kulas, "A new type of macro-elements for efficient two-dimensional FEM analysis," IEEE Antennas and Wireless Propagation Letters, Vol. 10, 270-273, Apr. 2011.
doi:10.1109/LAWP.2011.2134063

9. Podwalski, J., P. Kowalczyk, and M. Mrozowski, "Efficient multiscale finite difference frequency domain analysis using multiple macromodels with compressed boundaries," Progress In Electromagnetics Research, Vol. 126, 463-479, Apr. 2012.
doi:10.2528/PIER12012008

10. Kulas, L., P. Kowalczyk, and M. Mrozowski, "A novel modal technique for time and frequency domain analysis of waveguide components," IEEE Microwave and Wireless Components Letters, Vol. 21, No. 1, 7-9, Jan. 2011.
doi:10.1109/LMWC.2010.2089439

11. Kulas, L. and M. Mrozowski, "A fast high-resolution 3-D finite-difference time-domain scheme with macromodels," IEEE Trans. Microwave Theory Tech., Vol. 52, No. 9, 2330-2335, Sep. 2004.
doi:10.1109/TMTT.2004.834585

12. Kulas, L. and M. Mrozowski, "Multilevel model order reduction," IEEE Microwave and Wireless Components Letters, Vol. 14, No. 4, 165-167, Apr. 2004.
doi:10.1109/LMWC.2004.827113

13. Fotyga, G., P. Kowalczyk, L. Kulas, K. Nyka, J. Podwalski, and M. Mrozowski, "Reduced order models in computational electromagnetics (in memory of Ruediger Vahldieck)," 2012 Asia-Pacific Symposium on Electromagnetic Compatibility (APEMC), 705-708, May 2012.
doi:10.1109/APEMC.2012.6237900

14. Sheehan, B. N., "ENOR: Model order reduction of RLC circuits using nodal equations for efficient factorization," Proc. IEEE 36th Design Autom. Conf., 17-21, Jun. 1999.

15. Pelosi, G., R. Coccioli, and S. Selleri, Quick Finite Elements for Electromagnetic Waves, 2nd Edition, Artech House Antenna Library, 2009.

16. Ingelstrom, P., "A new set of H(curl)-conforming hierarchical basis functions for tetrahedral meshes," IEEE Trans. Microwave Theory Tech., Vol. 54, No. 1, 106-114, Jan. 2006..
doi:10.1109/TMTT.2005.860295

17. Dziekonski, A., P. Sypek, A. Lamecki, and M. Mrozowski, "Finite element matrix generation on a GPU," Progress In Electromagnetics Research, Vol. 128, 249-265, 2012.

18. Kusiek, A. and J. Mazur, "Application of hybrid finite-difference mode-matching method to analysis of structures loaded with axially symmetrical posts," Microwave and Optical Technology Letters, Vol. 53, No. 1, 189-194, Jan. 2011.
doi:10.1002/mop.25644

19. Szydlowski, L., A. Lamecki, and M. Mrozowski, "Coupled-resonator waveguide filter in quadruplet topology with frequency-dependent coupling a design based on coupling matrix," IEEE Microwave and Wireless Components Letters, Vol. 22, No. 11, 553-555, Nov. 2012.
doi:10.1109/LMWC.2012.2225604

20. Lech, R. and J. Mazur, "Tunable waveguide filter with bow-tie metallic posts," IEE Proceedings Microwaves, Antennas and Propagation, Vol. 151, No. 2, 156-160, Apr. 2004.
doi:10.1049/ip-map:20040166

Mrs. Grzegorz Fotyga

Dr. Krzysztof Nyka

Professor Michal Mrozowski