Diagonalized Macromodels in Finite Element Method for Fast Electromagnetic Analysis of Waveguide Components
Abstract
A new technique of local model-order reduction (MOR) in 3-D finite element method (FEM) for frequency-domain electromagnetic analysis of waveguide components is proposed in this paper. It resolves the problem of increasing solution time of the reduced-order system assembled from macromodels created in the subdomains, into which an analyzed structure is partitioned. This problem becomes particularly relevant for growing size and count of the macromodels, and when they are cloned in multiple locations of the structures or are used repeatedly in a tuning and optimization process. To significantly reduce the solution time, the diagonalized macromodels are created by means of the simultaneous diagonalization and subsequently assembled in the global system. For the resulting partially diagonal matrix, an efficient dedicated solver based on the Schur complement technique is proposed. The employed MOR method preserves frequency independence of the macromodels, which is essential for efficient diagonalization, as it can be performed once for the whole analysis bandwidth. The numerical validation of the proposed procedures with respect to accuracy and speed was carried out for varying size and count of macromodels. An exemplary finite periodical waveguide structure was chosen to investigate the influence of macromodel cloning on the resultant efficiency. The results show that the use of the diagonalized macromodels provided a significant solution speedup without any loss of accuracy
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- Category:
- Articles
- Type:
- artykuły w czasopismach
- Published in:
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Electronics
no. 8,
pages 1 - 23,
ISSN: 2079-9292 - Language:
- English
- Publication year:
- 2019
- Bibliographic description:
- Nyka K.: Diagonalized Macromodels in Finite Element Method for Fast Electromagnetic Analysis of Waveguide Components// Electronics -Vol. 8,iss. 3 (2019), s.1-23
- DOI:
- Digital Object Identifier (open in new tab) 10.3390/electronics8030260
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-
- Jin, J.M. The Finite Element Method in Electromagnetics, 3rd ed.; John Wiley & Sons: Hoboken, NJ, USA, 2014.
- Salazar-Palma, M.; Djordjevic, A.; Sarkar, T.K.; García-Castillo, L.E.; Roy, T. Iterative and Self-Adaptive Finite-Elements in Electromagnetic Modeling; Artech House: Norwood, MA, USA, 1998.
- Bai, Z. Krylov subspace techniques for reduced-order modeling of large-scale dynamical systems. Appl. Numer. Math. 2002, 43, 9-44. [CrossRef] open in new tab
- Feldmann, P.; Freund, R.W. Efficient linear circuit analysis by Padé approximation via the Lanczos process. IEEE Trans. Comput.-Aided Design Integr. Circuits Syst. 1995, 14, 639-649. [CrossRef] open in new tab
- Freund, R.W. Krylov-subspace methods for reduced-order modeling in circuit simulation. J. Comput. Appl. Math. 2000, 123, 395-421. [CrossRef] open in new tab
- Nguyen, T.S.; Le Duc, T.; Tran, T.S.; Guichon, J.M.; Chadebec, O.; Meunier, G. Adaptive multipoint model order reduction scheme for large-scale inductive PEEC circuits. IEEE Trans. Electromagn. Compat. 2017, 59, 1143-1151. [CrossRef] open in new tab
- Cangellaris, A.C. Electromagnetic macro-modeling: An overview of current successes and future opportunities. In Proceedings of the Computational Electromagnetics International Workshop, Izmir, Turkey, 10-13 August 2011; pp. 1-6. open in new tab
- Kulas, L.; Mrozowski, M. A fast high-resolution 3-D finite-difference time-domain scheme with macromodels. IEEE Trans. Microw. Theory Technol. 2004, 52, 2330-2335. [CrossRef] open in new tab
- Wu, H.; Cangellaris, A.C. A finite-element domain-decomposition methodology for electromagnetic modeling of multilayer high-speed interconnects. IEEE Trans. Adv. Packag. 2008, 31, 339-350.
- Zhu, Y.; Cangellaris, A.C. Macro-elements for efficient FEM simulation of small geometric features in waveguide components. IEEE Trans. Microw. Theory Technol. 2000, 48, 2254-2260. [CrossRef] open in new tab
- Odabasioglu, A.; Celik, M.; Pileggi, L.T. PRIMA: Passive reduced-order interconnect macromodeling algorithm. IEEE Trans. Comput.-Aided Des. Integr. Circuits Syst. 1998, 17, 645-654. [CrossRef] open in new tab
- Rubio, J.; Arroyo, J.; Zapata, J. SFELP-an efficient methodology for microwave circuit analysis. IEEE Trans. Microw. Theory Technol. 2001, 49, 509-516. [CrossRef] open in new tab
- Freund, R.W.; Feldmann, P. Reduced-order modeling of large passive linear circuits by means of the SyPVL algorithm. In Proceedings of the 1996 IEEE-ACM International Conference on Computer-Aided Design, San Jose, CA, USA, 10-14 November 1996; pp. 280-287. open in new tab
- de la Rubia, V.; Zapata, J. Microwave circuit design by means of direct decomposition in the finite-element method. IEEE Trans. Microw. Theory Technol. 2007, 55, 1520-1530. [CrossRef] open in new tab
- Fotyga, G.; Nyka, K.; Kulas, L. A new type of macro-elements for efficient two-dimensional FEM analysis. IEEE Antennas Wirel. Propag. Lett. 2011, 10, 270-273. [CrossRef] open in new tab
- Fotyga, G.; Nyka, K.; Mrozowski, M. Efficient model order reduction for FEM analysis of waveguide structures and resonators. Prog. Electromagn. Res. 2012, 127, 277-295. [CrossRef] open in new tab
- Czarniewska, M.; Fotyga, G.; Mrozowski, M. Local Mesh Deformation for accelerated parametric studies based on the Finite Element Method. In Proceedings of the 2017 IEEE MTT-S International Conference on Numerical Electromagnetic and Multiphysics Modeling and Optimization for RF, Microwave, and Terahertz Applications (NEMO), Seville, Spain, 17-19 May 2017; pp. 284-286. open in new tab
- Czarniewska, M.; Fotyga, G.; Lamecki, A.; Mrozowski, M. Parametrized Local Reduced-Order Models with Compressed Projection Basis for Fast Parameter-Dependent Finite-Element Analysis. IEEE Trans. Microw. Theory Tech. 2018, 66, 3656-3667. [CrossRef] open in new tab
- Fotyga, G.; Nyka, K.; Mrozowski, M. Automatic reduction order selection for finite-element macromodels. IEEE Microw. Compon. Lett. 2018, 28, 278-280. [CrossRef] open in new tab
- Fisher, A.; Rieben, R.N.; Rodrigue, G.H.; White, D.A. A generalized mass lumping technique for vector finite-element solutions of the time-dependent Maxwell equations. IEEE Trans. Antennas Propag. 2005, 53, 2900-2910. [CrossRef] open in new tab
- Zeng, K.; Jiao, D. Frequency-domain method having a diagonal mass matrix in arbitrary unstructured meshes for efficient electromagnetic analysis. In Proceedings of the 2017 IEEE International Symposium on Antennas and Propagation USNC/URSI National Radio Science Meeting, San Diego, CA, USA, 9-14 July 2017; open in new tab
- Laub, A.J. Matrix Analysis For Scientists And Engineers; Society for Industrial and Applied Mathematics: Philadelphia, PA, USA, 2004. open in new tab
- Zhu, Y.; Cangellaris, A.C. Multigrid Finite Element Methods for Electromagnetic Field Modeling; open in new tab
- Reddy, C.J.; Deshpande, D.M.; Cockrell, C.R.; Beck, F.B. Finite Element Method for Eigenvalue Problemsin Electromagnetics; Technical Report 3485; NASA: Pasadena, CA, USA, 1994. open in new tab
- Schöberl, J. NETGEN An advancing front 2D, 3D-mesh generator based on abstract rules. Comput. Vis. Sci. 1997, 1, 41-52. [CrossRef] open in new tab
- Fotyga, G.; Nyka, K.; Mrozowski, M. Multilevel model order reduction with generalized compression of boundaries for 3-D FEM electromagnetic analysis. Prog. Electromagn. Res. 2013, 139, 743-759. [CrossRef] open in new tab
- Sheehan, B.N. ENOR: Model order reduction of RLC circuits using nodal equations for efficient factorization. In Proceedings of the IEEE 36th Design Automation Conference, New Orleans, LA, USA, 21-25 June 1999; open in new tab
- Banerjee, S.; Roy, A. Linear Algebra and Matrix Analysis for Statistics; CRC Press: Roca Raton, FL, USA, 2014. c 2019 by the author. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/). open in new tab
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- Project Aggregate Farming in the Cloud
- Verified by:
- Gdańsk University of Technology
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