Fast Frequency Sweep of FEM Models via the Balanced Truncation Proper Orthogonal Decomposition
- 15 August 2011
- journal article
- Published by Institute of Electrical and Electronics Engineers (IEEE) in IEEE Transactions on Antennas and Propagation
- Vol. 59 (11), 4142-4154
- https://doi.org/10.1109/tap.2011.2164184
Abstract
A fast frequency sweep method for wideband antennas and infinite arrays based on a singular value decomposition (SVD)-Krylov model reduction method for frequency-domain tangential vector finite elements (TVFEMs) is presented. Reduced models are constructed using balanced congruence transformations constructed from the dominant invariant subspace of the system's Hankel matrix. Traditionally, forming such matrix requires the intensive computation of Gramians; the proposed method only forms their low-rank Cholesky factors via a novel adaptive proper orthogonal decomposition (POD) sampling strategy, leading to significant savings. Unlike some other model reduction methods, balanced truncation POD (BT-POD) is directly applicable to lossy and dispersive electromagnetic models. Numerical studies on large-scale wideband antennas and infinite arrays show that the method is stable, error controllable and, without memory overheads capable of up to two orders-of-magnitude speed-ups.Keywords
This publication has 27 references indexed in Scilit:
- An Adaptive Multi-Point Fast Frequency Sweep for Large-Scale Finite Element ModelsIEEE Transactions on Magnetics, 2009
- Adaptive Solution Space Projection for Fast and Robust Wideband Finite-Element Simulation of Microwave ComponentsIEEE Microwave and Wireless Components Letters, 2007
- p-Type Multiplicative Schwarz (pMUS) Method With Vector Finite Elements for Modeling Three-Dimensional Waveguide DiscontinuitiesIEEE Transactions on Microwave Theory and Techniques, 2004
- Well-conditioned asymptotic waveform evaluation for finite elementsIEEE Transactions on Antennas and Propagation, 2003
- Multipoint Galerkin asymptotic waveform evaluation for model order reduction of frequency domain FEM electromagnetic radiation problemsIEEE Transactions on Antennas and Propagation, 2001
- An optimal control approach to a posteriori error estimation in finite element methodsActa Numerica, 2001
- Electromagnetic model order reduction for system-level modelingIEEE Transactions on Microwave Theory and Techniques, 1999
- PRIMA: passive reduced-order interconnect macromodeling algorithmPublished by Institute of Electrical and Electronics Engineers (IEEE) ,1997
- Asymptotic waveform evaluation via a Lanczos methodApplied Mathematics Letters, 1994
- Principal component analysis in linear systems: Controllability, observability, and model reductionIEEE Transactions on Automatic Control, 1981