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Passivity-preserving parameterized model order reduction using singular values and matrix interpolation

Elizabeth Rita Samuel (UGent) , Francesco Ferranti (UGent) , Luc Knockaert (UGent) and Tom Dhaene (UGent)
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Abstract
We present a parameterized model order reduction method based on singular values and matrix interpolation. First, a fast technique using grammians is utilized to estimate the reduced order, and then common projection matrices are used to build parameterized reduced order models (ROMs). The design space is divided into cells, and a Krylov subspace is computed for each cell vertex model. The truncation of the singular values of the merged Krylov subspaces from the models located at the vertices of each cell yields a common projection matrix per design space cell. Finally, the reduced system matrices are interpolated using positive interpolation schemes to obtain a guaranteed passive parameterized ROM. Pertinent numerical results validate the proposed technique.
Keywords
LYAPUNOV EQUATIONS, IBCN, ALGORITHMS, NETWORKS, SYSTEMS, Grammians, interpolation, parameterized model order reduction (MOR), passivity, projection matrix, singular values

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Chicago
Samuel, Elizabeth Rita, Francesco Ferranti, Luc Knockaert, and Tom Dhaene. 2013. “Passivity-preserving Parameterized Model Order Reduction Using Singular Values and Matrix Interpolation.” Ieee Transactions on Components Packaging and Manufacturing Technology 3 (6): 1028–1037.
APA
Samuel, E. R., Ferranti, F., Knockaert, L., & Dhaene, T. (2013). Passivity-preserving parameterized model order reduction using singular values and matrix interpolation. IEEE TRANSACTIONS ON COMPONENTS PACKAGING AND MANUFACTURING TECHNOLOGY, 3(6), 1028–1037.
Vancouver
1.
Samuel ER, Ferranti F, Knockaert L, Dhaene T. Passivity-preserving parameterized model order reduction using singular values and matrix interpolation. IEEE TRANSACTIONS ON COMPONENTS PACKAGING AND MANUFACTURING TECHNOLOGY. 2013;3(6):1028–37.
MLA
Samuel, Elizabeth Rita, Francesco Ferranti, Luc Knockaert, et al. “Passivity-preserving Parameterized Model Order Reduction Using Singular Values and Matrix Interpolation.” IEEE TRANSACTIONS ON COMPONENTS PACKAGING AND MANUFACTURING TECHNOLOGY 3.6 (2013): 1028–1037. Print.
@article{4182175,
  abstract     = {We present a parameterized model order reduction method based on singular values and matrix interpolation. First, a fast technique using grammians is utilized to estimate the reduced order, and then common projection matrices are used to build parameterized reduced order models (ROMs). The design space is divided into cells, and a Krylov subspace is computed for each cell vertex model. The truncation of the singular values of the merged Krylov subspaces from the models located at the vertices of each cell yields a common projection matrix per design space cell. Finally, the reduced system matrices are interpolated using positive interpolation schemes to obtain a guaranteed passive parameterized ROM. Pertinent numerical results validate the proposed technique.},
  author       = {Samuel, Elizabeth Rita and Ferranti, Francesco and Knockaert, Luc and Dhaene, Tom},
  issn         = {2156-3950},
  journal      = {IEEE TRANSACTIONS ON COMPONENTS PACKAGING AND MANUFACTURING TECHNOLOGY},
  language     = {eng},
  number       = {6},
  pages        = {1028--1037},
  title        = {Passivity-preserving parameterized model order reduction using singular values and matrix interpolation},
  url          = {http://dx.doi.org/10.1109/TCPMT.2013.2248196},
  volume       = {3},
  year         = {2013},
}

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