paper 150203105626

Published: 2015-07-09

Application of Krylov-type Parametric Model Order Reduction in Efficient Uncertainty Quantification of Electro-thermal Circuit Models

Peter Benner,

Peter Benner

Max Planck Institute for Dynamics of Complex Technical Systems, Germany

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Peter Meuris,

Peter Meuris

MAGWEL NV, Belgium

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Lihong Feng,

Lihong Feng

Max Planck Institute for Dynamics of Complex Technical Systems, Germany

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Wim Schoenmaker,

Wim Schoenmaker

MAGWEL NV, Belgium

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Yao Yue

Max Planck Institute for Dynamics of Complex Technical Systems, Germany

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Proceedings of 2015 Photonics & Electromagnetics Research Symposium, Prague, July 6 - 9，Page(s)379-384

Abstract

As CMOS devices scale down to the nanoscale regime, it becomes increasingly more desired to design systems robust to device variations due to the fabrication process. In robust system design, uncertainty quantification plays an indispensable role. This paper con- siders uncertainty quantification of power-MOS devices used in energy harvesting. Uncertainty quantification of such a system is usually computationally demanding because it requires either simulating the high-order system at many sampling points, or simulating an even larger sys- tem. This paper uses parametric model order reduction techniques to accelerate uncertainty quantification of electro-thermal systems. We embed the reduced model into two uncertainty quantification methods, namely a Latin hypercube sampling method and a stochastic collocation method. Numerical results show that for both methods, uncertainty quantification based on a reduced model not only yields accurate results, but also achieves a significant speedup.

Citation

Peter Benner, Peter Meuris, Lihong Feng, Wim Schoenmaker, and Yao Yue, "Application of Krylov-type Parametric Model Order Reduction in Efficient Uncertainty Quantification of Electro-thermal Circuit Models," Proceedings of 2015 Photonics & Electromagnetics Research Symposium, Prague, July 6 - 9，Page(s)379-384

References

1. Bader, Brett and Tamara Kolda, "Efficient MATLAB computations with sparse and factored tensors," SIAM Journal on Scientific Computing, Vol. 30, 205-231, December 2006.
doi:10.2172/897641 Google Scholar

2. Bader, B. W., T. G. Kolda, et al. "Matlab tensor toolbox version 2.6", available online Matlab tensor toolbox version 2.6, 2015.
doi:10.2172/974890 Google Scholar

3. Benner, Peter and Lihong Feng, "A robust algorithm for parametric model order reduction based on implicit moment matching," Vol. 9 of MS&A — Modeling, Simulation and Applications, 159-185, Reduced Order Methods for Modeling and Computational Reduction, A. Quarteroni and G. Rozza, eds., Springer International Publishing, 2014.
doi:10.1007/978-3-319-02090-7_6 Google Scholar

4. Benner, P., S. Gugercin, and K. Willcox, "A survey of model reduction methods for parametric systems", Max Planck Institute Magdeburg, Preprint MPIMD/13-14, MPI-Magdeburg, Aug. 2013, available from http://www.mpi-magdeburg.mpg.de/preprints/. Google Scholar

5. Burkardt, J., "SGMGA: Sparse grid mixed growth anisotropic rules", http://people.sc.fsu. edu/∼jburkardt/m src/sgmga/sgmga.html. Google Scholar

6. Chen, Y., "Model order reduction for nonlinear systems", Master's Thesis, Massachusetts Institute of Technology, 1999.
doi:10.1088/1742-6596/2235/1/012073 Google Scholar

7. Helton, J. C. and F. J. Davis, "Latin hypercube sampling and the propagation of uncertainty in analyses of complex systems," Reliability Engineering & System Safety, Vol. 81, No. 1, 23–69, July 2003.
doi:10.1016/s0951-8320(03)00058-9 Google Scholar

8. Kolda, T. G. and B. W. Bader, "Tensor decompositions and applications," SIAM Review, Vol. 51, 455-500, 2009. Google Scholar

9. Le Maı̂tre, O. and O. Knio, Spectral Methods for Uncertainty Quantification: With Applications to Computational Fluid Dynamics, Scientific Computation, Springer, Netherlands, 2010. Google Scholar

10. Spirito, P., G. Breglio, V. d'Alessandro, and N. Rinaldi, "Thermal instabilities in high current power MOS devices: Experimental evidence, electro-thermal simulations and analytical modeling," 23rd International Conference on Microelectronics, MIEL, Vol. 1, 23-30, 2002. Google Scholar

11. Zhang, Zheng, Ibrahim Abe M. Elfadel, and Luca Daniel, "Uncertainty quantification for integrated circuits: Stochastic spectral methods," IEEE/ACM International Conference on Computer-Aided Design (ICCAD), 803–810, November 2013.
doi:10.1109/iccad.2013.6691205 Google Scholar