Open Access
Issue
ESAIM: M2AN
Volume 55, Number 5, September-October 2021
Page(s) 1895 - 1920
DOI https://doi.org/10.1051/m2an/2021040
Published online 17 September 2021
  1. F. Alsayyari, Z. Perkó, D. Lathouwers and J. Kloosterman, A nonintrusive reduced order modelling approach using Proper Orthogonal Decomposition and locally adaptive sparse grids. J. Comput. Phys. 399 (2019) 108912. [Google Scholar]
  2. D. Amsallem and C. Farhat, Interpolation Method for Adapting Reduced-Order Models and Application to Aeroelasticity. AIAA J. 46 (2008) 1803–1813. [Google Scholar]
  3. D. Amsallem and C. Farhat, An online method for interpolating linear parametric reduced-order models. SIAM J. Sci. Comput. 33 (2011) 2169–2198. [Google Scholar]
  4. A. Antoulas, Approximation of large-scale dynamical systems, Advances in design and control. SIAM (2005). [Google Scholar]
  5. V. Barthelmann, E. Novak and K. Ritter, High dimensional polynomial interpolation on sparse grids. Adv. Comput. Math. 12 (2000) 273–288. [Google Scholar]
  6. U. Baur, C. Beattie, P. Benner and S. Gugercin, Interpolatory Projection Methods for Parameterized Model Reduction. SIAM J. Sci. Comput. 33 (2011) 2489–2518. [Google Scholar]
  7. B. Beckermann, G. Labahn and A. Matos, On rational functions without Froissart doublets. Numer. Math. 138 (2018) 615–633. [Google Scholar]
  8. P. Benner and L. Feng, A robust algorithm for parametric model order reduction based on implicit moment matching, chap. 6 in Reduced Order Methods for Modeling and Computational Reduction, edited by A. Quarteroni and R. Gianluigi Rozza. Springer International Publishing (2014) 159–185. [Google Scholar]
  9. P. Benner, S. Gugercin and K. Willcox, A Survey of Projection-Based Model Reduction Methods for Parametric Dynamical Systems. SIAM Rev. 57 (2015) 483–531. [Google Scholar]
  10. T. Betcke, N. Higham, V. Mehrmann, C. Schröder and F. Tisseur, NLEVP: A collection of nonlinear eigenvalue problems. ACM Trans. Math. Softw. 39 (2013) 1–28. [Google Scholar]
  11. F. Bonizzoni, F. Nobile, I. Perugia and D. Pradovera, Fast Least-Squares Padé approximation of problems with normal operators and meromorphic structure. Math. Comput. 89 (2020) 1229–1257. [Google Scholar]
  12. P. Chen and A. Quarteroni, A new algorithm for high-dimensional uncertainty quantification based on dimension-adaptive sparse grid approximation and reduced basis methods. J. Comput. Phys. 298 (2015) 176–193. [Google Scholar]
  13. A. Chkifa, A. Cohen and C. Schwab, High-Dimensional Adaptive Sparse Polynomial Interpolation and Applications to Parametric PDEs. Found. Comput. Math. 14 (2014) 601–633. [Google Scholar]
  14. D. Crouse, On implementing 2D rectangular assignment algorithms. IEEE Trans. Aerosp. Electron. Syst. 52 (2016) 1679–1696. [Google Scholar]
  15. Z. Drmač, S. Gugercin and C. Beattie, Quadrature-Based Vector Fitting for Discretized Formula Approximation. SIAM J. Sci. Comput. 37 (2015) 625–652. [Google Scholar]
  16. Q. Du and M. Gunzburger, Centroidal Voronoi Tessellation Based Proper Orthogonal Decomposition Analysis. Control Estimat. Distrib. Parameter Syst. 143 (2003) 137–150. [Google Scholar]
  17. F. Ferranti, L. Knockaert and T. Dhaene, Passivity-preserving parametric macromodeling by means of scaled and shifted state-space systems. IEEE Trans. Microw. Theory Tech. 59 (2011) 2394–2403. [Google Scholar]
  18. S. Grivet-Talocia and E. Fevola, Compact Parameterized Black-Box Modeling via Fourier-Rational Approximations. IEEE Trans. Electromagn. Compat. 59 (2017) 1133–1142. [Google Scholar]
  19. S. Grivet-Talocia and B. Gustavsen, Passive Macromodeling: Theory and Applications, Wiley series in microwave and optical engineering. John Wiley & Sons Inc., Hoboken, New Jersey (2015). [Google Scholar]
  20. S. Grivet-Talocia and R. Trinchero, Behavioral, Parameterized, and Broadband Modeling of Wired Interconnects with Internal Discontinuities. IEEE Trans. Electromagn. Compat. 60 (2018) 77–85. [Google Scholar]
  21. B. Haasdonk, M. Dihlmann and M. Ohlberger, A training set and multiple bases generation approach for parameterized model reduction based on adaptive grids in parameter space. Math. Comput. Model. Dyn. Syst. 17 (2011) 423–442. [Google Scholar]
  22. R. Hiptmair, L. Scarabosio, C. Schillings and C.C. Schwab, Large deformation shape uncertainty quantification in acoustic scattering. Adv. Comput. Math. 44 (2018) 1475–1518. [Google Scholar]
  23. F. Ihlenburg and I. Babuška, Finite element solution of the Helmholtz equation with high wave number Part I: The h-version of the FEM. Comput. Math. Appl. 30 (1995) 9–37. [Google Scholar]
  24. A. Ionita and A. Antoulas, Data-Driven Parametrized Model Reduction in the Loewner Framework. SIAM J. Sci. Comput. 36 (2014) A984–A1007. [Google Scholar]
  25. R. Karp, Reducibility Among Combinatorial Problems, iconf-procn Proceedings of a symposium on the Complexity of Computer Computations, held March 20-22, 1972, at the IBM Thomas J. Watson Research Center, Yorktown Heights, New York, USA, edited by R. Miller and J. Thatcher. The IBM Research Symposia Series, Plenum Press, New York (1972) 85–103. [Google Scholar]
  26. S. Lefteriu, A. Antoulas and A. Ionita, Parametric model reduction in the Loewner framework, in Vol. 44 of IFAC Proceedings Volumes (2011) 12751–12756. [Google Scholar]
  27. B. Lohmann and R. Eid, Efficient order reduction of parametric and nonlinear models by superposition of locally reduced models, Methoden und Anwendungen der Regelungstechnik. Erlangen-Münchener Workshops 2007 und 2008 (2008) 1–9. [Google Scholar]
  28. X. Ma and N. Zabaras, An adaptive hierarchical sparse grid collocation algorithm for the solution of stochastic differential equations. J. Comput. Phys. 228 (2009) 3084–3113. [Google Scholar]
  29. F. Nobile, R. Tempone and C. Webster, A Sparse Grid Stochastic Collocation Method for Partial Differential Equations with Random Input Data. SIAM J. Numer. Anal. 46 (2008) 2309–2345. [Google Scholar]
  30. F. Nobile and D. Pradovera, Non-intrusive double-greedy parametric model reduction by interpolation of frequency-domain rational surrogates-numerical tests (2020) Preprint arXiv:2008.10864v3. [Google Scholar]
  31. H. Panzer, J. Mohring, R. Eid and B. Lohmann, Parametric model order reduction by matrix interpolation. At-Automatisierungstechnik 58 (2010) 475–484. [Google Scholar]
  32. D. Pflüger, B. Peherstorfer and H. Bungartz, Spatially adaptive sparse grids for high-dimensional data-driven problems, in Vol. 26 Journal of Complexity, Academic Press Inc., (2010) 508–522. [Google Scholar]
  33. G. Phillips, Interpolation and approximation by polynomials, Vol. 14 of CMS books in mathematics, Springer, New York (2003). [Google Scholar]
  34. D. Pradovera, Interpolatory rational model order reduction of parametric problems lacking uniform inf-sup stability. SIAM J. Numer. Anal. 58 (2020) 2265–2293. [Google Scholar]
  35. D. Pradovera and F. Nobile, Frequency-domain non-intrusive greedy model order reduction based on minimal rational approximation (2020) SCEE 2020 Proceedings DOI: 10.5075/epfl-MATHICSE-275533. (to appear). [Google Scholar]
  36. A. Quarteroni, A. Manzoni and F. Negri, Reduced Basis Methods for Partial Differential Equations: An Introduction, UNITEXT. Springer International Publishing (2015). [Google Scholar]
  37. M. Reed and B. Simon, Analysis of operators, Vol. 4 of Methods of modern mathematical physics. Academic Press, New York, 4th print ed. (1981). [Google Scholar]
  38. SCITAS, EPFL Helvetios cluster webpage, accessed August 24 (2020). [Google Scholar]
  39. K. Smetana, O. Zahm and A. Patera, Randomized residual-based error estimators for parametrized equations. SIAM J. Sci. Comput. 41 (2019) 900–926. [Google Scholar]
  40. P. Virtanen, et al., SciPy 1.0: Fundamental algorithms for scientific computing in sython. Nat. Methods 17 (2020) 261–272. [PubMed] [Google Scholar]
  41. D. Weile, E. Michielssen, E. Grimme and K. Gallivan, A method for generating rational interpolant reduced order models of two-parameter linear systems. Appl. Math. Lett. 12 (1999) 93–102. [Google Scholar]
  42. H. Wendland, Scattered Data Approximation, Cambridge Monographs on Applied and Computational Mathematics, Cambridge University Press (2004). [Google Scholar]
  43. Y. Yue, L. Feng and P. Benner, An Adaptive Pole-Matching Method for Interpolating Reduced-Order Models (2019) Preprint arXiv:1908.00820. [Google Scholar]
  44. Y. Yue, L. Feng and P. Benner, Reduced-order modelling of parametric systems via interpolation of heterogeneous surrogates. Adv. Model. Simul. Eng. Sci. 6 (2019). [Google Scholar]

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