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. [CrossRef] [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. [CrossRef] [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. [CrossRef] [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. [CrossRef] [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. [CrossRef] [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. [CrossRef] [MathSciNet] [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. [CrossRef] [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. [CrossRef] [MathSciNet] [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]

Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.

Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.

Initial download of the metrics may take a while.

Recommended for you