Open Access
Issue
ESAIM: M2AN
Volume 55, Number 4, July-August 2021
Page(s) 1461 - 1505
DOI https://doi.org/10.1051/m2an/2021029
Published online 26 July 2021
  1. M. Bachmayr, A. Cohen, R. DeVore and G. Migliorati, Sparse polynomial approximation of parametric elliptic PDEs. Part II: lognormal coefficients. ESAIM: M2AN 51 (2017) 341–363. [CrossRef] [EDP Sciences] [Google Scholar]
  2. M. Bachmayr, A. Cohen, D. Dũng and C. Schwab, Fully discrete approximation of parametric and stochastic elliptic PDEs. SIAM J. Numer. Anal. 55 (2017) 2151–2186. [Google Scholar]
  3. M. Bachmayr, A. Cohen and G. Migliorati, Representations of Gaussian random fields and approximation of elliptic PDEs with lognormal coefficients. J. Fourier Anal. App. 24 (2018) 621–649. [Google Scholar]
  4. J. Baldeaux and J. Dick, QMC rules of arbitrary high order: reproducing kernel Hilbert space approach. Constr. Approx. 30 (2009) 495–527. [Google Scholar]
  5. J. Baldeaux, J. Dick, G. Leobacher, D. Nuyens and F. Pillichshammer, Efficient calculation of the worst-case error and (fast) component-by-component construction of higher order polynomial lattice rules. Numer. Algorithms 59 (2012) 403–431. [Google Scholar]
  6. J. Dick and M. Gnewuch, Infinite-dimensional integration in weighted Hilbert spaces: anchored decompositions, optimal deterministic algorithms, and higher-order convergence. Found. Comput. Math. 14 (2014) 1027–1077. [Google Scholar]
  7. J. Dick, F.Y. Kuo, F. Pillichshammer and I.H. Sloan, Construction algorithms for polynomial lattice rules for multivariate integration. Math. Comput. 74 (2005) 1895–1921. [Google Scholar]
  8. J. Dick, F.Y. Kuo, Q.T. Le Gia, D. Nuyens and C. Schwab, Higher order QMC Petrov-Galerkin discretization for affine parametric operator equations with random field inputs. SIAM J. Numer. Anal. 52 (2014) 2676–2702. [Google Scholar]
  9. J. Dick, C. Irrgeher, G. Leobacher and F. Pillichshammer, On the optimal order of integration in Hermite spaces with finite smoothness. SIAM J. Numer. Anal. 56 (2018) 684–707. [Google Scholar]
  10. A.D. Gilbert, F.Y. Kuo, D. Nuyens and G.W. Wasilkowski, Efficient implementations of the multivariate decomposition method for approximating infinite-variate integrals. SIAM J. Sci. Comput. 40 (2018) A3240–A3266. [Google Scholar]
  11. M. Gnewuch, S. Mayer and K. Ritter, On weighted Hilbert spaces and integration of functions of infinitely many variables. J. Complexity 30 (2014) 29–47. [Google Scholar]
  12. M. Gnewuch, M. Hefter, A. Hinrichs and K. Ritter, Embeddings of weighted Hilbert spaces and applications to multivariate and infinite-dimensional integration. J. Approx. Theory 222 (2017) 8–39. [Google Scholar]
  13. T. Goda, Good interlaced polynomial lattice rules for numerical integration in weighted Walsh spaces. J. Comput. Appl. Math. 285 (2015) 279–294. [Google Scholar]
  14. I.G. Graham, F.Y. Kuo, J.A. Nichols, R. Scheichl, C. Schwab and I.H. Sloan, Quasi-Monte Carlo finite element methods for elliptic PDEs with lognormal random coefficients. Numer. Math. 131 (2015) 329–368. [Google Scholar]
  15. I.G. Graham, F.Y. Kuo, D. Nuyens, R. Scheichl and I.H. Sloan, Circulant embedding with QMC: analysis for elliptic PDE with lognormal coefficients. Numer. Math. 140 (2018) 479–511. [Google Scholar]
  16. L. Herrmann, Strong convergence analysis of iterative solvers for random operator equations. Calcolo 56 (2019) 46. [Google Scholar]
  17. L. Herrmann and C. Schwab, Multilevel quasi-Monte Carlo integration with product weights for elliptic PDEs with lognormal coefficients. ESAIM: M2AN 53 (2019) 1507–1552. [EDP Sciences] [Google Scholar]
  18. L. Herrmann and C. Schwab, QMC integration for lognormal-parametric, elliptic PDEs: local supports and product weights. Numer. Math. 141 (2019) 63–102. [Google Scholar]
  19. C. Irrgeher and G. Leobacher, High-dimensional integration on Formula , weighted Hermite spaces, and orthogonal transforms. J. Complexity 31 (2015) 174–205. [Google Scholar]
  20. C. Irrgeher, P. Kritzer, G. Leobacher and F. Pillichshammer, Integration in Hermite spaces of analytic functions. J. Complexity 31 (2015) 380–404. [Google Scholar]
  21. Y. Kazashi, Quasi-Monte Carlo integration with product weights for elliptic PDEs with log-normal coefficients. IMA J. Numer. Anal. 39 (2018) 1563–1593. [Google Scholar]
  22. F.Y. Kuo and D. Nuyens, Application of quasi-Monte Carlo methods to elliptic PDEs with random diffusion coefficients: a survey of analysis and implementation. Found. Comput. Math. 16 (2016) 1631–1696. [Google Scholar]
  23. F.Y. Kuo, I.H. Sloan, G.W. Wasilkowski and B.J. Waterhouse, Randomly shifted lattice rules with the optimal rate of convergence for unbounded integrands. J. Complexity 26 (2010) 135–160. [Google Scholar]
  24. F.Y. Kuo, I.H. Sloan, G.W. Wasilkowski and H. Woźniakowski, Liberating the dimension, J. Complexity 26 (2010) 422–454. [Google Scholar]
  25. F.Y. Kuo, I.H. Sloan, G.W. Wasilkowski and H. Woźniakowski, On decompositions of multivariate functions. Math. Comput. 79 (2010) 953–966. [Google Scholar]
  26. F.Y. Kuo, D. Nuyens, L. Plaskota, I.H. Sloan and G.W. Wasilkowski, Infinite-dimensional integration and the multivariate decomposition method. J. Comput. Appl. Math. 326 (2017) 217–234. [Google Scholar]
  27. D.T.P. Nguyen and D. Nuyens, Multivariate integration over Formula with exponential rate of convergence. J. Comput. Appl. Math. 315 (2017) 327–342. [Google Scholar]
  28. D.T.P. Nguyen and D. Nuyens, MDFEM: multivariate decomposition finite element method for elliptic PDEs with uniform random diffusion coefficients using higher-order QMC and FEM. Numer. Math. (2021). Accepted. [Google Scholar]
  29. J.A. Nichols and F.Y. Kuo, Fast CBC construction of randomly shifted lattice rules achieving Formula convergence for unbounded integrands over Formula in weighted spaces with POD weights. J. Complexity 30 (2014) 444–468. [Google Scholar]
  30. E. Novak and H. Woźniakowski, Tractability of Multivariate Problems. Volume II: Standard Information for Functionals. European Mathematical Society, Zürich 12 (2010). [Google Scholar]
  31. L. Plaskota and G.W. Wasilkowski, Tractability of infinite-dimensional integration in the worst case and randomized settings. J. Complexity 27 (2011) 505–518. [Google Scholar]
  32. G. Wahba, Spline Models for Observational Data. In: Vol. 59 of CBMS-NSF Regional Conference Series in Applied Mathematics. SIAM, Philadelphia, PA (1990). [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