Wu, Zhizhang; Zhang, Cheng; Zhang, Zhiwen Reduced-order model-based variational inference with normalizing flows for Bayesian elliptic inverse problems. (English) Zbl 07797178 J. Comput. Appl. Math. 441, Article ID 115659, 17 p. (2024). MSC: 35R30 35J25 35R60 62F15 68T07 78M34 PDFBibTeX XMLCite \textit{Z. Wu} et al., J. Comput. Appl. Math. 441, Article ID 115659, 17 p. (2024; Zbl 07797178) Full Text: DOI
Li, Sijing; Zhang, Cheng; Zhang, Zhiwen; Zhao, Hongkai A data-driven and model-based accelerated Hamiltonian Monte Carlo method for Bayesian elliptic inverse problems. (English) Zbl 1517.62030 Stat. Comput. 33, No. 4, Paper No. 90, 16 p. (2023). MSC: 62-08 35R60 60J22 65C05 65N21 65N30 78M34 PDFBibTeX XMLCite \textit{S. Li} et al., Stat. Comput. 33, No. 4, Paper No. 90, 16 p. (2023; Zbl 1517.62030) Full Text: DOI arXiv
Merkle, Robin; Barth, Andrea On properties and applications of Gaussian subordinated Lévy fields. (English) Zbl 1515.60090 Methodol. Comput. Appl. Probab. 25, No. 2, Paper No. 62, 33 p. (2023). MSC: 60G15 60E07 60G60 60E10 35R60 PDFBibTeX XMLCite \textit{R. Merkle} and \textit{A. Barth}, Methodol. Comput. Appl. Probab. 25, No. 2, Paper No. 62, 33 p. (2023; Zbl 1515.60090) Full Text: DOI arXiv
Merkle, Robin; Barth, Andrea Subordinated Gaussian random fields in elliptic partial differential equations. (English) Zbl 1518.60059 Stoch. Partial Differ. Equ., Anal. Comput. 11, No. 2, 819-867 (2023). MSC: 60H15 65C30 46E35 35R30 60G51 60G60 PDFBibTeX XMLCite \textit{R. Merkle} and \textit{A. Barth}, Stoch. Partial Differ. Equ., Anal. Comput. 11, No. 2, 819--867 (2023; Zbl 1518.60059) Full Text: DOI arXiv
Grote, Marcus J.; Michel, Simon; Nobile, Fabio Uncertainty quantification by multilevel Monte Carlo and local time-stepping for wave propagation. (English) Zbl 1506.65008 SIAM/ASA J. Uncertain. Quantif. 10, 1601-1628 (2022). MSC: 65C05 65L06 65M20 65M60 65M75 PDFBibTeX XMLCite \textit{M. J. Grote} et al., SIAM/ASA J. Uncertain. Quantif. 10, 1601--1628 (2022; Zbl 1506.65008) Full Text: DOI arXiv
Chada, N. K.; Hoel, H.; Jasra, A.; Zouraris, G. E. Improved efficiency of multilevel Monte Carlo for stochastic PDE through strong pairwise coupling. (English) Zbl 1507.65027 J. Sci. Comput. 93, No. 3, Paper No. 62, 29 p. (2022). MSC: 65C30 60H35 65C05 PDFBibTeX XMLCite \textit{N. K. Chada} et al., J. Sci. Comput. 93, No. 3, Paper No. 62, 29 p. (2022; Zbl 1507.65027) Full Text: DOI arXiv
Merkle, Robin; Barth, Andrea Multilevel Monte Carlo estimators for elliptic PDEs with Lévy-type diffusion coefficient. (English) Zbl 1509.65117 BIT 62, No. 4, 1279-1317 (2022). Reviewer: Vit Dolejsi (Praha) MSC: 65N30 65C05 65C30 60G60 60G65 60H25 60H35 60J74 76S05 35R60 PDFBibTeX XMLCite \textit{R. Merkle} and \textit{A. Barth}, BIT 62, No. 4, 1279--1317 (2022; Zbl 1509.65117) Full Text: DOI arXiv
Barth, Andrea; Stein, Andreas Numerical analysis for time-dependent advection-diffusion problems with random discontinuous coefficients. (English) Zbl 1501.65065 ESAIM, Math. Model. Numer. Anal. 56, No. 5, 1545-1578 (2022). MSC: 65M60 65M22 65N30 60H25 60H30 60H35 35R60 58J65 35K10 76S05 74A15 62C10 PDFBibTeX XMLCite \textit{A. Barth} and \textit{A. Stein}, ESAIM, Math. Model. Numer. Anal. 56, No. 5, 1545--1578 (2022; Zbl 1501.65065) Full Text: DOI arXiv
Li, Sijing; Zhang, Zhiwen; Zhao, Hongkai A data-driven approach for multiscale elliptic PDEs with random coefficients based on intrinsic dimension reduction. (English) Zbl 1459.35194 Multiscale Model. Simul. 18, No. 3, 1242-1271 (2020). MSC: 35J62 35J08 35R60 65N30 65N80 78M34 PDFBibTeX XMLCite \textit{S. Li} et al., Multiscale Model. Simul. 18, No. 3, 1242--1271 (2020; Zbl 1459.35194) Full Text: DOI arXiv
Stein, Andreas; Barth, Andrea A multilevel Monte Carlo algorithm for parabolic advection-diffusion problems with discontinuous coefficients. (English) Zbl 07240108 Tuffin, Bruno (ed.) et al., Monte Carlo and quasi-Monte Carlo methods. MCQMC 2018. Proceedings of the 13th international conference on Monte Carlo and quasi-Monte Carlo methods in scientific computing, Rennes, France, July 1–6, 2018. Cham: Springer. Springer Proc. Math. Stat. 324, 445-466 (2020). MSC: 65C05 PDFBibTeX XMLCite \textit{A. Stein} and \textit{A. Barth}, Springer Proc. Math. Stat. 324, 445--466 (2020; Zbl 07240108) Full Text: DOI arXiv
Petersson, Andreas Rapid covariance-based sampling of linear SPDE approximations in the multilevel Monte Carlo method. (English) Zbl 07240107 Tuffin, Bruno (ed.) et al., Monte Carlo and quasi-Monte Carlo methods. MCQMC 2018. Proceedings of the 13th international conference on Monte Carlo and quasi-Monte Carlo methods in scientific computing, Rennes, France, July 1–6, 2018. Cham: Springer. Springer Proc. Math. Stat. 324, 423-443 (2020). MSC: 65C05 PDFBibTeX XMLCite \textit{A. Petersson}, Springer Proc. Math. Stat. 324, 423--443 (2020; Zbl 07240107) Full Text: DOI arXiv
Ma, Dingjiong; Ching, Wai-ki; Zhang, Zhiwen Proper orthogonal decomposition method for multiscale elliptic PDEs with random coefficients. (English) Zbl 1439.35588 J. Comput. Appl. Math. 370, Article ID 112635, 19 p. (2020). Reviewer: Igor Bock (Bratislava) MSC: 35R60 65N30 65N12 78M34 PDFBibTeX XMLCite \textit{D. Ma} et al., J. Comput. Appl. Math. 370, Article ID 112635, 19 p. (2020; Zbl 1439.35588) Full Text: DOI
Barth, Andrea; Stein, Andreas A study of elliptic partial differential equations with jump diffusion coefficients. (English) Zbl 1405.60104 SIAM/ASA J. Uncertain. Quantif. 6, 1707-1743 (2018). MSC: 60H25 60H30 60H35 35R60 65C05 58J65 PDFBibTeX XMLCite \textit{A. Barth} and \textit{A. Stein}, SIAM/ASA J. Uncertain. Quantif. 6, 1707--1743 (2018; Zbl 1405.60104) Full Text: DOI arXiv
Kornhuber, Ralf; Youett, Evgenia Adaptive multilevel Monte Carlo methods for stochastic variational inequalities. (English) Zbl 1397.65275 SIAM J. Numer. Anal. 56, No. 4, 1987-2007 (2018). Reviewer: Wilhelm Heinrichs (Essen) MSC: 65N30 65N50 65N55 65C05 PDFBibTeX XMLCite \textit{R. Kornhuber} and \textit{E. Youett}, SIAM J. Numer. Anal. 56, No. 4, 1987--2007 (2018; Zbl 1397.65275) Full Text: DOI arXiv
Sun, Qi; Du, Qiang; Ming, Ju Asymptotically compatible schemes for stochastic homogenization. (English) Zbl 1452.35022 SIAM J. Numer. Anal. 56, No. 3, 1942-1960 (2018); erratum ibid. 56, No. 4, 2698-2699 (2018). MSC: 35B27 65N30 PDFBibTeX XMLCite \textit{Q. Sun} et al., SIAM J. Numer. Anal. 56, No. 3, 1942--1960 (2018; Zbl 1452.35022) Full Text: DOI
Brown, Donald L.; Hoang, Viet Ha A hierarchical finite element Monte Carlo method for stochastic two-scale elliptic equations. (English) Zbl 1365.65012 J. Comput. Appl. Math. 323, 16-35 (2017). MSC: 65C30 60H15 35R60 60H35 65N30 76S05 65C05 PDFBibTeX XMLCite \textit{D. L. Brown} and \textit{V. H. Hoang}, J. Comput. Appl. Math. 323, 16--35 (2017; Zbl 1365.65012) Full Text: DOI Link
Li, Jingshi; Wang, Xiaoshen; Zhang, Kai Multi-level Monte Carlo weak Galerkin method for elliptic equations with stochastic jump coefficients. (English) Zbl 1410.65454 Appl. Math. Comput. 275, 181-194 (2016). MSC: 65N30 65C05 65N75 60J75 PDFBibTeX XMLCite \textit{J. Li} et al., Appl. Math. Comput. 275, 181--194 (2016; Zbl 1410.65454) Full Text: DOI
Barth, Andrea; Schwab, Christoph; Šukys, Jonas Multilevel Monte Carlo simulation of statistical solutions to the Navier-Stokes equations. (English) Zbl 1382.76209 Cools, Ronald (ed.) et al., Monte Carlo and quasi-Monte Carlo methods. MCQMC. Proceedings of the 11th international conference on ‘Monte Carlo and quasi-Monte Carlo methods in scientific computing’, Leuven, Belgium, April 6–11, 2014. Cham: Springer (ISBN 978-3-319-33505-6/hbk; 978-3-319-33507-0/ebook). Springer Proceedings in Mathematics & Statistics 163, 209-227 (2016). MSC: 76M35 65C05 35Q30 65M75 76D06 76M12 PDFBibTeX XMLCite \textit{A. Barth} et al., Springer Proc. Math. Stat. 163, 209--227 (2016; Zbl 1382.76209) Full Text: DOI
Bierig, Claudio; Chernov, Alexey Approximation of probability density functions by the multilevel Monte Carlo maximum entropy method. (English) Zbl 1349.65007 J. Comput. Phys. 314, 661-681 (2016). MSC: 65C05 62B10 60B10 PDFBibTeX XMLCite \textit{C. Bierig} and \textit{A. Chernov}, J. Comput. Phys. 314, 661--681 (2016; Zbl 1349.65007) Full Text: DOI
Efendiev, Yalchin; Kronsbein, Cornelia; Legoll, Frédéric Multilevel Monte Carlo approaches for numerical homogenization. (English) Zbl 1328.65010 Multiscale Model. Simul. 13, No. 4, 1107-1135 (2015). MSC: 65C05 35R60 35B27 60H15 PDFBibTeX XMLCite \textit{Y. Efendiev} et al., Multiscale Model. Simul. 13, No. 4, 1107--1135 (2015; Zbl 1328.65010) Full Text: DOI arXiv
Abdulle, Assyr; Blumenthal, Adrian Stabilized multilevel Monte Carlo method for stiff stochastic differential equations. (English) Zbl 1349.65028 J. Comput. Phys. 251, 445-460 (2013). MSC: 65C30 60H10 60H35 65C05 PDFBibTeX XMLCite \textit{A. Abdulle} and \textit{A. Blumenthal}, J. Comput. Phys. 251, 445--460 (2013; Zbl 1349.65028) Full Text: DOI Link