Mishra, S.; Schwab, Ch.; Šukys, J. Multi-level Monte Carlo finite volume methods for uncertainty quantification of acoustic wave propagation in random heterogeneous layered medium. (English) Zbl 1351.76117 J. Comput. Phys. 312, 192-217 (2016). Summary: We consider the very challenging problem of efficient uncertainty quantification for acoustic wave propagation in a highly heterogeneous, possibly layered, random medium, characterized by possibly anisotropic, piecewise log-exponentially distributed Gaussian random fields. A multi-level Monte Carlo finite volume method is proposed, along with a novel, bias-free upscaling technique that allows to represent the input random fields, generated using spectral FFT methods, efficiently. Combined together with a recently developed dynamic load balancing algorithm that scales to massively parallel computing architectures, the proposed method is able to robustly compute uncertainty for highly realistic random subsurface formations that can contain a very high number (millions) of sources of uncertainty. Numerical experiments, in both two and three space dimensions, illustrating the efficiency of the method are presented. Cited in 17 Documents MSC: 76M12 Finite volume methods applied to problems in fluid mechanics 65M08 Finite volume methods for initial value and initial-boundary value problems involving PDEs 35Q35 PDEs in connection with fluid mechanics 65M75 Probabilistic methods, particle methods, etc. for initial value and initial-boundary value problems involving PDEs 76Q05 Hydro- and aero-acoustics Keywords:uncertainty quantification; acoustic wave equation; multi-level Monte Carlo; finite volume method; linear scaling; log-normal random layered media; bias-free upscaling; high performance computing Software:FFTW; ALSVID-UQ PDFBibTeX XMLCite \textit{S. Mishra} et al., J. Comput. Phys. 312, 192--217 (2016; Zbl 1351.76117) Full Text: DOI Link References: [1] ALSVID-UQ, available from [3] Abdulle, A.; Grote, M. J.; Stohrer, Ch., FE heterogeneous multiscale method for long-time wave propagation, C. R. Math. Acad. Sci., 351, 11-12, 495-499 (2013) · Zbl 1273.76263 [4] Adler, R. 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