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Multi-Level Monte Carlo Finite Volume methods for uncertainty quantification of acoustic wave propagation in random heterogeneous layered medium

by S. Mishra and Ch. Schwab and J. Sukys

(Report number 2014-22)

Abstract
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 novel, 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.

Keywords: Uncertainty quantification, acoustic wave equation, multi-level Monte Carlo, FVM, linear scaling, log-normal random layered media, bias-free upscaling, high performance computing

@Techreport{MSS14_572,
  author = {S. Mishra and Ch. Schwab and J. Sukys},
  title = {Multi-Level Monte Carlo Finite Volume methods for uncertainty quantification of acoustic wave propagation in random heterogeneous layered medium},
  institution = {Seminar for Applied Mathematics, ETH Z{\"u}rich},
  number = {2014-22},
  address = {Switzerland},
  url = {https://www.sam.math.ethz.ch/sam_reports/reports_final/reports2014/2014-22.pdf },
  year = {2014}
}

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