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 ...

For functions u ∈ H 1(Ω) in an open, bounded polyhedron Ω⊂Rd of dimension d = 1, 2, 3, which are analytic in Ω¯¯¯¯∖S with point singularities concentrated at the set S⊂Ω¯¯¯¯ consisting of a finite number of points in Ω¯¯¯¯, the exponential rate exp(−bN−−√d+1) of convergence of h p-version continuous Galerkin finite element methods on families of regular, simplicial meshes in Ω can be achieved. The simplicial meshes are assumed to be ...

We analyze the convergence of higher order Quasi-Monte Carlo (QMC) quadratures of solution-functionals to countably-parametric, nonlinear operator equations with distributed uncertain parameters taking values in a separable Banach space X. Such equations arise in numerical uncertainty quantification with random field inputs. Unconditional bases of X render the random inputs and the solutions of the forward problem countably parametric. ...

Computational Bayesian inversion of operator equations with distributed uncertain input parameters is based on an infinite-dimensional version of Bayes’ formula established in [31] and its numerical realization in [27, 28]. Based on the sparsity of the posterior density shown in [29], dimensionadaptive Smolyak quadratures afford higher convergence rates than MCMC in terms of the number M of solutions of the forward (parametric operator) ...