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Sparse second moment analysis for elliptic problems in stochastic domains

Harbrecht, Helmut ; Schneider, Reinhold ; Schwab, Christoph

Numerische Mathematik, 2008, Vol.109(3), pp.385-414 [Peer Reviewed Journal]

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  • Title:
    Sparse second moment analysis for elliptic problems in stochastic domains
  • Author/Creator: Harbrecht, Helmut ; Schneider, Reinhold ; Schwab, Christoph
  • Language: English
  • Subjects: 35J20 ; 35R60 ; 65N38
  • Is Part Of: Numerische Mathematik, 2008, Vol.109(3), pp.385-414
  • Description: We consider the numerical solution of elliptic boundary value problems in domains with random boundary perturbations. Assuming normal perturbations with small amplitude and known mean field and two-point correlation function, we derive, using a second order shape calculus, deterministic equations for the mean field and the two-point correlation function of the random solution for a model Dirichlet problem which are 3rd order accurate in the boundary perturbation size. Using a variational boundary integral equation formulation on the unperturbed, “nominal” boundary and a wavelet discretization, we present and analyze an algorithm to approximate the random solution’s mean and its two-point correlation function at essentially optimal order in essentially \mathcal{O}(N)} work and memory, where N denotes the number of unknowns required for consistent discretization of the boundary of the nominal domain.
  • Identifier: ISSN: 0029-599X ; E-ISSN: 0945-3245 ; DOI: 10.1007/s00211-008-0147-9