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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
Links
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