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A multiscale method for semi-linear elliptic equations with localized uncertainties and non-linearities. (arXiv:1704.05331v1 [math.NA])
来源于:arXiv
A multiscale numerical method is proposed for the solution of semi-linear
elliptic stochastic partial differential equations with localized uncertainties
and non-linearities, the uncertainties being modeled by a set of random
parameters. It relies on an overlapping domain decomposition method which
introduces several subdomains of interest (called patches) containing the
different sources of uncertainties and non-linearities. An iterative algorithm
is then introduced, which requires the solution of a sequence of linear global
problems (with deterministic operators and uncertain right-hand sides), and
non-linear local problems (with uncertain operators and/or right-hand sides)
over the patches. Non-linear local problems are solved using an adaptive
sampling-based least-squares method for the construction of sparse polynomial
approximations of local solutions as functions of the random parameters.
Consistency, convergence and robustness of the algorithm are proved under
general assumptio 查看全文>>