Article ID Journal Published Year Pages File Type
8902708 Applied Numerical Mathematics 2018 13 Pages PDF
Abstract
The present article is dedicated to the solution of elliptic boundary value problems on random domains. We apply a high-precision second order shape Taylor expansion to quantify the impact of the random perturbation on the solution. Thus, we obtain a representation of the solution with third order accuracy in the size of the perturbation's amplitude. The major advantage of this approach is that we end up with purely deterministic equations for the solution's moments. In particular, we derive representations for the first four moments, i.e., expectation, variance, skewness and kurtosis. These moments are efficiently computable by means of boundary integral equations. Numerical results are presented to validate the presented approach.
Related Topics
Physical Sciences and Engineering Mathematics Computational Mathematics
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