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Second Moment Analysis for Robin Boundary Value Problems on Random Domains

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Singular Phenomena and Scaling in Mathematical Models

Abstract

We consider the numerical solution of Robin boundary value problems on random domains. The proposed method computes the mean and the variance of the random solution with leading order in the amplitude of the random boundary perturbation relative to an unperturbed, nominal domain. The variance is computed from the solution’s two-point correlation which satisfies a deterministic boundary value problem on the tensor product of the nominal domain. We solve this moderatly high-dimensional problem by either a low-rank approximation by means of the pivoted Cholesky decomposition or the combination technique. Both approaches are presented and compared by numerical experiments with respect to their efficiency.

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Authors and Affiliations

  1. Mathematisches Institut, Universität Basel, Rheinsprung 21, CH-4051, Basel, Switzerland

    Helmut Harbrecht

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  1. Helmut Harbrecht
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Correspondence to Helmut Harbrecht .

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  1. Universität Bonn Institut für Numerische Simulation, Bonn, Germany

    Michael Griebel

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Harbrecht, H. (2014). Second Moment Analysis for Robin Boundary Value Problems on Random Domains. In: Griebel, M. (eds) Singular Phenomena and Scaling in Mathematical Models. Springer, Cham. https://doi.org/10.1007/978-3-319-00786-1_16

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