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Author: Neumann, Johannes × Subject: low-rank ×

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    Non-intrusive tensor reconstruction for high dimensional random PDEs
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2017) Eigel, Martin; Neumann, Johannes; Schneider, Reinhold; Wolf, Sebastian
    This paper examines a completely non-intrusive, sample-based method for the computation of functional low-rank solutions of high dimensional parametric random PDEs which have become an area of intensive research in Uncertainty Quantification (UQ). In order to obtain a generalized polynomial chaos representation of the approximate stochastic solution, a novel black-box rank-adapted tensor reconstruction procedure is proposed. The performance of the described approach is illustrated with several numerical examples and compared to Monte Carlo sampling.