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arXiv · 1810.01661

IGA-based Multi-Index Stochastic Collocation for random PDEs on arbitrary domains

Joakim Beck·Lorenzo Tamellini·Raúl Tempone
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Abstract

This paper proposes an extension of the Multi-Index Stochastic Collocation (MISC) method for forward uncertainty quantification (UQ) problems in computational domains of shape other than a square or cube, by exploiting isogeometric analysis (IGA) techniques. Introducing IGA solvers to the MISC algorithm is very natural since they are tensor-based PDE solvers, which are precisely what is required by the MISC machinery. Moreover, the combination-technique formulation of MISC allows the straight-forward reuse of existing implementations of IGA solvers. We present numerical results to showcase the effectiveness of the proposed approach.

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Joakim Beck, Lorenzo Tamellini, Raúl Tempone. 2018-10-03. IGA-based Multi-Index Stochastic Collocation for random PDEs on arbitrary domains. https://doi.org/10.1016/j.cma.2019.03.042

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