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

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

Beck, Joakim, Lorenzo Tamellini, and Raúl Tempone. "IGA-based Multi-Index Stochastic Collocation for random PDEs on arbitrary domains." arXiv preprint arXiv:1810.01661 (2018).​
Beck, Joakim, Lorenzo Tamellini, and Raúl Tempone
Isogeometric analysis, Uncertainty Quantification, Sparse Grids, Stochastic Collocation methods, multilevel methods, combination-technique
2018
​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.​