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", Computer Methods in Applied Mathematics and Engineering, Volume 351 (2019): 330-350
Joakim Beck, Lorenzo Tamellini, Raúl Tempone
Isogeometric analysis, Uncertainty quantification, Sparse grids, Stochastic collocation methods, Multilevel methods, Combination-technique
2019
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 straightforward reuse of existing implementations of IGA solvers. We present numerical results to showcase the effectiveness of the proposed approach.