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 straightforward reuse of existing implementations of IGA solvers. We present numerical results to showcase the effectiveness of the proposed approach.
•Isogeometric solvers used in a MISC framework for forward UQ problems.•The combination-technique formulation of the method allows straightforward reuse of legacy IGA solvers.•We show advantages of MISC over multi-level/multi-index Monte Carlo methods.