IGA-based Multi-Index Stochastic Collocation for random PDEs on arbitrary domains
It addresses a limitation of MISC for uncertainty quantification in complex geometries, but the improvement is incremental as it combines existing methods.
This paper extends the Multi-Index Stochastic Collocation method to handle random PDEs on arbitrary domains by integrating isogeometric analysis, enabling uncertainty quantification on non-square/cube geometries. Numerical results demonstrate the effectiveness of the approach.
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.