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

TL;DR

This paper extends the Multi-Index Stochastic Collocation method for uncertainty quantification in complex-shaped domains by integrating isogeometric analysis, enabling efficient and flexible solutions for random PDEs.

Contribution

It introduces IGA-based solvers into the MISC framework, allowing for effective UQ on arbitrary domains with existing IGA implementations.

Findings

Demonstrates the effectiveness of IGA-MISC through numerical experiments.

Enables straightforward reuse of existing IGA solvers within the MISC framework.

Shows improved flexibility for complex domain shapes in UQ problems.

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.