Stochastic isogeometric analysis on arbitrary multipatch domains by spline dimensional decomposition

This paper presents a new stochastic method by integrating spline dimensional decomposition (SDD) of high-dimensional random function and isogeometric analysis (IGA) on arbitrary multipatch geometries to solve boundary-value problems from linear elasticity . The method, referred as SDD-mIGA, involves (1) analysis-suitable T-splines with significant approximating power for geometrical modeling, field discretization , stress analysis; (2) Bézier extraction operator mesh refinement; (3) novel Fourier-like expansion output in terms measure-consistent orthonormalized splines. proposed can handle domains IGA uses standard least-squares regression efficiently estimate the SDD coefficients uncertainty quantification applications. Analytical formulae have been derived calculate second-moment properties an SDD-mIGA approximation general variable interest. Numerical results, including those obtained 54-dimensional, industrial-scale problem, demonstrate that low-order is capable delivering accurate probabilistic solutions when compared benchmark results crude Monte Carlo simulation • A fusion between analysis. Standard least squares estimating coefficients. geometric discretization, Low-order, low-variate methods provide efficient results. Applications industrially relevant elasticity.