Anisotropic multi-element polynomial chaos expansion for high-dimensional non-linear structural problems

This work presents an hp-adaptive variant of multi-element polynomial chaos expansion (ME-gPCE), referred to as anisotropic multi-element polynomial chaos expansion (AME-gPCE). The main advantage of the proposed framework is that the basis functions of the local gPCE are selected adaptively within each local element. The p-adaptivity allows the order of the local uni-variate polynomials to be increased only for the dimensions associated with highly non-linear behaviour of the response surface, while the h-adaptivity allows the mesh refinement to be applied only where the local response surface behaves non-smoothly. Thus, the computational cost can be significantly reduced compared with standard methods, which opens the door to high-dimensional problems. The efficiency, accuracy and convergence of AME-gPCE are studied numerically and compared with the traditional ME-gPCE for non-linear structural analysis. It outperforms the traditional ME-gPCE for the elasto-plastic problem, considering the material proprieties as random variable and random fields.