Novel adaptive reduced order spectral non-deterministic FEM approach to problems with general interval-fuzzy-stochastic uncertainties

Abstract The aim of the current work is the development of the fast, efficient, and accurate approach towards problems with uncertain parameters. This approach is initially based on the spectral local non-deterministic FEM that is able to deal with all types of uncertain parameters: interval-like, fuzzy, stochastic and mixed types. The on-fly order reduction via low-rank tensor decomposition is implemented into the algorithm in order to reduce computational costs and to achieve parsimonious spectral representation of the parameter dependencies. The non-intrusive spectral FEM formulation with sparse adaptive grid of samples is utilized. This allows to use any conventional FEM code as the black-box within the non-deterministic framework. The samples are selected on the basis of the semi-optimal greedy algorithm. The crucial aspect of the proposed novel approach is the use of the IsoGeometrical basis functions and adaptive automatic refinement in the non-deterministic domain. Comparison with the unmodified spectral FEM demonstrates persuasive advantages of the novel approach.