Efficient component-wise and solver-based intrusive SFEM analysis of complex structures

In this study, important computational aspects of intrusive stochastic finite element methods (SFEM) are investigated. The importance of the interaction with 3rd party deterministic finite element (FE) solvers is emphasized within this context. Especially, data management is in the focus. Two implementation techniques, namely the component-wise and the solver-based implementations, have been introduced in order to improve the computational efficiency. It is shown that by reducing the quantity and the size of the transferred system matrices, a significant reduction in the computational cost can be achieved. This is demonstrated on representative FE models, which are analyzed with the perturbation method, the Neumann expansion method and the polynomial chaos expansion method, respectively. Finally, a procedure is introduced in order to efficiently model and propagate the uncertainties in parameters, which do not appear in linear terms inside the components of the system matrices.