A variability response function (VRF)-based adaptive spectral Galerkin stochastic finite element method

In this work the concept of variability response function (VRF) is utilized in the framework of Galerkin, spectral stochastic finite element method (SSFEM) in order to achieve an a priori low-cost estimate of the spatial distribution of the statistical second-order error of the response, as a function of the truncation order of the Karhunen-Loève (KL) decomposition. This way the optimal encapsulation of the information contained in the correlation structure of the random input is achieved through a spatial variation of the truncated KL terms. The criterion for selecting the number of KL terms at different parts of the structure is the uniformity of the spatial distribution of the second-order error. As a consequence, an increase of sparsity of the coefficient matrix of the corresponding linear system of equations is achieved, leading to a reduction of the computational cost of the method.

This work has been supported by the European Research Council Advanced Grant MASTER - Mastering the computational challenges in numerical modeling and optimum design of CNT reinforced composites (ERC-2011-ADG-20110209).