Adaptive sparse grid approximation for high dimensional interval field construction

This paper introduces a novel approach to model interval fields in high dimensional Finite Element models containing thousands of degrees of freedom. Typically, to simulate with interval fields in such high dimensional model spaces, a non-negligible computational cost has to be dedicated to the calculation of a combinatorial amount of distances in order to determine the interval field basis functions (e.g, via Inverse Distance Weighting interpolation). It is proposed to alleviate this computational cost by applying so-called sparse grid interpolants to construct the interval field basis functions over the high-dimensional model domain, rather than computing the distances over the underlying finite element grid. First, a theoretical framework hereto is presented to compute interval field basis functions via Smolyak’s algorithm, including rates of error convergence. Then, a case study on an L-shaped beam model with holes is performed. The performed case study shows that a highly accurate representation of the interval field basis can be obtained at strongly reduced computational expense, as compared to the full combinatorial calculation.

ISBN:978-1-62410-595-1

Jaar van publicatie:2020