An adaptive multi-element stochastic collocation method for PDEs with parametrized uncertainty

Jasmine Foo, Brown University

Three dimensional problems in linear/nonlinear solid mechanics with uncertain material properties or loadings are solved using the stochastic collocation method and the adaptive multi-element stochastic collocation method, which will be introduced here. These methods enable the numerical solution of PDEs with finite-dimensional noise inputs without modification of the deterministic solver. The multi-element collocation method involves discretizing the range space of the random inputs and performing collocation on each of the resulting elements. This approach was introduced for the generalized Polynomial Chaos method by Wan and Karniadakis. Additional adaptivity results from h-refinement on this random space. In both the linear and nonlinear cases the deterministic problems are solved numerically by a p-finite element solver.

Realistic three-dimensional riser structures undergoing elastic small and large deformations due to random fluid loads are considered. Also modeled is a riser with stochastic Young modulus (with variability data taken from experimental results) undergoing deterministic fluid loads. In these problems, we will compare the performance and efficiency of the stochastic collocation method to its multi-element analog.

Abstract Author(s): Jasmine Foo