Development of Intrusive Uncertainty Quantification Method Based on Edge Detection Technique

Abstract

A new intrusive uncertainty quantification method, namely a polynomial annihilation-based stochastic Galerkin method, is proposed to efficiently capture discontinuous system responses in stochastic space. The proposed method is based on the multi-element method and the polynomial annihilation edge detection, and achieves a minimal and optimal decomposition of the stochastic space so that the computational cost is minimized. The performance of the proposed method is demostrated on a one-dimensional test problem whose solutions exhibit discontinuous behavior in stochastic space: an ordinary differential equation problem for uncertainty propagation. The results obtained for the test problem show that the proposed method is consistently more accurate and more efficient than the conventional stochastic Galerkin method even when the solution contains a discontinuity in the stochastic space.