Gegenbauer reconstruction method with edge detection for multi-dimensional uncertainty propagation

• Published in: Journal of computational physics Vol. 468; p. 111505
• Main Authors: Kawai, Shigetaka, Yamazaki, Wataru, Oyama, Akira
• Format: Journal Article
• Language: English
• Published: Cambridge Elsevier Inc 01-11-2022; Elsevier Science Ltd
• Subjects: Computational fluid dynamics; Computational physics; Discontinuity; Edge detection; Gibbs phenomenon; Hyperspaces; Polynomial chaos expansion; Polynomials; Propagation; Reconstruction; Uncertainty; Uncertainty quantification; Uncertainty quantification; Gibbs phenomenon; Computational fluid dynamics; Polynomial chaos expansion; Edge detection
• ISSN: 0021-9991; 1090-2716
• DOI: 10.1016/j.jcp.2022.111505

This paper proposes an edge-detection-based method for discontinuous functions in multi-dimensional uncertainty propagation problems. We develop the Gegenbauer reconstruction method for multivariate functions to resolve the Gibbs phenomenon. To this end, we extend the concentration edge detector to approximate discontinuity hypersurfaces and use the Rosenblatt transformation to treat irregular space decomposition. Numerical experiments for an algebraic test function and an aerodynamic design problem of the supersonic biplane airfoil flow show that the proposed method can reconstruct spectral expansions that are consistently accurate and free from the Gibbs phenomenon from given polynomial chaos coefficients and without additional model computation.
•This paper treats uncertainty propagation with a multivariate discontinuous function.•The proposed method applies a reconstruction scheme to multivariate polynomial chaos.•It is shown that the proposed method could efficiently remove the Gibbs phenomenon.