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

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.(c) 2022 Elsevier Inc. All rights reserved.

Automated summary

This paper proposes an edge-detection-based method to handle discontinuous functions in multi-dimensional uncertainty propagation problems. By utilizing the Gegenbauer reconstruction method and the Rosenblatt transformation, the proposed method can accurately reconstruct spectral expansions without the occurrence of Gibbs phenomenon.