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.

本文针对多维不确定性传播问题中的不连续函数提出了一种基于边缘检测的方法。我们开发了多元函数的 Gegenbauer 重建方法来解决 Gibbs 现象。为此，我们将浓度边缘检测器扩展到近似不连续超曲面，并使用 Rosenblatt 变换来处理不规则空间分解。代数测试函数和超音速双翼翼型流的空气动力学设计问题的数值实验表明，所提出的方法可以从给定的多项式混沌系数重建频谱扩展，其始终准确且不受吉布斯现象的影响，并且无需额外的模型计算。