SIAM Journal on Scientific Computing, Volume 42, Issue 4, Page A2037-A2061, January 2020.
In the last few years, several methods have been developed to deal with jump singularities in parametric or stochastic hyperbolic PDEs. They typically use some alignment of the jump-sets in physical space before performing well-established reduced order modeling techniques such as reduced basis methods, proper orthogonal decomposition, or simply interpolation. In the current literature, the transforms are typically of low resolution in space, mostly low order polynomials, Fourier modes, or constant shifts. In this paper, we discuss higher resolution transforms in one of the recent methods, the transformed snapshot interpolation. We introduce a new discretization of the transforms with an appropriate behavior near singularities and consider their numerical computation via an optimization procedure.

中文翻译：

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具有高分辨率变换的变换快照插值

SIAM科学计算杂志，第42卷，第4期，第A2037-A2061页，2020年1月。
在最近几年中，已经开发出几种方法来处理参数或随机双曲PDE中的跳跃奇点。他们通常在执行公认的降阶建模技术（例如降基方法，适当的正交分解或简单的插值）之前，使用物理空间中跳跃集的某种对齐方式。在当前文献中，变换通常在空间上具有低分辨率，主要是低阶多项式，傅立叶模式或常数移位。在本文中，我们讨论了一种最新方法，即转换后的快照插值，该方法可实现更高的分辨率。我们介绍了一种新的离散化方法，该方法具有接近奇异点的适当行为，并考虑了通过优化程序进行的数值计算。