Transformed Snapshot Interpolation with High Resolution Transforms
Transformed Snapshot Interpolation with High Resolution Transforms
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DOI：
10.1137/19m126356x
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发表时间：
2019-01
期刊：
影响因子：
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通讯作者：
G. Welper
中科院分区：
文献类型：
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作者：
G. Welper
在过去的几年中，已经发展了几种方法来处理参数或随机双曲偏微分方程中的跳变奇点。他们通常在执行完善的降阶建模技术（如降基方法、POD或简单的插值）之前，在物理空间中对跳跃集进行一些对齐。在目前的文献中，变换在空间上通常是低分辨率的，主要是低阶多项式，傅里叶模式或常数位移。本文讨论了一种最新的方法——变换快照插值（TSI）的高分辨率变换。我们引入了一种新的离散化变换，在奇异点附近具有适当的行为，并考虑了它们的数值计算通过优化过程。
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 modelling techniques such as reduced basis methods, POD 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 (TSI). We introduce a new discretization of the transforms with an appropriate behaviour near singularities and consider their numerical computation via an optimization procedure.