Transformed Snapshot Interpolation with High Resolution Transforms

Understand

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).